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.
Every area formula is a way of counting unit squares.
How the area calculator works
Every area formula is a way of counting unit squares. Rectangles do it directly, length × width. A triangle is half a rectangle, so ½ × base × height. A parallelogram is a rectangle with the slant sheared away, so it keeps base × height. A trapezoid averages its two parallel sides then multiplies by the height. Circles are the odd one out — π appears because no arrangement of squares tiles a circle exactly.
The height in these formulas is always the perpendicular height, not the sloping side. Using the slant length instead is the single most common mistake in the parallelogram and trapezoid cases.
Formula: square a²; rectangle ab; triangle ½bh; circle πr²; parallelogram bh; trapezoid ½(a+b)h; ellipse πab
Worked examples
| Inputs | Area | Note |
|---|---|---|
| A 8 × 5 rectangle | 40 | area 40, perimeter 26 |
| A circle of radius 5 | 78.5398 | 78.54 |
| A trapezoid with sides 8 and 5, height 4 | 26 | 26 |
| A regular hexagon of side 8 | 166.2769 | 166.28 |
FAQFrequently asked questions
What is the difference between area and perimeter?
Area is the surface inside a shape, measured in square units; perimeter is the distance around its edge, in ordinary units.
Which height do I use for a triangle or parallelogram?
The perpendicular height — straight up from the base — never the sloping side. Using the slant is the commonest error in these formulas.
Why is a circle πr² and not something simpler?
Because no whole number of squares tiles a circle. π is the ratio that falls out of the limit, and it is irrational, so the area never comes out exactly in squares.
How do I find the area of an odd shape?
Split it into rectangles and triangles, work each out, and add them. Almost every floor plan reduces this way.
What units does the answer use?
The square of whatever you entered: meters in gives square meters, feet in gives square feet.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.