Eight common shapes in one widget — including Heron's-formula triangles and regular polygons.
Eight common 2D shapes are covered: rectangle, square, circle, triangle (either base × height or all three sides via Heron’s formula), trapezoid, ellipse, and regular polygon. Inputs are unitless — the output is in the square of whatever you typed in. Use feet in to get square feet, meters in to get square meters.
Output is in the square of whatever unit you typed in (e.g. meters in → square meters out, inches in → square inches out).
The dropdown swaps the input fields to match. Two triangle modes are offered for the two common ways triangles are described (base/height vs three sides).
All in the same linear unit. The widget doesn't care which unit — just that the inputs match.
The result is in the square of your input unit. 5 m × 3 m = 15 m²; 60 in × 40 in = 2400 in².
| Shape | Formula |
|---|---|
| Rectangle | A = w × h |
| Square | A = s² |
| Circle | A = π × r² |
| Triangle (base/h) | A = ½ × b × h |
| Triangle (3 sides) | A = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2 |
| Trapezoid | A = ½ × (a + b) × h |
| Ellipse | A = π × a × b |
| Regular n-gon | A = (n × s²) / (4 × tan(π/n)) |
When you have all three sides of a triangle but not the height, Heron's formula is the most direct way to the area: no trigonometry, no need to pick a base. It's been around since Hero of Alexandria in the 1st century — older than most things in the modern math curriculum.
Derived by splitting the n-gon into n isoceles triangles with apex at the center; each has area s² / (4·tan(π/n)). Limit as n→∞ recovers the circle area π·r² where r is the apothem.