How to use the area calculator
- Choose the shape. The input boxes change to match it.
- Choose the length unit you measured in: millimeters through miles.
- For a regular polygon, enter the number of sides.
- Enter the measurements. Every length must be in the same unit.
- For a sector, enter the central angle in degrees.
- Read the area in your unit squared, the formula with your numbers in it, and a table of the same area in other units.
Area formulas for each shape
Here s is a side length, l and w are length and width, b and h are a base and the height measured at a right angle to it, and r is a radius. For the ellipse, a and b are the half-axes: half the longest and half the shortest width. The three-sides triangle uses Heron's formula, where s is half the perimeter. For a regular polygon, n is the number of equal sides.
Worked example
The calculator opens with a rectangle 12 ft long and 10 ft wide, about the size of a small bedroom:
- A = length × width = 12 × 10 = 120 ft²
- In square meters: 1 ft² = 0.09290304 m², so 120 × 0.09290304 = 11.1484 m²
- The perimeter is 2 × (12 + 10) = 44 ft, and the diagonal is √(12² + 10²) = √244 = 15.6205 ft
Two more checks you can try. A circle with a 5 cm radius has an area of π × 25 = 78.5398 cm². A triangle with sides 3, 4 and 5 m has s = 6, so A = √(6 × 3 × 2 × 1) = √36 = 6 m², the same as ½ × 3 × 4 because it is a right triangle.
Units: why the conversion factor is squared
Area units are lengths multiplied by lengths, so a length factor gets squared. One foot is 12 inches, but one square foot is 12 × 12 = 144 square inches. One meter is 100 cm, so one square meter is 10,000 cm². This is the most common mistake in hand calculations: converting the final area with the length factor instead of its square.
| From | To | Multiply by |
|---|---|---|
| ft² | m² | 0.09290304 |
| m² | ft² | 10.7639 |
| in² | cm² | 6.4516 |
| acres | ft² | 43,560 |
| hectares | acres | 2.47105 |
If your measurements are in mixed units, such as feet and inches, convert them all to one unit first. A wall 10 ft 6 in wide is 10.5 ft, not 10.6 ft.
Irregular shapes
Most real rooms, gardens and plots aren't a single shape. Split the outline into rectangles, triangles and circle parts, find each area, then add them. For an L-shaped room, two rectangles do the job. To remove an area, such as a kitchen island from a floor, subtract it. For floors and decks priced by the square foot, the square footage calculator is set up for that job.
Frequently asked questions
What is the difference between area and perimeter?
Area measures the surface inside a shape, in square units such as ft² or m². Perimeter is the distance around the edge, in plain length units. A 12 × 10 ft room has an area of 120 ft² but a perimeter of 44 ft.
How do I find the area of a triangle without its height?
If you know all three sides, use Heron's formula: choose "Triangle (three sides)" and enter them. The calculator checks that the sides can form a triangle, because each side must be shorter than the other two added together.
Why is the ellipse perimeter an approximation?
An ellipse's area has an exact formula, π × a × b, but its perimeter doesn't have a simple closed form. The calculator uses Ramanujan's second approximation, which is accurate to well under 0.01% for everyday shapes.
How do I measure the height of a parallelogram or trapezoid?
Measure straight across at a right angle between the two parallel sides, not along the slanted side. Using the slanted side gives an area that is too large.
Related calculators
- Volume Calculator — Volume of a cube, box, cylinder, cone, sphere, pyramid, capsule or tube, in cubic units, liters and gallons.
- Surface Area Calculator — Lateral and total surface area of a cube, box, cylinder, cone, sphere, pyramid, capsule or tube.
- Square Footage Calculator — Add up the area of up to six rectangles, circles, triangles, trapezoids or L-shapes in sq ft or m², with cost.
- Circle Calculator — Radius, diameter, circumference and area from any one of them, plus arc length and sector area for an angle.
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