Area Calculator
Choose a shape, type its dimensions and get the area (and the perimeter or circumference where one exists) in the unit of your choice.
Result
- Perimeter
- 16 m
- Formula used
- A = length × width
What is area?
Area is the measure of a two-dimensional surface: how many unit squares it takes to cover a shape. Floor plans, paint and carpet estimates, land sizes and material orders all depend on it. The unit is always a length unit squared, so a rectangle measured in meters has an area in square meters (m²).
Area formulas
| Shape | Area | Perimeter |
|---|---|---|
| Rectangle | length × width | 2 × (length + width) |
| Square | side² | 4 × side |
| Triangle | ½ × base × height | sum of the sides |
| Triangle (3 sides) | √[s(s−a)(s−b)(s−c)], s = half the perimeter | a + b + c |
| Circle | π × r² | 2 × π × r |
| Trapezoid | ½ × (a + b) × height | — |
| Ellipse | π × a × b | ≈ Ramanujan formula |
| Parallelogram | base × height | — |
| Sector | (θ ÷ 360) × π × r² | arc + 2r |
Worked example: a rectangular room 5 m long and 3 m wide has an area of 5 × 3 = 15 m² and a perimeter of 2 × (5 + 3) = 16 m. To order flooring, add about 10% for cuts and waste, so buy roughly 16.5 m².
How to use this calculator
- Select the shape. The input fields change to match its formula, which is shown above them.
- Choose the unit you are measuring in. The result is reported in that unit squared.
- Enter the dimensions. For a triangle with three known sides, pick the "three sides" option; the calculator checks that the sides can form a triangle.
Tips
- Height always means the perpendicular distance between the base and the opposite vertex or side, not the slanted edge.
- Measure in one unit throughout. Converting a finished area needs the square of the length factor (1 ft = 12 in, so 1 ft² = 144 in²). The unit converter handles lengths.
- For a right triangle with two known sides, the Pythagorean theorem calculator gives the third side and the area together.
Frequently asked questions
What is the difference between area and perimeter?
Area is the amount of surface inside a shape, measured in square units such as m² or ft². Perimeter is the distance around the outside, measured in ordinary length units. A long thin rectangle can have a large perimeter and a small area.
How do I convert an area from one unit to another?
Square the length conversion factor. There are 12 inches in a foot, so there are 12² = 144 square inches in a square foot, and 1 m² = 10.7639 ft² because 1 m = 3.2808 ft. Converting the lengths first and then calculating the area avoids this trap.
How do I find the area of an irregular shape?
Split it into rectangles, triangles and other simple shapes, calculate each area with this calculator and add them up. For a room with an alcove, for example, treat the alcove as a separate rectangle.
Why is the ellipse circumference labelled approximate?
Unlike a circle, an ellipse has no simple closed formula for its circumference. The calculator uses Ramanujan's approximation, which is accurate to better than 0.01% for everyday proportions.