Area and perimeter calculator for 2D shapes

How to calculate area and perimeter

Area is the surface inside a flat shape, in square units; perimeter is the length around it. For a rectangle, multiply length by width: a room 12 ft long and 10 ft wide covers 12 × 10 = 120 ft², and its perimeter is 2(12 + 10) = 44 ft.

Area formulas for common shapes

In every formula below, h is the perpendicular height, measured at right angles to the base, never along a slanted side.

• Square: A = a², P = 4a.
• Rectangle: A = l × w, P = 2(l + w).
• Triangle: A = ½ × base × height.
• Parallelogram: A = b × h, P = 2(b + s), where s is the slanted side.
• Trapezoid (trapezium): A = (a + b)/2 × h, the average of the two parallel sides times the height.
• Rhombus: A = pq/2, half the product of the diagonals.
• Circle: A = πr², circumference C = 2πr.
• Ellipse: A = πab, where a and b are the semi-axes, half the full length and half the full width.
• Regular polygon: A = ns²/(4 tan(180°/n)) for n equal sides of length s.
• Annulus (ring): A = π(R² − r²), the outer disk minus the hole.

Area of a triangle from base and height or three sides

Half the base times the perpendicular height: a base of 8 cm and a height of 4 cm give ½ × 8 × 4 = 16 cm². Those two numbers fix the area but not the two slanted sides, so the perimeter stays unknown. From three sides instead, use Heron's formula.

With all three sides, use Heron's formula: s = (a + b + c)/2, then A = √(s(s − a)(s − b)(s − c)). Sides of 3, 4 and 5 cm give s = 6 and A = √(6 × 3 × 2 × 1) = 6 cm².

Three lengths close into a triangle only if each is shorter than the other two combined, so 2, 3 and 6 cannot form one.

Area and perimeter examples

All dimensions are in centimeters. "Not determined" marks inputs that fix the area but leave a side length open.

A semicircle's perimeter adds the 10 cm diameter to the curved edge, and a sector's adds two radii to the arc. A segment is bounded by its arc and chord, so the 180° segment is the same region as the semicircle.

Given its slanted legs, the trapezoid has a perimeter too: legs of 5 cm each make it 10 + 4 + 5 + 5 = 24 cm. The annulus row repeats 50.265482 by coincidence: 16π cm² of area and 16π cm of edge around both circles.

Floors, L-shaped rooms and walls

Split an L-shaped floor into rectangles that do not overlap and add their areas. A 12 × 10 ft room with a 4 × 6 ft alcove covers 120 + 24 = 144 ft². Measuring the outer rectangle and subtracting the missing corner gives the same answer.

For wall area, multiply the perimeter by the wall height and subtract doors and windows. The 12 × 10 ft room with 8 ft walls has 44 × 8 = 352 ft² of wall before openings.

Flooring and tile orders need extra for cuts and pattern on top of the geometric area; the room area calculator and tile calculator cover those jobs.

Converting square feet and square meters

Area converts with the square of the length factor. One foot is exactly 0.3048 m, so 1 ft² = 0.3048² = 0.09290304 m².

The 120 ft² room is therefore 11.1483648 m². For an area you already know, the square feet to square meters converter does this step.

Common mistakes

• Using the slanted side as the height. A parallelogram with base 8 cm, slanted side 5 cm and height 4 cm covers 8 × 4 = 32 cm², not 8 × 5 = 40 cm².
• Forgetting the ½ for a triangle. Base × height is the area of the rectangle around the triangle, twice the triangle's area.
• Using the diameter as the radius. A circle 10 cm across has r = 5 cm and an area of 78.54 cm²; plugging in 10 gives 314.16 cm², four times too much.
• Converting area with a length factor. 120 ft² × 0.3048 = 36.576 means nothing; multiply by 0.09290304 instead.

Which measurements each shape needs

• Triangle (base and height) gives the area only; Triangle (three sides) adds the perimeter and checks that the sides can close.
• Trapezoid from bases and height gives the area only; from bases and legs it also finds the height and perimeter.
• Kite takes its two different side lengths and the angle between them, A = ab sin α.
• Ellipse perimeter has no exact elementary formula, so Ramanujan's approximation is used, accurate to 0.04% or better.

For a solid with depth, use the volume calculator. For an irregular plot given as corner coordinates, use polygon area from coordinates.