Area Calculator

How to use the area calculator

Area measures how much flat surface a shape covers, and it is always expressed in square units: square centimeters, square feet, square miles and so on. This calculator handles nine common shapes with one form.

1. Pick the shape under Area of. The boxes below change to show only the measurements that shape needs.
2. Set Metric to the unit you want the answer in.
3. Type each measurement. Every box has its own unit selector, so you can enter a width in meters and a length in centimeters in the same calculation; the tool converts them before multiplying.
4. Press Calculate area. The result is rounded to six decimals, with thousands separators for large values.

If a needed box is empty or zero, no area is produced. Negative values are rejected, since a length cannot be below zero.

Square, rectangle, parallelogram and trapezoid

These four shapes all come down to a base multiplied by a height, with small adjustments.

square: A = s²

rectangle: A = w × l

parallelogram: A = b × h

trapezoid: A = (b₁ + b₂) ÷ 2 × h

For a parallelogram, the height is the perpendicular distance between the two parallel sides, not the length of the slanted side. A trapezoid averages its two parallel bases and multiplies by the height between them.

Example: a trapezoid with bases of 4 cm and 6 cm and a height of 3 cm has area (4 + 6) ÷ 2 × 3 = 15 cm². A parallelogram with base 7 cm and height 3.3 cm has area 23.1 cm².

Dedicated pages exist for the rectangle, the square and the parallelogram.

Triangles: seven ways to solve

A triangle can be pinned down by different combinations of known measurements, so the form offers a Solve triangle by choice. Sides are labeled a, b and c; the angles α, β and γ sit opposite them.

Example (SSS): a triangle with sides 3, 4 and 5 has s = 6, so A = √(6 × 3 × 2 × 1) = 6. Example (SAS): sides 4 and 5 with a 30° angle between them give A = ½ × 4 × 5 × sin 30° = 5.

For ASA and AAS the calculator works out the missing angle from the 180° total first. In the AAS case, enter α and γ and it finds β for you.

SSA can be ambiguous. With sides 4 and 5 and a 30° angle opposite the 4, two different triangles fit, with areas 9.315783 and 1.509535; the second appears as “Area (2-nd possible)”. If no triangle fits, you will see “Such a triangle cannot exist!”, and the same message appears for HL when the leg is not shorter than the hypotenuse.

A full triangle tool with more detail is on the triangle area page.

Circle, ellipse and sector

circle: A = π × r²

ellipse: A = π × a × b

sector: A = (α ÷ 360) × π × r²

An ellipse has a major radius a and a minor radius b; when they are equal it is a circle. A sector is the slice of a circle between two radii, and its area is the matching fraction of the whole disc, with α measured in degrees.

Example: a circle with radius 3 cm has area π × 9 = 28.274334 cm². An ellipse with radii 4 ft and 2 ft has area 8π = 25.132741 ft². A 90° sector of radius 5 m covers a quarter of π × 25, which is 19.634954 m². For circles on their own see the circle area calculator and the sector area calculator.

Regular octagon

A regular octagon with side s can be built from a square with its four corners cut off, which gives a compact formula.

A = 2 × (1 + √2) × s² ≈ 4.828427 × s²

Example: for s = 4 cm, A = 4.828427 × 16 = 77.254834 cm². Other regular polygons are covered by the hexagon calculator and the dedicated octagon area calculator.

Square units and conversions

Squaring a length unit squares its conversion factor too, which is why one square foot is not 12 square inches but 144. These exact values come from the international definitions of the inch (2.54 cm), foot, yard and mile.

To convert a finished answer into another unit, use the area unit converter.

Where area calculations are used

• Home projects: flooring, paint, tiles, turf and roofing are all bought by the square meter or square foot. A 4.2 m by 3.6 m room is 15.12 m².
• Land and property: plots are often irregular, so owners split them into rectangles, triangles and trapezoids and add the pieces.
• Design and manufacturing: cutting sheet material, estimating coating and working out how much a shape weighs when thickness and density are known.
• Science and school: pressure is force per unit area, and the geometry chapters of nearly every curriculum start with these formulas.

A common slip is mixing units, for example multiplying meters by centimeters. Here each box converts for you, but when you work by hand, convert every length to the same unit first.