An area calculator finds the space inside a flat shape, in square units, from its measurements. A 10 by 5 rectangle covers 50 square units and a circle with a radius of 10 covers about 314.16.
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How to use the area calculator
- Choose the shape.
- Enter side A (or the base, or the radius for a circle).
- Enter side B (or the height of a triangle).
- For a trapezoid, enter the two parallel sides as A and B and the height in the height field.
- Read the area in square units of whatever length unit you used.
Area calculator formulas
| Shape | Formula | Example | Area |
|---|---|---|---|
| Rectangle | length × width | 10 by 5 | 50 |
| Square | side² | side 10 | 100 |
| Triangle | ½ × base × height | base 10, height 5 | 25 |
| Circle | π × r² | radius 10 | 314.16 |
| Trapezoid | ½ × (a + b) × h | bases 10 and 6, height 5 | 40 |
| Parallelogram | base × height | base 10, height 5 | 50 |
| Ellipse | π × a × b | semi-axes 10 and 5 | 157.08 |
Area is measured in square units. If the lengths are in feet, the area is in square feet; in meters, square meters. Always use the same unit for every length before you multiply.
Area calculator worked example
A rectangle 10 by 5 has an area of 10 × 5 = 50 square units. A triangle with base 10 and height 5 covers half of that rectangle, 25. A circle with radius 10 has an area of π × 10² ≈ 314.16. For a trapezoid with parallel sides 10 and 6 and a height of 5, average the two parallel sides, (10 + 6) ÷ 2 = 8, and multiply by the height to get 40.
Trapezoids in the area calculator
A trapezoid needs three measurements: the two parallel sides and the perpendicular height between them. In the area calculator, enter the parallel sides as A and B and the distance between them in the separate height field. With parallel sides of 10 and 6 and a height of 5, the result is 40 square units.
Height means the perpendicular height
For triangles, parallelograms and trapezoids, the height is the straight-line distance at a right angle to the base, not the length of a slanted side. Using a slanted side gives an area that is too large. If you know only the three sides of a triangle, use Heron’s formula: with s = half the perimeter, area = √(s(s − a)(s − b)(s − c)).
Irregular shapes and rooms
- Split an L-shaped room or plot into rectangles, find each area and add them.
- For a cut-out, such as a fireplace, find its area and subtract it.
- Half circles and quarter circles are ½ or ¼ of π × r².
- To convert, 1 square meter is about 10.764 square feet, and 1 square yard is 9 square feet.
Getting the units right
The most common mistake with any area calculator is mixing units. If one side is measured in feet and the other in inches, convert one of them first: 12 feet by 30 inches is 12 × 2.5 = 30 square feet, not 360. Area also scales with the square of length, so converting square units is not the same as converting lengths. There are 12 inches in a foot but 144 square inches in a square foot, and 9 square feet in a square yard. One square meter is 10,000 square centimeters.
When you plan materials such as flooring, tile, paint or turf, find the area with the area calculator and then add a waste allowance. Flooring installers often add 5% to 10% for cuts, and more for diagonal layouts or rooms with many corners. Paint coverage is usually given on the can in square feet per gallon, so divide the wall area, minus doors and windows, by that figure.
Area versus perimeter
Area measures the surface inside a shape; perimeter measures the distance around it. You need area for flooring, sod or fabric, and perimeter for fencing, trim or edging. Two shapes can share the same perimeter but have very different areas: a 10 by 10 square and a 19 by 1 rectangle both have a perimeter of 40, yet the square covers 100 square units and the rectangle only 19. The area calculator gives area only, so measure the perimeter separately when you need it.
Related converters and calculators
Related calculators:
- Square footage calculator: rooms
- Triangle calculator: triangles
- Circle calculator: circles
- Volume calculator: 3D shapes
Sources
Questions about this calculator
How do you calculate area?
Use the shape’s formula, such as length × width for a rectangle.
What is the area of a circle with radius 10?
About 314.16 square units.
What is the area of a triangle?
½ × base × perpendicular height.
How do I find the area of a trapezoid?
½ × (sum of the parallel sides) × height.
How do I find the area of an L-shaped room?
Split it into rectangles and add their areas.
Check the assumptions and units before relying on a result. Financial, tax and health estimates do not replace advice for your individual circumstances.
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