About the Area Calculator
This area calculator works out the area of the flat shapes people measure most often: rectangles, squares, triangles, circles, ellipses, trapezoids, parallelograms, rhombuses, circular sectors and regular polygons. Pick a shape, type the dimensions shown for it, and the calculator returns the area together with the perimeter wherever the inputs are enough to define it.
It is useful for homework and exam revision, but also for everyday jobs such as sizing a room for flooring, estimating a garden bed, checking a plot plan or pricing a countertop. Choose the length unit you measured in and the result is also converted to square meters and square feet, so you can compare with product coverage figures quoted in either system.
All dimensions must use the same unit. The area comes out in that unit squared — measure in feet and the answer is in square feet. For irregular rooms, split the floor into rectangles and triangles, calculate each piece and add them together.
With the default inputs, the area is 120. Change any value above to recalculate instantly.
How to use the area calculator
- 1Choose the shape you want to measure.
- 2Select the unit you measured in (feet, meters, inches…).
- 3Enter the dimensions shown for that shape, all in the same unit.
- 4Read the area in square units, plus the square-meter and square-foot conversions.
- 5For irregular spaces, split them into simple shapes and add the areas.
Formula and method
Every formula measures how many unit squares fit inside the shape. A rectangle is length times width; a triangle is half of the rectangle that encloses it, so ½ × base × height, where height is measured at right angles to the base. A parallelogram keeps base × height because sliding one end across does not change the area, and a trapezoid averages its two parallel sides before multiplying by the height.
Curved shapes use π: a circle is πr², an ellipse stretches this to πab, and a sector takes the fraction θ/2π of the full circle, giving ½r²θ with θ in radians. A regular polygon splits into n identical triangles around its centre, giving n s² ÷ (4 tan(π/n)). The ellipse perimeter uses Ramanujan’s approximation, accurate to within about 0.1% unless the ellipse is extremely elongated (more than about 10:1).
- l, w
- Length and width of a rectangle
- b, h
- Base and perpendicular height
- a, b (trapezoid)
- The two parallel sides
- r
- Radius
- θ
- Central angle in radians (degrees × π/180)
- n, s
- Number of sides and side length of a regular polygon
Worked examples
Room floor: 12 ft × 10 ft rectangle
A 12 × 10 ft room has an area of 12 × 10 = 120 square feet. The perimeter, useful for baseboards, is 2 × (12 + 10) = 44 ft. In metric that is 120 × 0.3048² ≈ 11.15 m².
Circular patio with a 5 m radius
Area = π × 5² = 78.54 m², and the circumference is 2π × 5 = 31.42 m of edging. Converted, the patio covers about 845 square feet.
Trapezoid with bases 8 cm and 5 cm, height 4 cm
Average the parallel sides, (8 + 5) ÷ 2 = 6.5 cm, and multiply by the height of 4 cm to get 26 cm².
Triangle with base 10 and height 6
Half of base × height: ½ × 10 × 6 = 30 square units. The triangle fills exactly half of the 10 × 6 rectangle around it.
Frequently asked questions
How do you calculate area?+
Area is the space inside a flat shape, measured in square units. For a rectangle multiply length by width; for a triangle take half of base × height; for a circle use π × radius².
What is the difference between area and perimeter?+
Area measures the surface inside a shape (square units, e.g. ft²), while perimeter measures the length of its boundary (plain units, e.g. ft). Flooring is bought by area, trim and fencing by perimeter.
How do I find the area of an irregular room?+
Divide the room into rectangles and triangles that do not overlap, calculate each area with the same unit, and add them. Subtract any cut-outs such as a chimney breast.
Why does the triangle need the perpendicular height?+
The ½ × base × height formula only works when height is measured at right angles to the base. If you know three sides instead, use Heron’s formula in the triangle calculator.
How do I convert square feet to square meters?+
One square foot equals 0.09290304 m², so multiply square feet by 0.0929 (or divide by 10.764). This calculator shows both conversions automatically when you choose a real unit.