About the area calculator
The area calculator finds the area of eleven common 2D shapes: rectangle, square, triangle (from base and height, or from three sides), circle, ellipse, circular sector, parallelogram, trapezoid (trapezium), rhombus and regular polygon. Pick a unit and see the area in that unit squared and in square metres, square feet, hectares and acres.
Extra measurements such as perimeter or arc length are shown where they are useful.
Who should use the area calculator
- Students and teachers.
- Home owners and builders measuring floors, gardens and plots.
- Anyone comparing plot sizes in different units.
How to use the area calculator: what each input means
- Shape
- Choose the shape and its measurements appear.
- Length unit
- mm, cm, m, km, in, ft, yd or mi; area comes out in that unit squared.
How the area calculator works: method and formula
Each shape uses its standard formula. The area in your unit is converted to square metres using the exact definition of the unit, and from there to square feet, hectares and acres.
- Rectangle
- A = l × w
- Triangle
- A = ½ × b × h
- Circle
- A = π r²
- Trapezoid
- A = ½ (a + b) h
How to read your area calculator result
Doubling every length multiplies area by four. Keep all measurements in the same unit before entering them. For an irregular shape, split it into simple parts, calculate each, and add them.
Area Calculator worked example
A rectangle 8 m by 5 m, and a triangle with sides 7, 8 and 9.
- Rectangle: 8 × 5 = 40 m².
- That is 430.6 square feet.
- Triangle with sides 7, 8 and 9: s = 12, area = √(12 × 5 × 4 × 3) = 26.8328.
- A circle of radius 5 has area π × 25 = 78.5398.
The 8 m × 5 m rectangle has an area of 40 m².
Practical uses of the area calculator
- Estimating flooring, paint or turf.
- Comparing plots in square metres and acres.
- Homework and exam practice.
Assumptions and limitations of this calculator
- Ideal shapes; real rooms and plots need splitting into simple parts.
- Ellipse perimeter uses Ramanujan's approximation; areas are exact formulas.