How to use the area calculator
- Pick a shape and the unit you measured in.
- Enter the measurements shown for that shape. Optional boxes, such as the legs of a trapezoid, add a perimeter.
- Read the area in your unit and in square feet, square meters and acres, plus the perimeter or circumference where it applies.
Formula
Rectangle: length x width. Triangle: base x height / 2. Parallelogram: base x height
Circle: pi x r². Ellipse: pi x a x b. Sector: (angle / 360) x pi x r²
Trapezoid: (base 1 + base 2) / 2 x height. Regular polygon: n x s² / (4 x tan(pi / n))
Heron: s = (a + b + c) / 2, area = sqrt(s(s - a)(s - b)(s - c))
Conversions use exact definitions: 1 in = 0.0254 m, 1 ft = 0.3048 m, 1 yd = 0.9144 m and 1 acre = 4,046.8564224 square meters.
Worked examples
Rectangle 12 ft by 8 ft: 12 x 8 = 96 square feet. That is 96 x 0.09290304 = 8.91869184 square meters and 96 / 43,560 = 0.002203856749 acres. The perimeter is 2 x (12 + 8) = 40 ft.
Triangle with sides 13, 14 and 15: s = 21, so the area is sqrt(21 x 8 x 7 x 6) = sqrt(7056) = 84. The perimeter is 42.
Circle with radius 3: pi x 9 = 28.27433388, and the circumference is 6 x pi = 18.84955592.
Regular hexagon with side 5: 6 x 25 / (4 x tan 30 degrees) = 64.95190528. The perimeter is 30.
Trapezoid with bases 3 and 5 and height 6: (3 + 5) / 2 x 6 = 24.
Triangles from three sides
Heron's formula needs only the three side lengths. The tool first checks the triangle inequality: the longest side must be shorter than the sum of the other two. Sides of 1, 2 and 3 fail, because they would lie flat. It then uses a rearranged form of the formula that stays accurate for very thin triangles.
Units and square units
Area is measured in square units, so doubling each side of a shape multiplies its area by four. When you convert, square the length factor: 1 ft is 12 in, but 1 square foot is 144 square inches. The table lists nine area units, and acres and hectares help with land. To convert other quantities, use the unit converter.
Perimeter, circumference and the ellipse
The perimeter is the distance around a shape and is shown in your unit, feet and meters. For an ellipse there is no exact simple formula, so the tool uses Ramanujan's approximation, which is accurate to a tiny fraction of a percent for ordinary shapes. A triangle given by base and height has no perimeter, because its slanted sides are unknown. Use the three-sides option for that, or the Pythagorean theorem calculator for right triangles.
Assumptions and limits
- All measurements must be positive and in the unit you choose. Mixed units are not supported.
- The shape is flat and the sides are straight, apart from the circle, ellipse and sector arcs.
- The polygon is regular, meaning equal sides and equal angles, with 3 to 100 sides.
- Results show 10 significant digits. The ellipse perimeter is approximate.
- Nothing you enter leaves your browser.
Frequently asked questions
How many square feet are in an acre?
An acre is 43,560 square feet, which is 4,046.8564224 square meters. The tool uses that exact relationship for every acre value.
Why is the circle area based on the radius, not the diameter?
The formula pi x r² uses the radius because area grows with its square. If you have the diameter, halve it first. A circle with diameter 6 has radius 3 and area 28.27.
What is the height of a triangle or parallelogram?
It is the perpendicular distance from the base to the opposite side or vertex, not the length of a slanted side. Measuring the slanted side gives an area that is too large.
Can I find the area of an irregular shape?
Split it into rectangles, triangles and other shapes from this list, calculate each area and add them. Subtract any cut-outs such as a door in a wall.
What is a sector of a circle?
It is a slice, like a piece of pie, bounded by two radii and an arc. Its area is the fraction angle / 360 of the full circle.