Engineering & Mechanics Calculators — United States

Find average speed from a distance and a time — in km/h, m/s and mph — with the pace per kilometer.

Calculate acceleration from initial speed, final speed and time — in m/s², in g, and as km/h per second — with the distance covered.

How long an object takes to fall from a height and how fast it is going when it lands, ignoring air resistance.

Find how far a projectile travels, how high it goes and how long it flies from its launch speed and angle, with an optional launch height.

Calculate the kinetic energy of a moving mass — ½mv² — in joules, kilojoules, kilowatt-hours and food calories.

Find the gravitational potential energy of a mass at a height — mgh — and the speed it would reach if it fell.

Calculate momentum (mass × velocity) and the average force needed to bring the object to rest in a given time.

Find the centripetal force and acceleration that keep a mass moving in a circle, with the speed in revolutions per minute.

Calculate the escape velocity and low-orbit speed of Earth, the Moon, Mars, Jupiter, the Sun or any body from its mass and radius.

The swing period of a simple pendulum from its length — and the length that gives exactly one second, which is how the meter was nearly defined.

The speed at which drag balances weight and a falling object stops accelerating — for a skydiver, a raindrop or anything else.

The complete trajectory of a projectile — range, maximum height, time of flight, and the position and velocity at any moment.

An object launched horizontally from a height — how far it travels, how long it falls, and how fast it lands.

Centripetal acceleration, force and period for an object moving in a circle — plus the g-force it experiences.

Period, frequency, maximum speed and acceleration for a mass on a spring — the oscillation behind every vibration problem.

The energy stored in a spinning object — ½Iω² — for a disc, ring, sphere or a moment of inertia you supply.

Angular momentum of a spinning body, and the new speed when its moment of inertia changes — the skater-pulling-in-arms calculation.

The energy stored in a stretched or compressed spring — ½kx² — and the speed it can launch a given mass to.

How much energy a flywheel stores, how long it can supply a load, and whether the rim stress is survivable.

Solve any constant-acceleration problem — the SUVAT equations, given any three of displacement, initial and final velocity, acceleration and time.

Kinetic energy in foot-pounds from mass and velocity — the unit used for muzzle energy, torque work and imperial mechanics.

A pendulum’s period from its length — and the surprizing fact that mass does not appear in the answer.

The velocities after a head-on collision — elastic, inelastic or anywhere between — with the momentum and energy accounting.

Motion under constant acceleration — enter any three of initial velocity, final velocity, acceleration, time and distance, and the other two follow from the SUVAT equations.

Relativistic time dilation and length contraction from a speed — the Lorentz factor, how much a moving clock lags, and what the effect amounts to at everyday and at spacecraft speeds.

The fundamental frequency and harmonics of a stretched string from its length, tension and linear density — Mersenne's laws — with the wave speed, the wavelengths and what tightening or shortening the string does.

A motion in three phases — accelerate, cruize, brake — worked as a velocity–time graph: the speed at each corner, the distance under each segment, the total displacement and the average velocity.

How the uncertainties of two measured quantities combine into the uncertainty of a result — added in quadrature for a sum or difference, in relative terms for a product or quotient, with a power on the first quantity — against the pessimistic worst case.

The length of belt that joins two pulleys — open or crossed — from their diameters and the center distance, with the wrap angle on the small pulley, the speed ratio, and the center distance that would suit a standard belt length you already have.

A rotation expressed every way — revolutions per minute, radians per second, degrees per second, period and frequency — with the linear speed and centripetal acceleration at a chosen radius, and the rpm that would give a target tip speed.

The beat you hear when two tones close in pitch sound together — the beat frequency and the seconds between beats — with the tone you perceive, the gap in cents, and how many beats to count in ten seconds when tuning.

Angular acceleration from a spin-up or spin-down in rpm over a time, or from a torque acting on a known moment of inertia — with the revolutions turned during the change.

The contracted length of a moving object as seen by an observer it passes, with the Lorentz factor and the speed in ordinary units.

A perfectly inelastic collision — two objects that collide and move off together — with the shared final velocity, the kinetic energy before and after, and how much was lost to deformation, heat and sound.

The coefficient of restitution — how elastic a collision is — from the speeds before and after, or from how high a ball bounces back, with the energy retained and the height of the next bounce.

Calculate force from mass and acceleration — Newton's second law — in newtons, kilonewtons, kilograms-force and pounds-force.

Calculate pressure from force and area, in pascals, kilopascals, bar, psi and atmospheres.

Calculate the gravitational attraction between two masses at a distance with Newton's law, F = G m₁ m₂ ÷ r².

Calculate the friction force on an object from its mass, the coefficient of friction and the slope angle — and whether it slides.

Calculate the force a spring exerts, the energy it stores and how far a hanging mass stretches it, from the spring constant.

Calculate torque from force, lever arm and angle — in newton-meters, pound-feet and kilogram-force meters — and the power that torque delivers at a given rpm.

Calculate the work done by a force over a distance and the power that work represents over time, in joules, watts and horsepower.

Find the mechanical advantage of a lever and the effort needed to lift a load from the effort arm and load arm lengths.

Calculate a gear ratio from tooth counts and see the output speed and torque for a given input, ideal and with an efficiency allowance.

The upward force on a submerged or floating object, whether it floats, and how much of it sits below the surface.

The force needed to change momentum over a given time — the calculation behind crumple zones, airbags and every landing technique.

The force of an impact from the fall height and the stopping distance — with the g-force and how much a softer surface would help.

The velocities after a one-dimensional collision — perfectly elastic, perfectly inelastic, or anywhere between — with the energy lost.

Spring constant from force and extension — with the energy stored, and the extension any other load produces.

The banking angle a curve needs so a vehicle holds the corner without relying on friction — and the speeds friction then allows.

How far a beam deflects under load — simply supported or cantilever, point load or distributed — with the span-to-deflection ratio builders actually check.

The moment of inertia of a solid cylinder, hollow cylinder, sphere, rod or point mass — and the angular momentum and rotational kinetic energy at a given spin.

The strength of gravity at a height above a planet's surface — falling with the square of distance from the center — with the weight change, the altitude where gravity halves, and why astronauts float in an orbit where g is still 90% of the ground value.

The reactions at the two supports of a simply supported beam under a uniform load and a point load — plus the maximum bending moment and shear, and where the moment peaks — the first calculation in sizing any beam.

The force a pneumatic cylinder delivers on the push and pull strokes at a given air pressure — from the bore and rod diameters — with the air consumed per cycle, the consumption at a cycle rate, and the bore needed for a target force.

The factor of safety of a component — its strength divided by the stress it will actually carry — from a material strength and a working load on a cross-section, with the load at which it would fail, the allowable stress for a required factor, and the section that would achieve it.

How far a round shaft twists under a torque — from its length, diameter and shear modulus — with the maximum shear stress at the surface, the polar moment of area, the torsional stiffness, and the diameter that would hold the twist to a limit.

How intensity falls with distance from a point source — light, sound, radiation, a radio signal or gravity — and the distance at which it reaches a level you choose.

The output force of a hydraulic press or jack from the input force and the two piston sizes, with the system pressure, the mechanical advantage and how far each piston moves.

The maximum bending stress in a beam from the bending moment and the cross-section — rectangle, circle or a section you enter — with the second moment of area, the section modulus and the utilization against an allowable stress.

The effort needed to lift a load with a pulley system, how much rope you pull for each meter of lift, and the mechanical advantage — ideal and with friction.

Solve Ohm's law for voltage, current or resistance — V = I R — with the power dissipated.

Find the voltage across a component from the current through it and its resistance — V = I × R, with the power it dissipates alongside.

Find the current a circuit draws from the supply voltage and the resistance — I = V ÷ R, with the power alongside.

Find the resistance from the voltage across a component and the current through it — R = V ÷ I.

Find the equivalent resistance of up to four resistors connected in series and in parallel.

Find the equivalent capacitance of up to four capacitors in parallel and in series, and the energy stored at a voltage.

Calculate the output voltage of a two-resistor voltage divider, with the current drawn and the power in each resistor.

Secondary voltage, current and turns from a transformer's ratio — with the power check that shows why current goes up as voltage comes down.

How fast a capacitor charges or discharges through a resistor — the time constant, and the voltage at any moment.

The energy and charge stored in a capacitor at a given voltage — with the discharge time constant into a load.

The energy stored in an inductor's magnetic field, its time constant, and the voltage spike if the current is interrupted.

The energy stored per cubic meter in an electric or magnetic field — the physics behind capacitors, inductors and electromagnetic waves.

The electrostatic force between two point charges from Coulomb's law — its size, whether it attracts or repels, and how it changes with distance.

The magnetic field around a long straight wire carrying a current — and, for comparison, the field inside a solenoid of the same current — from the Biot–Savart result.

The force on a charged particle moving through a magnetic field — and the radius and period of the circle it is bent into, which is how mass spectrometers, cyclotrons and the aurora all work.

The reactance a capacitor presents at a given frequency, the current it passes at a voltage, and — with an inductor entered — the inductive reactance and the resonant frequency of the pair.

The magnetic field inside a solenoid from its turns, length, current and core material, and the inductance of the coil.

The magnetic flux through a loop from the field, its area and the angle it sits at, and the voltage Faraday’s law induces when that flux changes over a time.

The radius a charged particle circles at in a magnetic field, with the period, cyclotron frequency and centripetal acceleration — for an electron, proton, alpha particle or any mass and charge you enter.

What a uniform electric field does to a charged particle: the force on it, its acceleration, the speed and energy it gains crossing a distance from rest, and how long that takes.

Calculate density from mass and volume in kg/m³, g/cm³ and lb/ft³, with the specific gravity and whether the material floats in water.

Calculate the heat needed to change the temperature of a mass of water, metal, air or another material — Q = m c ΔT — and how long a heater takes to supply it.

Calculate how much a length of steel, aluminium, concrete, glass or plastic grows or shrinks with a temperature change.

Solve the ideal gas law for pressure, volume, amount or temperature — PV = nRT — with pressure in kPa, volume in liters and temperature in kelvin or Celsius.

Convert a ratio of powers or amplitudes into decibels and back — the logarithmic scale behind sound levels, signal gain and attenuation.

Convert frequency to wavelength for sound in air or water, light and radio in a vacuum, or any wave speed you enter.

The angle light bends to when it crosses between two materials — with the critical angle beyond which it reflects instead.

Where a lens forms an image and how large it is — from the focal length and the object distance, with whether the image is real or virtual.

The frequency you hear when a source or observer is moving — the reason a siren drops in pitch as it passes.

The heat needed to change a material's temperature — with the time it takes at a given power, and the cost of the energy.

The energy absorbed or released by a phase change — melting, freezing, boiling or condensing — at constant temperature.

The rate of heat conduction through a wall, window or insulation layer — with the R-value, U-value and running cost.

The total energy to take a substance from one temperature to another — including any melting or boiling the range crosses.

The energy of a single photon from its wavelength or frequency — in joules and electronvolts, with the part of the spectrum it belongs to.

Convert between wavelength, frequency, wavenumber and energy — the four ways spectroscopists label the same photon.

How much a hot object radiates and at what color — the Stefan–Boltzmann law and Wien's displacement law together.

Convective heat transfer from a surface — Newton's law of cooling — with the coefficient solved in whichever direction you need.

The pressure and force exerted by light on a surface — absorbing or reflecting — and what it means for a solar sail.

The sensible heat carried by a flow of air or water — the HVAC load calculation, from flow rate and temperature rize.

Where a lens forms an image and how large it is — with whether the image is real or virtual, upright or inverted.

The ideal gas law solved for pressure, volume, moles or temperature — with the mass of gas and the density that follows.

The heat needed to change a material’s temperature — and how long a given heater takes to deliver it.

Radiation dose from energy deposited in tissue — absorbed dose in gray, effective dose in sievert once the radiation type is weighted — and where it sits against background, a chest X-ray and the occupational limit.

Pressure and speed at two points along a flow from Bernoulli's equation — and what a change in pipe diameter does to both, which is how a venturi meter measures flow.

How many decibels a solid wall or panel blocks, from its surface mass and the frequency — the mass law of acoustics — with the level that gets through and what doubling the mass or the frequency does.

The de Broglie wavelength of a particle from its mass and speed — the scale on which it behaves as a wave — with its momentum, the equivalent frequency, and how the wavelength compares with an atom.

The binding energy of a nucleus from its measured atomic mass and its proton and neutron counts — the mass defect converted by E = mc² — with the energy per nucleon that decides which nuclei can release energy by fusion or fission.

How long a star burns hydrogen on the main sequence, from its mass — luminosity rises steeply with mass, so heavy stars live fast and die young — with what it becomes at the end.

An energy in electronvolts expressed every way a physicist uses it — joules, temperature, frequency, wavelength, wavenumber and mass equivalent — with the constants that link them.

Express a length, time, mass, energy or temperature in Planck units — the natural scales built from G, c, ħ and k — and see the five Planck units themselves and what they mean.

The water flow a pipe carries for a given pressure drop over its length — from the diameter and the pipe material's roughness coefficient — by the Hazen–Williams formula, with the velocity, the head loss per meter and the flow at a different diameter.

The density of air at a given temperature, pressure and relative humidity — dry and moist — with the water-vapour pressure, the density altitude, and how the figure compares with standard sea-level air.

Air pressure at an altitude from the barometric formula — with the standard temperature there, the share of sea-level pressure, the oxygen available compared with sea level, and the altitude that matches a pressure you have measured.

How much water a cubic meter of air actually holds — absolute humidity in grams — from temperature and relative humidity, with the vapour pressure, the mixing ratio, the dew point, and how much more the air could hold before saturating.

The flat length of sheet metal that becomes a bend — the bend allowance from thickness, inside radius, bend angle and K-factor — with the bend deduction, the setback, and the flat blank length for a part with two flanges.

Brewster’s angle — the angle of incidence at which reflected light is completely polarized — for any pair of refractive indices, with the critical angle for total internal reflection when it exists.

The acoustic impedance of two media from their density and speed of sound, and the share of sound energy reflected and transmitted at the boundary between them.

The speed of sound in air at a given temperature, in every common unit, and the time sound takes to cover a distance — the lightning-and-thunder count made exact.

The energy equivalent of a mass by E = mc², expressed in joules, kilowatt-hours, tonnes of TNT and years of a household’s electricity.

Einstein’s photoelectric equation: the energy of a photon at a wavelength, the maximum kinetic energy of the electrons it knocks out of a metal, the stopping voltage, and the threshold wavelength below which nothing is emitted.

The Compton shift — how much a photon’s wavelength grows when it scatters off an electron at a given angle — with the photon energies before and after and the energy handed to the electron.

The Reynolds number of a flow from the fluid, its speed and the pipe diameter — and whether that makes the flow laminar, transitional or turbulent.