Area calculator for plane shapes
Calculate the area and perimeter of squares, circles, triangles, trapezoids and ellipses.
Calculator inputs
Results
Enter your values and press “Calculate” to see the result.
In short
- What it calculates
- Calculate the area and perimeter of squares, circles, triangles, trapezoids and ellipses.
- Formula used
Square: A = s²- Example
- Example 1: Circle with radius 5 m:
Area calculator
Pick the shape and the calculator asks only for the measurements it needs.
You choose the units: enter metres and the area comes out in square metres.
How it works
Each shape has its classic formula. Circles and ellipses involve π; the trapezoid uses the average of the two bases times the height.
The perimeter is only shown for shapes where it can be derived from the values you entered.
Formula
Square: A = s²
Rectangle: A = b × h
Triangle: A = b × h / 2
Circle: A = π × r²
Trapezoid: A = (B + b) × h / 2
Rhombus: A = D × d / 2
Ellipse: A = π × a × b
Worked example
Example 1: Circle with radius 5 m:
A = π × 5² = 78.5398 m²
Perimeter = 2 × π × 5 = 31.4159 m
Example 2: Trapezoid with bases of 8 m and 5 m and a height of 4 m:
A = (B + b) × h ÷ 2 = (8 + 5) × 4 ÷ 2 = 26 m²
No perimeter is shown: it would also need the two slanted sides.
Explanation
Area grows with the square, not in a straight line
Doubling the side of a square does not double its area: it multiplies it by four. That is why a 30 cm pizza has more than twice the surface of a 20 cm one, even though the difference in diameter looks modest. When comparing prices by size, work out the area rather than trusting the linear measurement.
Watch the units when squaring
If you measure in centimetres the area comes out in square centimetres, and converting to square metres means dividing by ten thousand, not by a hundred. It is one of the costliest mistakes when quoting for flooring, paint or fabric.
Irregular shapes
Any complicated polygon can be broken into triangles and rectangles whose areas add up. An L-shaped room is two rectangles. For plots with irregular sides, the surveyor's formula works directly from the coordinates of the vertices.
Always buy extra material
When calculating tiles, turf or paint, add between five and ten per cent for cuts, breakages and waste. Buying exactly guarantees a second trip to the shop, and sometimes a batch in a different shade.
Frequently asked questions
What units does the result use?
Whatever unit you entered, squared. Centimetres give cm², metres give m².
Why is the perimeter missing for some shapes?
Because the values requested are not enough to derive it. A triangle perimeter needs all three sides, not the base and height.
How much bigger is a 30 cm pizza than a 20 cm one?
More than twice: 707 cm² against 314 cm². Area grows with the square of the diameter, not proportionally.
How do I convert square centimetres to square metres?
By dividing by ten thousand, not a hundred. One square metre is 10,000 square centimetres.
How do I find the area of an L-shaped room?
Split it into two rectangles, work out each area and add them. An L made of 4 × 3 m plus 2 × 2 m covers 12 + 4 = 16 m².
What is the height of a triangle?
The perpendicular distance from the base to the opposite corner, not the length of a slanted side. Using the side instead of the height overstates the area.
How many square metres are in a hectare?
10,000 m², a square 100 m on each side. A square kilometre is 100 hectares.
Sources and references
The formula behind this calculator is not ours. These are the sources it comes from, in APA 7 format, in case you want to go to the original or cite them in your own work.
- Weisstein, E. W. (s. f.). Area. MathWorld—A Wolfram Web Resource. https://mathworld.wolfram.com/Area.html https://mathworld.wolfram.com/Area.html Definition of area and formulas for the common plane figures.
- Bureau International des Poids et Mesures. (2019). The International System of Units (SI) (9th ed.). BIPM. https://www.bipm.org/en/publications/si-brochure https://www.bipm.org/en/publications/si-brochure The square metre as the SI unit of area.
Need to calculate something else?
These tools are often used alongside this calculator.
Volume
Volume and surface area of cubes, spheres, cylinders, cones, prisms and pyramids.
Pythagoras
Find the hypotenuse or a leg of a right triangle, with area and perimeter.
Room area
Floor, walls, perimeter and volume from three measurements.
Area
Square metres, hectares, acres, square feet and more.
Calculator
Type the whole expression and get the result instantly, brackets and functions included.
Percentage
The four most common percentage calculations in a single tool.