Math & Statistics Calculators — United States
Every calculator shows its formula and a worked example. The math is the same everywhere; only the spelling and number formatting follow local practice.
Percentages & ratios
Percentage Calculator
Work out what X% of a number is, what percentage one number is of another, and the percentage change between two numbers — the three questions behind almost every percentage problem.
Open calculator →
Decimal to Percent Calculator
Turn a decimal into a percentage — multiply by 100.
Open calculator →
Percent to Decimal Calculator
Turn a percentage into a decimal — divide by 100.
Open calculator →
Percentage Increase Calculator
Work out the percentage increase from one value to another.
Open calculator →
Percentage of a Number Calculator
Work out what a percentage of a number comes to — tips, discounts, commission, VAT, a share of a total.
Open calculator →
What Percent Of Calculator
Find what percentage one number is of another — a score out of a total, a share of a budget, a part of a whole.
Open calculator →
Percentage Change Calculator
The percentage change between two numbers — a rize or a fall, measured against where it started.
Open calculator →
Percentage Decrease Calculator
How far a number has fallen in percentage terms — a price cut, a drop in sales, a reduction in weight or cost.
Open calculator →
Percent Error Calculator
Measure how far an experimental or estimated value is from the true or accepted value, as an absolute error and a percentage.
Open calculator →
Percentage Difference Calculator
Compare two values symmetrically — the percentage difference divides by their average, so neither one is treated as the baseline.
Open calculator →
Unit Rate Calculator
Reduce a rate to "per one" — and compare two package sizes to see which is actually cheaper.
Open calculator →
Ratio Calculator
Simplify a ratio, scale it up, or solve for a missing term in a proportion.
Open calculator →
Percentage Increase Calculator
Percentage increase or decrease between two numbers.
Open calculator →
Ratio Calculator
Simplify and scale ratios.
Open calculator →
Proportion Calculator
Solve a/b = c/x.
Open calculator →
Algebra & equations
Exponent Calculator
Raize any base to any exponent — including negative and fractional powers — and see the result in full, in scientific notation and as a reciprocal.
Open calculator →
Root Calculator
Square roots, cube roots and any nth root of a number, with the check that raizing the answer back gives the original.
Open calculator →
Square Root Calculator
The square root of any number — the value that multiplied by itself gives what you entered.
Open calculator →
Cube Root Calculator
The cube root of any number — the value that multiplied by itself three times gives what you entered.
Open calculator →
Logarithm Calculator
Logarithms to any base — log₁₀, natural log (ln), log₂ and a base of your choice — with the antilog check.
Open calculator →
Log Base 10 Calculator
The common logarithm — how many times you multiply 10 by itself to reach your number.
Open calculator →
Log Base 2 Calculator
The binary logarithm — how many times you double from 1 to reach your number, and the bits it takes to store it.
Open calculator →
Natural Log Calculator
The natural logarithm — the logarithm to base e, the one that appears wherever growth is continuous.
Open calculator →
Quadratic Equation Calculator
Solve ax² + bx + c = 0 — real or complex roots, the discriminant, the vertex and the axis of symmetry — with the quadratic formula shown.
Open calculator →
Linear Equation Calculator
Find the equation of the straight line through two points: slope, y-intercept, slope-intercept and standard forms, plus the x-intercept.
Open calculator →
CAGR Calculator
The compound annual growth rate that takes a starting value to an ending value over a number of years — the single steady rate behind any growth path.
Open calculator →
Long Division Calculator
Divide one whole number by another and see the quotient, the remainder and the long-division working step by step — plus the exact decimal, including the repeating part.
Open calculator →
Matrix Calculator
Enter a 2×2 or 3×3 matrix and get its determinant, inverse, transpose and trace — with a note on whether it can be inverted at all.
Open calculator →
Absolute Value Calculator
The absolute value of a number — its distance from zero, without a sign — and the distance between two numbers.
Open calculator →
Vector Calculator
Dot product, cross product, magnitudes and the angle between two 3-D vectors.
Open calculator →
Simplify Radical Calculator
Reduce a square root to its simplest exact form — √72 becomes 6√2.
Open calculator →
FOIL Calculator
Multiply two binomials and see each of the four products — First, Outer, Inner, Last.
Open calculator →
Completing the Square Calculator
Rewrite ax² + bx + c as a(x − h)² + k — the vertex form, which shows the turning point directly.
Open calculator →
Cubic Equation Calculator
Solve ax³ + bx² + cx + d = 0 — all three roots, real and complex, with the discriminant that tells you which to expect.
Open calculator →
Polynomial Derivative Calculator
For a polynomial given by its coefficients — the derivative and the indefinite integral as new polynomials, the value and slope at a chosen x, the tangent line there, and the definite integral between two bounds.
Open calculator →
Geometry
Distance Between Two Points Calculator
The straight-line distance between two points on a plane, their midpoint and the slope of the line joining them — the distance formula from Pythagoras.
Open calculator →
Pythagorean Theorem Calculator
Find the missing side of a right triangle from the other two, plus its area, perimeter and the two acute angles.
Open calculator →
Circle Calculator
Enter any one measurement of a circle — radius, diameter, circumference or area — and get all the others.
Open calculator →
Triangle Area Calculator
The area of any triangle from base and height, from three sides (Heron's formula) or from two sides and the angle between them.
Open calculator →
Rectangle Calculator
Area, perimeter and diagonal of a rectangle or square from its length and width.
Open calculator →
Cylinder Volume Calculator
Volume, lateral surface area and total surface area of a cylinder from its radius and height — tanks, pipes, cans and columns.
Open calculator →
Sphere Calculator
Volume, surface area and circumference of a sphere from its radius or diameter — balls, tanks, planets.
Open calculator →
Cube and Cuboid Calculator
Volume, surface area and space diagonal of a box (cuboid) or cube from its length, width and height.
Open calculator →
Surface Area Calculator
Surface area of a cube, box, sphere, cylinder, cone or square pyramid — total and curved — with the volume alongside for painting, wrapping, plating and heat-loss work.
Open calculator →
Cube Surface Area Calculator
Six identical square faces — enter one edge for the total surface area, along with the volume and the area of a single face.
Open calculator →
Box Surface Area Calculator
The outside area of a rectangular box — for wrapping, cardboard, plating or working out how much paint a crate takes.
Open calculator →
Sphere Surface Area Calculator
The surface area of a sphere from its radius — exactly four times the circle you see when you look at it.
Open calculator →
Cylinder Surface Area Calculator
The surface area of a cylinder — total, or just the curved part if you only need the label that wraps around it.
Open calculator →
Cone Surface Area Calculator
The surface area of a cone from its radius and height — including the slant height it needs along the way.
Open calculator →
Pyramid Surface Area Calculator
The surface area of a square pyramid — its square base plus four triangular faces, from the base side and the height.
Open calculator →
Triangle Calculator
Solve a triangle from whatever you know — three sides, two sides and an angle, two angles and a side — and get every side, every angle, the area, perimeter, heights and the circle radii.
Open calculator →
SSS Triangle Calculator
Know all three sides? Get every angle, the area, the perimeter and the heights — and a check that the three lengths can actually close into a triangle.
Open calculator →
SAS Triangle Calculator
Two sides with the angle between them fix a triangle exactly.
Open calculator →
ASA Triangle Calculator
Two angles with the side between them determine a triangle completely.
Open calculator →
AAS Triangle Calculator
Two angles and a side that is not between them still fix a triangle exactly.
Open calculator →
SSA Triangle Calculator (the ambiguous case)
Two sides and an angle that is not between them — the one case that can describe two different triangles, one, or none.
Open calculator →
Equilateral Triangle Calculator
Every side equal, every angle 60°.
Open calculator →
Isosceles Triangle Calculator
Two equal sides and a base — enter both for the apex and base angles, the area, the height and the perimeter.
Open calculator →
Triangle Perimeter Calculator
Add up the three sides of a triangle — with a check that they can actually form one, and the area, angles and heights alongside.
Open calculator →
Triangle Height Calculator
The height of a triangle measured to side a — the perpendicular distance from the opposite corner — worked out from the three sides, with the area and angles alongside.
Open calculator →
Right Triangle Calculator
Enter the two short sides of a right triangle for the hypotenuse, both acute angles, the area and the perimeter — Pythagoras and the trigonometry in one place.
Open calculator →
Area Calculator
The area of any common shape — square, rectangle, triangle, circle, parallelogram, trapezoid, rhombus, kite, ellipse, regular polygon, sector, annulus or semicircle — with its perimeter alongside.
Open calculator →
Square Area Calculator
The area of a square from one side — side times side, with the perimeter and diagonal alongside.
Open calculator →
Parallelogram Area Calculator
The area of a parallelogram — base times perpendicular height, exactly like a rectangle.
Open calculator →
Trapezoid Area Calculator
The area of a trapezoid (a trapezium in British usage) — average the two parallel sides, then multiply by the height.
Open calculator →
Rhombus Area Calculator
The area of a rhombus from its two diagonals — half their product, with the side length and perimeter alongside.
Open calculator →
Kite Area Calculator
The area of a kite from its two diagonals — half their product, the same rule as a rhombus.
Open calculator →
Ellipse Area Calculator
The area of an ellipse — π times the two semi-axes, with a good approximation of its perimeter.
Open calculator →
Regular Polygon Area Calculator
The area of any regular polygon from its side length and number of sides — triangle to decagon and beyond.
Open calculator →
Hexagon Area Calculator
The area of a regular hexagon from its side — six equilateral triangles, so a√3 × 3a ÷ 2.
Open calculator →
Pentagon Area Calculator
The area of a regular pentagon from its side length, with its perimeter.
Open calculator →
Octagon Area Calculator
The area of a regular octagon from its side length — about 4.828 times the side squared.
Open calculator →
Sector Area Calculator
The area of a slice of a circle from its radius and angle, with the arc length and the perimeter of the slice.
Open calculator →
Annulus Area Calculator
The area of a ring or washer — the outer circle minus the hole in the middle.
Open calculator →
Semicircle Area Calculator
The area of a half circle from its radius, with the perimeter including the straight edge.
Open calculator →
Solid Volume Calculator
The volume of a cone, pyramid, prism, torus, capsule, hemisphere, frustum or ellipsoid — with the size of the cube and the sphere that would hold the same amount.
Open calculator →
Cone Volume Calculator
The volume of a cone from its base radius and height — exactly one third of the cylinder around it.
Open calculator →
Pyramid Volume Calculator
The volume of a rectangular pyramid — a third of the box that would contain it.
Open calculator →
Triangular Prism Volume Calculator
The volume of a triangular prism — the area of its triangular end multiplied by its length.
Open calculator →
Torus Volume Calculator
The volume of a torus — a doughnut, an O-ring, an inner tube — from the ring radius and the tube radius.
Open calculator →
Capsule Volume Calculator
The volume of a capsule — a cylinder with a hemisphere on each end, the shape of a pill or a gas tank.
Open calculator →
Hemisphere Volume Calculator
The volume of a half sphere — a dome, a bowl, a hemispherical end — from its radius alone.
Open calculator →
Frustum Volume Calculator
The volume of a frustum — a cone with the top cut off, the shape of a bucket, a plant pot or a lampshade.
Open calculator →
Ellipsoid Volume Calculator
The volume of an ellipsoid — a sphere stretched along three axes, the shape of an egg, a rugby ball or a planet.
Open calculator →
Golden Ratio Calculator
Divide a length in the golden ratio, or find the whole from a part — φ = 1.6180339887.
Open calculator →
Trigonometric Functions Calculator
All six trigonometric functions of an angle, in degrees or radians, with the inverse of the sine as well.
Open calculator →
Slope Calculator
The slope between two points, plus the full equation of the line through them.
Open calculator →
Midpoint Calculator
The point exactly halfway between two points, and the perpendicular bisector through it.
Open calculator →
Law of Cosines Calculator
The third side of a triangle from two sides and the angle between them — the law of cosines — with the other two angles, the area, the perimeter and the type of triangle it makes.
Open calculator →
Law of Sines Calculator
The remaining sides of a triangle from two angles and one side — the law of sines — with the third angle, the area, the perimeter and the circumscribed circle's diameter, which the ratio in the law equals.
Open calculator →
Volume Calculator
Volume of common solids.
Open calculator →
Statistics & probability
Weighted Average Calculator
Average a list of values where each carries a different weight — grades with credit points, prices with quantities, survey scores with sample sizes.
Open calculator →
Factorial Calculator
n! — the product of all whole numbers from 1 to n — exact up to 170 and in scientific notation beyond, with the number of digits and trailing zeros.
Open calculator →
Permutations and Combinations Calculator
How many ways can you choose r items from n — when order matters (permutations, nPr) and when it doesn't (combinations, nCr)?.
Open calculator →
Probability Calculator
The probability of a single event from favorable and possible outcomes, its odds and complement, and the chance of two independent events both happening or either happening.
Open calculator →
Standard Deviation Calculator
Sample and population standard deviation and variance of a list of numbers, with the mean, sum of squares and count — the working shown.
Open calculator →
Z-Score Calculator
How many standard deviations a value sits from the mean, and the percentile and tail probabilities it implies under a normal distribution.
Open calculator →
Sample Size Calculator
How many people to survey for a given confidence level and margin of error — with the finite-population correction for small populations.
Open calculator →
Confidence Interval Calculator
A confidence interval for a mean from the sample mean, standard deviation and size — with the standard error and margin of error shown.
Open calculator →
Percentile Calculator
The value at any percentile of a list of numbers (quartiles included), and the percentile rank of a value you enter.
Open calculator →
Random Number Generator
Generate random whole numbers or decimals in any range — one, or a whole list, with or without repeats — from a seed you control, so the same seed always gives the same draw.
Open calculator →
Dice Roller
Roll any number of dice with any number of sides — 2d6, 4d6, 1d20 with a modifier — and see the total, every individual die, and how likely that total was.
Open calculator →
Normal Distribution Calculator
The probability of a value falling below, above or between any points on a normal distribution — from the mean and standard deviation.
Open calculator →
Binomial Distribution Calculator
The probability of getting exactly, at most, or at least a given number of successes in a fixed number of independent trials.
Open calculator →
Poisson Distribution Calculator
The probability of a given number of events in a fixed interval, when events happen independently at a constant average rate.
Open calculator →
Correlation Coefficient Calculator
Pearson's correlation coefficient between two sets of paired values — how strongly they move together, and whether the relationship is statistically significant.
Open calculator →
Linear Regression Calculator
The line of best fit through paired data — slope, intercept, r², and a prediction for any value of x.
Open calculator →
T-Test Calculator
A one-sample or two-sample t-test with the exact p-value — whether a mean differs from a claimed value, or two groups differ from each other.
Open calculator →
Chi-Square Calculator
The chi-square statistic and its exact p-value, for testing whether observed counts differ from what was expected.
Open calculator →
Variance Calculator
The variance of a data set — sample and population — with the sum of squares it is built from.
Open calculator →
Quartile Calculator
Q1, the median, Q3 and the interquartile range — with the outlier fences a box plot draws.
Open calculator →
Descriptive Statistics Calculator
Every summary statistic for a data set at once — center, spread, shape and the five-number summary.
Open calculator →
P-Value Calculator
Convert a test statistic into a p-value — z, t or chi-square, one-tailed or two.
Open calculator →
Coin Flipper
Flip a coin any number of times from a seed you choose — reproducible, so the same seed always gives the same run.
Open calculator →
Mean, Median and Mode Calculator
The three averages at once — and what it means when they disagree.
Open calculator →
Coin Flip Probability Calculator
The probability of getting a given number of heads in a run of coin flips — exactly, at least, at most — for a fair or a biased coin.
Open calculator →
Two Dice Probability Calculator
The probability of rolling a given total on two dice — exactly, at least or at most — with the full distribution behind it.
Open calculator →
Conditional Probability Calculator
P(A given B) from the joint and marginal probabilities — with Bayes' theorem run in both directions and a check on whether the two events are independent.
Open calculator →
Bayes' Theorem Calculator
Turn a base rate and a test's accuracy into the probability that actually matters — the chance the condition is present given a positive result.
Open calculator →
Implied Probability Calculator
Convert odds to a probability and back — decimal, fractional and moneyline — and see the margin built into a set of quoted odds.
Open calculator →
Combinations Calculator (nCr)
How many ways to choose r items from n when order does not matter — nCr, with the permutation count alongside for comparison.
Open calculator →
Permutations Calculator (nPr)
How many ordered arrangements of r items from n — nPr — with the combination count and the full-ordering count alongside.
Open calculator →
Combinations with Repetition Calculator
How many ways to choose r items from n types when you may take the same type more than once and order does not matter — the doughnut-box problem.
Open calculator →
Permutations with Repetition Calculator
How many ordered sequences of length r you can build from n symbols when repeats are allowed — passwords, PINs, number plates and DNA.
Open calculator →
Binomial Coefficient Calculator
The coefficient of xᵏ in (1 + x)ⁿ — the entry at row n, position k of Pascal's triangle — with its neighbours and the row sum.
Open calculator →
Birthday Paradox Calculator
The chance that two people in a group share a birthday — the result that reaches 50% at just 23 people and surprises almost everyone.
Open calculator →
Lottery Odds Calculator
The odds of matching a lottery draw — jackpot and each lower division — for any pick-r-from-n game, with or without a supplementary ball.
Open calculator →
Probability of A or B Calculator
The probability that at least one of two events happens — with the inclusion–exclusion correction that catches the overlap.
Open calculator →
Three Event Probability Calculator
The chance that at least one of three independent events happens, that all three happen, and that exactly one or exactly two do.
Open calculator →
Expected Value Calculator
The long-run average of a set of outcomes weighted by their probabilities — with the variance, standard deviation and a check that the probabilities sum to one.
Open calculator →
Monty Hall Problem Calculator
Whether to switch doors — the counter-intuitive game-show problem, generalized to any number of doors and any number the host opens.
Open calculator →
Hypergeometric Distribution Calculator
The probability of drawing a given number of successes when sampling without replacement — cards from a deck, defectives from a batch, an audit sample from a ledger.
Open calculator →
Negative Binomial Distribution Calculator
How many trials it takes to reach a target number of successes — the distribution of waiting, rather than of counting.
Open calculator →
Joint Probability Calculator
The probability that two events both happen — independent or not — with the conditional probabilities and an independence test.
Open calculator →
Sample Proportion Calculator
The proportion in a sample, its standard error and a confidence interval — with the Wilson interval, which behaves properly when the count is small.
Open calculator →
Bernoulli Distribution Calculator
The simplest distribution of all — one trial, two outcomes — with its mean, variance, entropy and the value of n trials in a row.
Open calculator →
Post-Test Probability Calculator
Update a probability with a likelihood ratio — the odds form of Bayes' theorem, and the fastest way to see what a test result is actually worth.
Open calculator →
Geometric Mean Calculator
The average of a set of growth rates or ratios — the mean that compounds correctly, where the arithmetic mean does not.
Open calculator →
Harmonic Mean Calculator
The average of rates — speeds, prices per unit, work rates — where the arithmetic mean gives the wrong answer.
Open calculator →
Root Mean Square (RMS) Calculator
The quadratic mean — square, average, take the root — the measure behind AC voltage, signal power and the magnitude of an error.
Open calculator →
Five Number Summary Calculator
Minimum, first quartile, median, third quartile and maximum — everything a box plot draws, with the outlier fences.
Open calculator →
Interquartile Range (IQR) Calculator
The spread of the middle half of your data — the robust alternative to the standard deviation, and the basis of the outlier rule.
Open calculator →
Mean Absolute Deviation Calculator
The average distance from the mean, without squaring — a spread measure in the same units as the data and easier to explain than a standard deviation.
Open calculator →
Median Absolute Deviation Calculator
The most robust spread measure there is — the median of the distances from the median, which half your data can be corrupted before it moves.
Open calculator →
Coefficient of Variation Calculator
Relative variability — the standard deviation as a percentage of the mean, which lets you compare the spread of things measured on different scales.
Open calculator →
Skewness Calculator
Whether your data leans left or right — the third moment, with the sample-adjusted G₁ statistic and a plain reading of what it means.
Open calculator →
Kurtosis Calculator
How heavy your distribution's tails are — the fourth moment, reported as excess kurtosis so that a normal distribution reads zero.
Open calculator →
Percentile Rank Calculator
Where a value sits in a dataset — the percentage of observations at or below it, by each of the standard conventions.
Open calculator →
Outlier Calculator
Find the values that do not belong — by the IQR fence rule, by z-score and by the modified z-score, which is the one that works when the outliers are large.
Open calculator →
Standard Error Calculator
How precisely your sample mean estimates the true mean — the standard error, with the confidence interval it produces.
Open calculator →
Margin of Error Calculator
The ± figure quoted after every poll — what it means, how sample size drives it, and why the difference between two candidates has a bigger one.
Open calculator →
Covariance Calculator
How two variables move together — the sample and population covariance, with the correlation coefficient that puts it on a readable scale.
Open calculator →
Pooled Standard Deviation Calculator
Combine the spread of two groups into a single estimate — the denominator of a two-sample t-test and of Cohen's d.
Open calculator →
Sum of Squares Calculator
The total, within and residual sums of squares — the quantity every variance, regression and ANOVA is built on.
Open calculator →
Grouped Data Standard Deviation Calculator
Mean and standard deviation from a frequency table — when you have counts per class rather than the raw observations.
Open calculator →
Midrange Calculator
The midpoint between the largest and smallest value — the simplest measure of center, and the least robust.
Open calculator →
Trimmed Mean Calculator
The mean after discarding a percentage from each end — the compromize between the mean's efficiency and the median's robustness.
Open calculator →
Z-Test Calculator
Test a sample mean against a known population mean when the population standard deviation is known — the one-sample z-test, with the p-value and confidence interval.
Open calculator →
Welch's T-Test Calculator
Compare two group means without assuming equal variances — the test that should be the default for two independent samples.
Open calculator →
Paired T-Test Calculator
Test whether a before-and-after change is real — the paired t-test, which works on the differences and is far more powerful than comparing two groups.
Open calculator →
Chi-Square Test Calculator
Test whether two categorical variables are related — the chi-square test of independence on a 2×2 table, with the expected counts and effect size.
Open calculator →
Fisher's Exact Test Calculator
The exact p-value for a 2×2 table — no approximation, valid at any sample size, and the correct choice when counts are small.
Open calculator →
McNemar's Test Calculator
Test whether a paired binary outcome changed — before-and-after on the same subjects, where only the disagreements carry information.
Open calculator →
Mann-Whitney U Test Calculator
Compare two independent groups without assuming normality — the rank-based alternative to the t-test, also called the Wilcoxon rank-sum test.
Open calculator →
Sign Test Calculator
The simplest paired test there is — count how many pairs went up and how many went down, and ask whether the split is fair.
Open calculator →
F-Test Calculator (Equality of Variances)
Test whether two samples have the same variance — the F-test, with the warning about how badly it behaves when the data is not normal.
Open calculator →
One-Way ANOVA Calculator
Compare three or more group means at once — one-way ANOVA, with the full sum-of-squares table and the effect size.
Open calculator →
Effect Size Calculator (Cohen's d)
How big the difference actually is — Cohen's d, Hedges' g and the overlap between two groups, which a p-value never tells you.
Open calculator →
Odds Ratio Calculator
The odds ratio from a 2×2 table, with its confidence interval — and the relative risk beside it, because the two are routinely confused.
Open calculator →
Relative Risk Calculator
The risk ratio between two groups, with its confidence interval — plus the absolute risk difference, which is what actually tells you whether the effect matters.
Open calculator →
A/B Test Calculator
Whether variant B really beat variant A — the two-proportion test on conversion rates, with the lift, its confidence interval, and an honest note on peeking.
Open calculator →
Critical Value Calculator
The cut-off your test statistic must beat — z, t, chi-square and F critical values for any significance level and degrees of freedom.
Open calculator →
95% Confidence Interval Calculator
The 95% confidence interval for a mean — the most-quoted interval in science, with a plain statement of what it does and does not mean.
Open calculator →
99% Confidence Interval Calculator
The 99% confidence interval for a mean — wider than the usual 95%, and the right choice when a false positive is expensive.
Open calculator →
90% Confidence Interval Calculator
The 90% confidence interval for a mean — narrower than the usual 95%, and standard in one-sided settings and equivalence testing.
Open calculator →
Least Squares Regression Calculator
The line of best fit through a set of points — slope, intercept, R² and the residual spread, with the full working.
Open calculator →
Quadratic Regression Calculator
Fit a parabola y = ax² + bx + c to your data — for relationships that rize then fall, or curve away from a straight line.
Open calculator →
Exponential Regression Calculator
Fit y = ae^(bx) to data that grows or decays by a constant percentage — populations, compound growth, radioactive decay, cooling.
Open calculator →
R Squared Calculator
How much of the variation your model explains — R² from observed and predicted values, with the adjusted version that penalises extra predictors.
Open calculator →
Spearman Correlation Calculator
Correlation of ranks rather than values — the measure that catches any consistent trend, not just a straight-line one, and shrugs off outliers.
Open calculator →
Inverse Normal Distribution Calculator
Go backwards from a probability to a value — the quantile function, which answers "what score puts me in the top 5%?".
Open calculator →
Uniform Distribution Calculator
The continuous distribution where every value in a range is equally likely — probabilities, mean, variance and percentiles.
Open calculator →
Exponential Distribution Calculator
The distribution of waiting times between random events — probabilities, mean, median and the memoryless property that makes it unique.
Open calculator →
Log-Normal Distribution Calculator
The distribution of anything that grows by multiplication — incomes, particle sizes, share prices — where the logarithm is normal and the values are right-skewed.
Open calculator →
Entropy Calculator (Shannon)
How much information a probability distribution carries — Shannon entropy in bits, with the redundancy and the perplexity.
Open calculator →
Gini Coefficient Calculator
Inequality in a distribution on a 0-to-1 scale — the Gini coefficient, with the shares that show what it is actually measuring.
Open calculator →
Moving Average Calculator
Smooth a series to see the trend — simple, weighted and exponential moving averages side by side, with the lag each one introduces.
Open calculator →
Z-Score to Percentile Calculator
Turn a z-score into a percentile — the share of a normal distribution below it, with both tails and the two-sided probability.
Open calculator →
Percentile to Z-Score Calculator
Turn a percentile into a z-score — the inverse normal, which tells you how many standard deviations a given rank sits from the mean.
Open calculator →
Inverse T-Distribution Calculator
The t value for a given tail probability and degrees of freedom — the number behind every confidence interval built from a small sample.
Open calculator →
Frequency Distribution Calculator
Turn a list of values into a frequency table — counts, relative frequencies and cumulative frequencies, in classes chosen for you or by you.
Open calculator →
Relative Frequency Calculator
Convert counts to proportions and percentages — with cumulative shares and each category's share of the total.
Open calculator →
Cumulative Frequency Calculator
Running totals across ordered classes — with the cumulative percentages and the interpolated median and quartiles they give.
Open calculator →
Exponential Smoothing Calculator
Smooth and forecast a series with exponentially decaying weights — the workhorse of short-term forecasting, with its error measures.
Open calculator →
Cohen's Kappa Calculator
How much two raters agree beyond chance — the statistic that shows why raw agreement percentages are almost always misleading.
Open calculator →
Number Needed to Treat Calculator
How many people must be treated for one to benefit — the number that turns a relative risk reduction into something a person can actually weigh.
Open calculator →
Normal Approximation to the Binomial Calculator
Approximate a binomial probability with a normal curve — with the continuity correction, the exact answer for comparison, and a check on whether the approximation is valid at all.
Open calculator →
Hypothesis Testing Calculator
Turn a test statistic into a p-value and a decision — for z, t, chi-square or F — with the critical value and a plain reading of what it means.
Open calculator →
Standard Normal Distribution Calculator
Probabilities under the standard normal curve — below, above, between or outside any pair of z-values, with the density at each point.
Open calculator →
Circular Permutations Calculator
How many distinct arrangements there are around a circle — where rotations count as the same — for n objects, or for k chosen from n, with the necklace count where reflections are also the same, and the linear count for comparison.
Open calculator →
Average Calculator
Mean, median and mode of a list of numbers.
Open calculator →
Numbers & notation
Fraction to Decimal Calculator
Turn any fraction into a decimal and a percentage, simplify it to lowest terms, and see the mixed-number form.
Open calculator →
Decimal to Fraction Calculator
Turn a decimal into the simplest fraction that matches it, or the closest fraction with a denominator up to a limit you choose — handy for measurements in eighths, sixteenths and thirty-seconds.
Open calculator →
GCD and LCM Calculator
Find the greatest common divisor (highest common factor) and the least common multiple of two or more whole numbers, with the prime factors that explain them.
Open calculator →
GCF Calculator (Greatest Common Factor)
The greatest common factor of two or more whole numbers — the largest number that divides them all exactly.
Open calculator →
Least Common Denominator Calculator
The least common denominator of two or more fractions — enter the denominators and get the smallest one they all divide into.
Open calculator →
LCM Calculator (Least Common Multiple)
The least common multiple of two or more whole numbers — the smallest number they all divide into.
Open calculator →
Rounding Calculator
Round a number to any number of decimal places or significant figures, to the nearest 10, 100 or 1,000, and up or down — every common convention side by side.
Open calculator →
Scientific Notation Calculator
Write any number in scientific notation (a × 10ⁿ), engineering notation (exponent a multiple of 3) and E-notation, and see its order of magnitude.
Open calculator →
Standard Form Calculator
Write a number in standard form — a × 10ⁿ with a between 1 and 10.
Open calculator →
Prime Factorization Calculator
Break a whole number into its prime factors, test whether it is prime, and count and list its divisors.
Open calculator →
Number Base Converter
Convert whole numbers between binary, octal, decimal, hexadecimal and any base from 2 to 36.
Open calculator →
Binary to Hex Converter
Convert binary to hexadecimal — four binary digits make exactly one hex digit, which is why the two go together so neatly.
Open calculator →
Hex to Binary Converter
Convert hexadecimal to binary — each hex digit expands to exactly four bits.
Open calculator →
Binary to Octal Converter
Convert binary to octal — three bits to each octal digit.
Open calculator →
Octal to Binary Converter
Convert octal to binary — each octal digit expands to three bits.
Open calculator →
Decimal to Octal Converter
Convert decimal to octal — repeated division by eight, remainders read upwards.
Open calculator →
Octal to Decimal Converter
Convert octal to decimal — each place is a power of eight.
Open calculator →
Binary to Decimal Converter
Convert a binary number to ordinary decimal — each digit is a power of two, doubling as you move left.
Open calculator →
Decimal to Binary Converter
Convert an ordinary decimal number to binary — the ones and zeros a computer actually stores.
Open calculator →
Hex to Decimal Converter
Convert hexadecimal to decimal — base sixteen, where the digits run 0–9 then A–F.
Open calculator →
Decimal to Hex Converter
Convert a decimal number to hexadecimal — the compact base-sixteen form used for colors, bytes and addresses.
Open calculator →
Roman Numeral Converter
Convert a number to Roman numerals or a Roman numeral back to a number — years, film credits, clock faces, monarchs.
Open calculator →
Fraction Calculator
Add, subtract, multiply or divide two fractions and get the answer in lowest terms — with the mixed number, the decimal and the working that gets you there.
Open calculator →
Adding Fractions Calculator
Add two fractions and get the answer in lowest terms, as a mixed number and as a decimal.
Open calculator →
Subtracting Fractions Calculator
Subtract one fraction from another, reduced to lowest terms.
Open calculator →
Multiplying Fractions Calculator
Multiply two fractions — the easiest of the four operations, with no common denominator needed.
Open calculator →
Dividing Fractions Calculator
Divide one fraction by another — flip the second and multiply.
Open calculator →
Factors Calculator
Every factor of a whole number, in pairs, with the prime factorization, how many there are, what they add to — and the factors it shares with a second number.
Open calculator →
Modulo Calculator
The remainder after division — with both conventions, because programming languages disagree about negative numbers.
Open calculator →
Fibonacci Calculator
The nth Fibonacci number and the sequence up to it — plus how quickly the ratio of neighbours closes on the golden ratio.
Open calculator →
Prime Number Calculator
Test whether a number is prime, and find the primes on either side of it.
Open calculator →
Pascal's Triangle Calculator
A row of Pascal's triangle, the binomial coefficients it holds, and the row sum.
Open calculator →
Place Value Calculator
Break a number into the value each digit carries — thousands, hundreds, tens, tenths — and read it back in words.
Open calculator →
Long Addition Calculator
Add numbers in columns and see every carry — the written method, step by step.
Open calculator →
Long Multiplication Calculator
Multiply two numbers the written way, with every partial product shown.
Open calculator →
Expanded Form Calculator
Write a number as the sum of its place values, in all three forms schools use — and in words.
Open calculator →
Mixed Number to Improper Fraction Calculator
Convert a mixed number to an improper fraction and back — 2⅓ becomes 7/3.
Open calculator →
Log Base 2 Calculator
The binary logarithm — how many doublings a number represents, and the unit behind bits, octaves and algorithmic complexity.
Open calculator →
Negative Log Calculator
The negative logarithm — the transform behind pH, pKa, decibels of loss and the log-loss of a machine-learning model.
Open calculator →
About these calculators
These calculators implement standard formulas from school and first-year university mathematics and statistics (see the sources on each page). Nothing here depends on tax years or regulations.