How the Geometry Calculator Works
Area tells you how much flat space a shape covers, and perimeter tells you the distance around its edge. The 2D Geometry Calculator finds both for three common shapes: a circle, a rectangle and a right triangle. You can use it for school work, floor plans, gardens, fences and craft projects.
What you enter
- Shape: Circle, Rectangle or Right Triangle.
- Circle: the radius (the distance from the centre to the edge).
- Rectangle: the width and the height.
- Right triangle: the base and the height (the two sides that meet at the right angle).
All numbers must be greater than 0. The units can be anything (meters, feet, inches), as long as you use the same one for all the sides. The area is in square units of the same kind.
The formulas
| Shape | Area | Perimeter |
|---|---|---|
| Circle | π x r x r | 2 x π x r (the circumference) |
| Rectangle | width x height | 2 x (width + height) |
| Right triangle | base x height / 2 | base + height + hypotenuse |
For the triangle, the hypotenuse (the long side) comes from the Pythagorean theorem: hypotenuse = the square root of (base x base + height x height). The calculator shows it too. Results are rounded to 4 decimal places.
Worked examples
These use the default numbers:
| Shape | Size | Area | Perimeter |
|---|---|---|---|
| Circle | radius 5 | 78.5398 | 31.4159 |
| Rectangle | 4 by 6 | 24 | 20 |
| Right triangle | base 4, height 6 | 12 | 17.2111 |
For the triangle, the hypotenuse is the square root of (16 + 36) = the square root of 52 = 7.2111. So the perimeter is 4 + 6 + 7.2111 = 17.2111.
Chart: the area of a circle
The area grows with the square of the radius. Double the radius and the area is four times bigger:
radius 1 ██ 3.14 radius 2 ██████ 12.57 radius 3 ██████████████ 28.27 radius 4 ██████████████████████████ 50.27 radius 5 ████████████████████████████████████████ 78.54
Chart: same perimeter, different area
All these rectangles have a perimeter of 20, but the closer to a square, the larger the area:
1 x 9 ██████████████ 9 2 x 8 ██████████████████████████ 16 3 x 7 ██████████████████████████████████ 21 4 x 6 ██████████████████████████████████████ 24 5 x 5 ████████████████████████████████████████ 25
Real-life uses
- Flooring and paint: the area tells you how much material to buy.
- Fences and edging: the perimeter tells you how long it must be.
- Round tables and pots: the circumference is the distance around.
- Ramps and roofs: a right triangle with a hypotenuse gives the slope length.
Tips
- Radius or diameter? The diameter is twice the radius. If you have the diameter, divide it by 2 first.
- Use one unit for all sides. Do not mix feet and inches.
- This is for a right triangle only. For other triangles, the perimeter needs all three sides, which this tool does not ask for.
- To change area units (for example m² to ft²), use the Area Converter.
This tool gives an estimate for general information only. For building or cutting materials, measure again and allow for waste.