Area formula chart
The area formulas for the common two-dimensional shapes, in one place. Area measures the surface a shape covers and is always given in square units. Match your shape to the row and plug in the dimensions.
Area formulas
| Shape | Area formula |
|---|---|
| Square | A = s² |
| Rectangle | A = l × w |
| Triangle | A = ½ × b × h |
| Parallelogram | A = b × h |
| Trapezoid | A = ½(a + b) × h |
| Circle | A = πr² |
| Ellipse | A = π × a × b |
| Rhombus | A = ½ × d₁ × d₂ |
| Regular polygon | A = ½ × perimeter × apothem |
| Circle sector | A = ½ × r² × θ (radians) |
Area is measured in square units, such as square metres or square inches. Notice the pattern among triangles and related shapes: a triangle is half of a rectangle of the same base and height, which is why its formula carries the one-half. For curved shapes, the constant pi appears.
Need volumes or circle details?
See the Volume Formula Chart and the Circle Formula Chart.
How the formulas relate
Many area formulas connect to the rectangle. A parallelogram has the same area as a rectangle of equal base and height, since you can cut a triangle from one end and slide it to the other. A triangle is exactly half that, hence the one-half. A trapezoid averages its two parallel sides, then multiplies by the height.
Working with circles
The circle and its relatives bring in pi, roughly 3.14159, the ratio of a circle circumference to its diameter. The area of a circle is pi times the radius squared, and an ellipse generalizes this to pi times its two semi-axes. A sector is a pie slice, a fraction of the full circle area set by its angle.
FAQ
What is the area formula for a triangle?
One half times the base times the height, written A = ½bh. The height must be measured perpendicular to the chosen base.
What is the area of a circle?
Pi times the radius squared, A = πr². For a radius of 5, the area is about 78.5 square units.
What units is area measured in?
Square units, such as square metres, square feet, or square centimetres, because area covers two dimensions.