Area Calculator — Triangle, Circle, Trapezoid & More

Area formulas

Shape	Area	Example
Rectangle	length × width	12 × 10 = 120
Square	side²	10² = 100
Triangle	base × height ÷ 2	8 × 5 ÷ 2 = 20
Triangle, three sides	√(s(s − a)(s − b)(s − c))	sides 3, 4, 5 → 6
Circle	π × r²	r = 5 → 25π ≈ 78.54
Semicircle	π × r² ÷ 2	r = 5 → 12.5π ≈ 39.27
Sector	angle ÷ 360 × π × r²	60°, r = 5 → 13.09
Ellipse	π × a × b	6, 4 → 24π ≈ 75.40
Trapezoid	(a + b) × h ÷ 2	(6 + 10) × 4 ÷ 2 = 32
Parallelogram	base × height	10 × 6 = 60
Rhombus	diagonal₁ × diagonal₂ ÷ 2	6 × 8 ÷ 2 = 24
Ring	π × (R² − r²)	5 and 3 → 16π ≈ 50.27

Every result comes in the square of the unit you measured in: feet give square feet, meters give square meters. The calculator also converts to square feet, square meters, square inches and acres, so you can measure in one unit and quote in another.

Heights, radii and semi-axes

Most mistakes come from measuring the wrong length. A triangle’s or parallelogram’s height is measured at a right angle to the base, not along the slanted side. A circle’s radius is half its diameter — measure across the widest point and halve it. An ellipse’s semi-axes are half of its longest and shortest widths. When you know the three sides of a triangle but not its height, choose Triangle (three sides): Heron’s formula works from the half-perimeter s, and the calculator checks that the sides can form a triangle at all. For a right triangle’s missing side, use the Pythagorean theorem calculator.

Semicircles, sectors and rings

A semicircle is half a circle, so its area is π r² ÷ 2; its perimeter is the curved half, π r, plus the straight diameter, 2r. A sector — a pie slice — takes the fraction of the circle given by its angle: a 60° slice is one sixth of the circle. A ring, or annulus, is a circle with a hole: subtract the inner circle’s area from the outer one. For everything about a full circle — area, circumference and diameter from any one of them — the circle calculator goes further.

Rooms, yards and land

For floors, walls and yards, add up simple shapes: split an L-shaped room into two rectangles, or a bay window into a rectangle and a trapezoid, and add the areas. The square footage calculator does this for several areas at once and prices the material. Large areas are easier to read in acres — 43,560 square feet each — and the result shows acres once the area passes a hundredth of an acre. For the space a shape takes up in three dimensions, such as concrete or soil, use the volume calculator.

Frequently asked questions

How do you find the area of a triangle?

Multiply the base by the height and halve it: a triangle with an 8 ft base and a 5 ft height covers 8 × 5 ÷ 2 = 20 ft². If you know only the three sides, use Heron's formula — the calculator has both.

What is the area of a semicircle?

Half the area of the circle: π × r² ÷ 2. A semicircle with a 5 ft radius covers about 39.27 ft²; its perimeter, the arc plus the diameter, is π × 5 + 10 ≈ 25.71 ft.

How do you find the area of a trapezoid?

Add the two parallel sides, multiply by the height and halve it: (6 + 10) × 4 ÷ 2 = 32.

How do I convert the area to acres?

An acre is 43,560 square feet. Divide the square feet by 43,560; the calculator shows acres whenever the area is at least a hundredth of one.

Is the area of an ellipse πab?

Yes, with a and b the two semi-axes — half the longest and half the shortest width. A 12 × 8 oval has a = 6 and b = 4, so its area is 24π ≈ 75.40.

Why is there no perimeter for some shapes?

A triangle given by base and height, a trapezoid or a parallelogram needs the slanted sides as well, which the area formula does not use. Enter a triangle by its three sides to get its perimeter.