Area Calculator — square, rectangle, triangle, circle

How it works

Area is the amount of surface a two-dimensional shape encloses, measured in square units. Pick a shape and its area comes from a standard formula:

• Square: side × side = a²
• Rectangle: length × width = a × b
• Triangle: ½ × base × height = ½ a b
• Circle: π × radius² = π a²

A common thread runs through them: area grows with the square of a linear size. Double a shape's dimensions and its area quadruples, because you've scaled it in two directions at once.

Worked example

A rectangle 5 by 3 has area 5 × 3 = 15 square units. A circle of radius 4 has area π × 4² = 16π ≈ 50.27. A triangle with base 6 and height 4 has area ½ × 6 × 4 = 12 — half the 6 × 4 rectangle it fits inside. And a square of side 5 is 5² = 25.

Frequently asked questions

How do I find the area of a rectangle?

Multiply length by width: area = a × b. A 5-by-3 rectangle is 15 square units. A square is the special case where the two sides are equal, so its area is just side².

How do I find the area of a triangle?

Multiply the base by the perpendicular height and halve it: ½ × base × height. A triangle with base 6 and height 4 has area 12. The height must be the perpendicular distance from the base to the opposite vertex, not a slanted side. (If you only know the three side lengths, use Heron's formula instead — see the triangle calculator.)

How do I find the area of a circle?

Square the radius and multiply by π: area = πr². A circle of radius 4 has area π × 16 ≈ 50.27. If you know the diameter instead, halve it to get the radius first, since the radius is half the diameter.

What units does area come out in?

Square units of whatever you measured in — if the sides are in metres, the area is in square metres (m²); centimetres give cm². This calculator treats the dimensions as plain numbers, so keep every dimension in the same unit and the area is in that unit squared.

Why does area grow with the square of the size?

Because area spans two dimensions. Scaling a shape by a factor stretches it in both directions, so the area scales by that factor squared. Tripling a square's side makes it 9 times the area — which is why a slightly larger pizza is a lot more food.

How do I find a missing dimension from the area?

Reverse the formula. For a rectangle of known area and one side, the other side is area ÷ side. For a circle, the radius is √(area ÷ π). For a triangle, the height is 2 × area ÷ base. Each just undoes the multiplication in the area formula.