How to use
- Choose the shape.
- Enter the dimensions shown in the diagram, all in the same unit.
- The area and perimeter appear on the right, with the formula below.
Options explained
- Unit
- Only changes the unit shown after the result (square units for area); nothing is converted. Sides in centimetres give an area in square centimetres.
- Triangle (three sides)
- Uses Heron's formula. Any two sides must add up to more than the third, or there is no triangle.
- Ellipse perimeter
- There is no exact elementary formula, so Ramanujan's approximation is used; the error is far below 0.01%.
- Sector
- The central angle is in degrees, 0 to 360. The perimeter includes the arc and both radii.
Examples
| Shape | Dimensions | Area | Perimeter |
|---|---|---|---|
| Circle | r = 5 | 78.5398 | 31.4159 |
| Trapezoid | a = 3, b = 5, h = 4 | 16 | — |
| Triangle | sides 5, 6, 7 | 14.6969 | 18 |
Frequently asked questions
How do I find the area of a circle?
Area = π × radius². A circle with a 5 cm radius has an area of about 78.54 cm² and a circumference of 2 × π × 5 ≈ 31.42 cm.
What is the formula for the area of a trapezoid?
(top + bottom) × height ÷ 2. A trapezoid with parallel sides 3 and 5 and height 4 has an area of 16.
Why is there no perimeter for a trapezoid or a base-and-height triangle?
The perimeter depends on the slanted sides, which base and height don't determine. For a triangle's perimeter, choose Triangle (three sides).
How do square units convert?
Square the length factor. 1 m² = 10,000 cm², and 1 ft² = 144 in².
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