What this calculator does
The area of shapes calculator handles four of the most common 2D shapes, circle, square, rectangle and triangle, in a single tool with a shape selector, so there is no need to remember or look up a separate formula for each one. Pick the shape, enter its dimensions, and the area comes back straight away.
Every shape here uses its own formula: πr² for a circle, side squared for a square, length times width for a rectangle, and Heron's formula (working from all three side lengths, with no need for a separate height measurement) for a triangle. This calculator is a quick, general hub; anyone wanting a deeper page for one particular shape, such as apothem and circumradius options, can follow the links below to that shape's dedicated calculator.
The formula
The area formula depends on which shape is selected. A circle uses π times the radius squared. A square uses the side length squared. A rectangle multiplies its two side lengths. A triangle from three known sides uses Heron's formula: half the perimeter (s) is worked out first, then the area is the square root of s times (s minus each side) multiplied together.
| Term | Meaning |
|---|---|
| r | Radius of a circle, the distance from its centre to its edge. |
| a, b, c | The side lengths used for a square, rectangle or triangle, depending on the shape selected. |
| s | The semiperimeter of a triangle, half of a + b + c, used inside Heron's formula. |
The inputs explained
| Field | What to enter |
|---|---|
| Shape | Choose which shape to calculate the area of. |
| Radius / side a / length (see shape) | For a circle this is the radius. For a square or rectangle it is one side length. For a triangle it is one of the three sides. |
| Side b / width (rectangle & triangle only) | The second side, used only for a rectangle (width) or a triangle (second side). |
| Side c (triangle only) | The third side, used only for a triangle. |
When to use it
Comparing several different shapes quickly
Switching the shape selector rather than opening a different calculator each time makes it faster to compare, say, how much a circular tabletop covers against a rectangular one of similar size.
Working from three side lengths with no height
A triangle plot or panel is often measured by its three edges rather than a perpendicular height, and Heron's formula gets the area directly from those three lengths without needing to construct a height first.
Estimating material needed for flooring, paint or turf
Area is the starting figure for most material-quantity estimates; getting the shape's area right before adding a coverage rate avoids ordering the wrong amount.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the area of a circle grows with its radius
The area of a circle across a range of radius values.
| Radius | Area | Side of a square with the same area |
|---|---|---|
| 2 | 12.566 | 3.545 |
| 5 | 78.540 | 8.862 |
| 8 | 201.062 | 14.180 |
| 10 | 314.159 | 17.725 |
| 15 | 706.858 | 26.587 |
| 20 | 1,256.64 | 35.449 |
Area of the same three side lengths across each shape type
The same set of dimensions (10, 6, 8) run through each shape option, to show how differently each formula treats the same numbers.
| Shape | Area | Shape used |
|---|---|---|
| Circle | 314.159 | Circle |
| Square | 100.000 | Square |
| Rectangle | 60.000 | Rectangle |
| Triangle | 24.000 | Triangle |
Questions
Which shapes does this calculator cover?
Circle, square, rectangle and triangle. For other shapes, the site has dedicated pages, including pentagon, hexagon and any regular polygon through the regular polygon calculator.
Do I need a height measurement for the triangle option?
No. This calculator uses Heron's formula, which only needs the three side lengths. If you do have a base and perpendicular height instead, the dedicated triangle area calculator handles that version directly.
What happens if I enter triangle sides that cannot form a real triangle?
The calculator checks that each side is shorter than the sum of the other two, the basic condition for a triangle to exist, and returns a message instead of a nonsense result if that check fails.
Why is there a "side of an equal-area square" figure in the results?
It is a quick way to compare shapes of different types on equal footing: two shapes with the same area, whatever their outline, will always have the same equivalent square side length.
For a deeper look at a single shape, see the area of a circle calculator or the triangle area calculator. For perimeter rather than area, use the perimeter of common shapes calculator.