⬛ Area Calculator
Calculate the area of seven common shapes – pick the shape, enter its measurements and see the formula and working.
Quick answer: Area of a rectangle = length × width, so a 12 m × 8 m floor is 96 m². A triangle with base 10 and height 6 has area ½ × 10 × 6 = 30.
Updated · Free · No sign-up · Works on any device
Area Calculator inputs
Result
Area of the rectangle
96 m²
- Formula
- A = length × width
- Perimeter
- 40 m
- In square feet
- 1,033.34 ft²
Working
- Use the formula A = length × width
- Substitute: A = 12 × 8
- A = 96 m²
Area formulas for common shapes
Area is the amount of flat surface inside a shape, measured in square units such as cm², m² or sq ft. Every formula below multiplies two lengths together.
| Shape | Formula |
|---|---|
| Rectangle | length × width |
| Square | side² |
| Triangle | ½ × base × height |
| Circle | π × radius² |
| Trapezoid | ½ × (a + b) × height |
| Parallelogram | base × height |
| Ellipse | π × a × b |
Rectangle: A = l × w · Triangle: A = ½bh · Circle: A = πr²
Worked examples
- Floor: a 12 m × 8 m floor has area 12 × 8 = 96 m² (about 1,033 sq ft).
- Triangle: base 10, height 6 → ½ × 10 × 6 = 30 square units.
- Trapezoid: parallel sides 6 and 10, height 4 → ½ × 16 × 4 = 32.
- Circle: radius 3 → π × 9 ≈ 28.2743.
Why the formulas work
A triangle is exactly half of a parallelogram with the same base and height, which is why its formula has the ½. A trapezoid’s area uses the average of its two parallel sides as an effective width. A parallelogram can be cut and slid into a rectangle, so it keeps the base × height formula even though its sides slope. An ellipse is a stretched circle, so the single radius is replaced by its two semi-axes.
Tips for real-world measuring
- Use the same unit for every measurement before you multiply.
- Break irregular rooms or gardens into rectangles and triangles, then add the pieces.
- Always use the perpendicular height, not a slanted side.
- Add 5–10% extra when buying flooring, tiles or turf to allow for cutting and waste.
Frequently asked questions
How do I calculate the area of a room in square feet?
Measure the length and width in feet and multiply them. A 12 ft × 15 ft room is 180 sq ft. For an L-shaped room, split it into two rectangles, find each area and add them.
What height do I use for a triangle?
The perpendicular height – the straight-line distance from the base to the opposite corner, meeting the base at a right angle. It is not the length of a sloping side (unless the triangle is right-angled).
How do I find the area of a circle from its diameter?
Halve the diameter to get the radius, then use A = πr². A circle 10 cm across has radius 5 cm and area π × 25 ≈ 78.5398 cm².
Why is area in square units?
Area counts how many unit squares fit inside a shape, so multiplying two lengths gives square units: metres × metres = m². When converting, square the length factor too – 1 m² is 10.764 sq ft, not 3.281.