What the area calculator does
The area calculator computes the surface area of a 2D shape from its dimensions, supporting twelve shape modes that together cover almost every problem people meet in geometry class, DIY, gardening, flooring and design work. Each shape shows its formula explicitly, so the tool doubles as a quick reference when you remember "I need this area" but not the exact equation.
Formulas covered
- Rectangle: A = w × h
- Square: A = s²
- Triangle (base × height): A = ½ × b × h
- Triangle (three sides — Heron's): A = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2
- Circle: A = π × r²
- Ellipse: A = π × a × b (semi-major × semi-minor)
- Trapezoid: A = ½ × (a + b) × h (parallel sides a, b; perpendicular height h)
- Parallelogram: A = b × h
- Rhombus (diagonals): A = ½ × d₁ × d₂
- Circular sector: A = ½ × r² × θ (θ in radians) — pie-slice of a circle
- Annulus (ring): A = π × (R² − r²)
- Regular hexagon: A = (3√3 / 2) × s²
Be consistent with units
The calculator is unit-agnostic — it does not know whether your inputs are in centimetres or inches. Whatever unit you put in, the area comes out in the square of it. Mixing units in one shape (length in feet, width in metres, say) will give a meaningless answer. Convert everything to the same unit first.
Heron's formula for triangles
When you know all three sides of a triangle but not the height, Heron's formula gives the area directly. Compute the semi-perimeter s = (a + b + c) / 2, then A = √[s(s − a)(s − b)(s − c)]. The calculator's "Triangle (three sides)" mode does this, and detects impossible triangles where the three sides cannot meet (when one side is at least as long as the sum of the other two).
Why circles use π
The circle area πr² appears because π itself is defined as the ratio of a circle's circumference to its diameter. The factor links the curved boundary to the enclosed surface in a way that cannot be avoided without introducing approximations. Ellipses, sectors and annuluses all inherit π for the same reason: they are pieces or transformations of a circle.
Practical tips
- For flooring or paint, round areas up to the next standard buy quantity — overlap, cuts and mistakes consume more material than the bare area suggests.
- For gardening, the area covered by a sprinkler is a circle (or sector). A 5 m-radius sprinkler covers π × 25 ≈ 78.5 m².
- For irregular shapes, split them into the standard shapes here, compute each, and add.
Use with the other tools
For powers and roots that come up in geometry, see the exponent calculator and square root calculator. For a full expression evaluator, the scientific calculator handles arbitrary maths.