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.
Common area units
Factors use the international foot (1 ft = 0.3048 m exactly) and 1 acre = 43,560 ft², consistent with NIST conversion tables.
| 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.
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
Measurement limits
These formulas use straight-line, planar dimensions. They do not account for slope, surface contours, wall thickness, openings, or material waste unless you measure and subtract or add those areas yourself. Split an irregular outline into simple shapes, keep the measurements at the same reference surface, and avoid reporting more precision than the original measurements support. For flooring, paint, concrete, or landscaping purchases, continue to the related material calculator so package sizes, coverage, and waste can be handled separately.
Irregular garden worksheet: split, add, and subtract
Model an irregular bed as an 18 ft × 12 ft rectangle, add a triangular extension with an 8 ft base and 6 ft height, then subtract a circular utility cover with a 2 ft radius:
| Piece | Calculation | Area |
|---|---|---|
| Main rectangle | 18 × 12 | 216 ft² |
| Triangular extension | 8 × 6 ÷ 2 | 24 ft² |
| Circular exclusion | π × 2² | 12.57 ft² |
| Usable bed | 216 + 24 − 12.57 | 227.43 ft² |
Enter each simple shape separately and combine the results. A 3-inch layer over 227.43 ft² is about 56.86 ft³, or 2.11 yd³; that connection can be checked in the Mulch Calculator. The outline is an approximation, so keep the field measurements and a sketch with the estimate. Do not subtract the same exclusion from both a component and the combined total.
Start with the measurement you have
For a circle whose circumference or area is known, the Circle Calculator can recover the radius and diameter. An area alone does not give a material quantity: for a slab, take the area and thickness to the Concrete Calculator, and check the product’s stated yield before ordering.