Compute the area of seven common plane shapes — rectangle, triangle, trapezoid, circle, sector, ellipse, and parallelogram. Lengths can be feet, yards, inches, miles, meters, kilometers, or centimeters. Mixed units produce a square result in each unit you used. Complex outlines can be split into these shapes and added together.
Formula
Each length is converted into a common unit, the shape formula is applied, and the area is printed to 14 significant digits. Zero dimensions are allowed and give zero area; empty or negative values are rejected.
rectangle A = l × w
triangle A = √(s(s − a)(s − b)(s − c)) s = (a + b + c) / 2
trapezoid A = ((b1 + b2) / 2) × h
circle A = π r²
sector A = (θ / 360) × π r² (θ in degrees)
A = (θ / 2) × r² (θ in radians)
ellipse A = π a b
parallelogram A = b × h
Common area units
Factors use the international foot (1 ft = 0.3048 m exactly) and the survey acre of 43,560 ft².
| Unit | Area in m² |
|---|---|
| square meter | SI unit |
| hectare | 10,000 |
| square kilometre (km²) | 1,000,000 |
| square foot | 0.09290304 |
| square yard | 0.83612736 |
| acre | 4,046.8564224 (43,560 ft²) |
| square mile | 2,589,988.110336 (640 acres) |
Examples
30 ft by 20 ft rectangle
Length 30 ft and width 20 ft is 600 ft². The same numbers as a parallelogram (base × height) are also 600 ft². A 220 ft by 99 ft plot is 21,780 ft².
Mixed units
A rectangle 12 in by 1 ft is 144 in² and 1 ft². A trapezoid with bases 9 ft and 9 m and height 9 ft is 173.37401574803 ft² and 16.10697312 m².
Circle, sector, and ellipse
A 30 ft radius circle is 900π = 2827.4333882308 ft². A 90° sector of the same radius is a quarter of that: 225π = 706.8583470577 ft². An ellipse with semi-axes 18 ft and 20 ft is 360π = 1130.9733552923 ft².
Triangle by three sides
Edges 30 ft, 45 ft, and 50 ft give 666.58528149067 ft² by Heron's formula. An equilateral triangle with 77 ft sides is 2567.332309519 ft².