What the Area Calculator does
This area calculator finds the area of fifteen common shapes - square, rectangle, three kinds of triangle, circle from its radius, diameter or circumference, ellipse, trapezoid, parallelogram, rhombus or kite, sector, regular polygon and ring - from measurements in millimetres, centimetres, metres, kilometres, inches, feet, yards or miles. It shows the formula, the numbers substituted into it, the perimeter where there is one, and the same area converted into square metres, square feet, acres, hectares and other units.
It is meant for homework, for checking a textbook answer, and for practical jobs such as working out a floor, a garden bed or a table top. A small diagram shows which measurement goes in which box. Everything is calculated in your browser.
How to use it
- Choose the shape. For a triangle, pick the version that matches what you know: base and height, all three sides, or two sides and the angle between them. For a circle, pick radius, diameter or circumference.
- Choose the unit your measurements are in. All lengths must be in the same unit; convert first if one side is in feet and another in inches.
- Type the measurements into the boxes labelled on the diagram.
- Read the area in square units at the top, with the formula and the substituted working underneath.
- Use the conversion table for the area in other units - square metres to square feet, for instance - and copy the answer if you need it.
Reading the results
Area is always in square units: a rectangle measured in metres has an area in square metres (m²), one measured in feet in square feet (ft²). Converting area is not the same as converting length - 1 metre is about 3.28 feet, but 1 square metre is about 10.76 square feet, because both sides are converted.
The height of a triangle, trapezoid or parallelogram is the perpendicular distance between the base and the opposite side or corner, not the length of a slanted side. Using a sloping side instead of the height overstates the area.
Circle results involve π, an irrational number, so they are rounded for display. The working shows where π enters, which is usually what a teacher wants to see.
Worked example: a room, a circle and a triangle
A room 12 ft by 10 ft is a rectangle: 12 x 10 = 120 ft². One foot is exactly 0.3048 m, so one square foot is 0.3048 x 0.3048 = 0.09290304 m², and the room is 120 x 0.09290304 = 11.15 m².
A circle with a radius of 7 cm has area π x 7² = 49π = 153.94 cm², and circumference 2 x π x 7 = 43.98 cm.
A triangle with sides 13, 14 and 15 m uses Heron's formula. Half the perimeter is s = (13 + 14 + 15) / 2 = 21. The area is √(21 x 8 x 7 x 6) = √7,056 = 84 m².
Formulas and scoring rules
- Square and rectangle
A = a²; A = length x width- Triangle
A = ½ x base x height; A = √(s(s - a)(s - b)(s - c)) with s = (a + b + c) / 2 (Heron); A = ½ a b sin C- Circle
A = π r² = π d² / 4 = c² / (4π); circumference = 2 π r- Ellipse
A = π a b, with a and b the semi-axesPerimeter uses Ramanujan's second approximation, accurate to a few parts per million for ordinary ellipses.- Trapezoid, parallelogram, rhombus
A = (a + b) / 2 x h; A = base x height; A = d1 x d2 / 2- Sector, regular polygon, ring
A = (θ / 360) π r²; A = n s² / (4 tan(π / n)); A = π (R² - r²)- Unit conversions
1 ft² = 0.09290304 m²; 1 in² = 6.4516 cm²; 1 yd² = 0.83612736 m²; 1 acre = 4,046.8564224 m² = 43,560 ft²; 1 ha = 10,000 m²Exact definitions from NIST SP 811. Results are shown to about ten significant figures, then trimmed.
Measuring awkward real-world shapes
Most rooms and plots are not one neat shape. Split an L-shaped room into two rectangles, work out each, and add them; for a shape with a bite out of it, work out the whole and subtract the missing part. A semicircular bay window is half a circle - a sector with an angle of 180 degrees.
For flooring, paint or turf, add a margin for cutting and waste after you have the area. For land with four unequal sides or a list of corner coordinates, the Acreage Calculator handles irregular plots and gives acres and hectares directly.
Limitations: what the result does not prove
- Shapes are ideal flat figures. Real surfaces that slope or curve, such as a pitched roof or a dome, have more surface area than their footprint.
- A triangle from three sides needs the sides to be possible: any two must add up to more than the third. The calculator refuses impossible sets rather than returning nonsense.
- Results are only as precise as the measurements. A tape reading rounded to the nearest centimetre on a 4 m wall gives an area accurate to a fraction of a percent, not to the last decimal shown.
- It does not work out volume. For concrete, soil or water, multiply the area by the depth in the same unit.
Privacy: where your data goes
Everything you paste, type or drop is processed in this browser tab. It is not uploaded, logged, stored or sent to analytics. Session recording and tag-manager scripts are switched off on this page.
Standards and sources
- NIST SP 811 - Guide for the Use of the International System of Units - checked 19 Sep 2026
- NIST Handbook 44 Appendix C - General tables of units of measurement
- Wolfram MathWorld - Heron's formula
- Wolfram MathWorld - Ellipse (area and perimeter approximations)
Frequently asked questions
How do you calculate the area of a circle?
Square the radius and multiply by π: A = π r². A circle with a 7 cm radius has an area of 49 x 3.14159 = 153.94 cm². If you know the diameter, halve it first, or choose Circle - diameter and the calculator does it for you.
How do I find the area of a triangle without the height?
If you know all three sides, use Heron's formula: work out half the perimeter s, then A = √(s(s - a)(s - b)(s - c)). If you know two sides and the angle between them, use A = ½ a b sin C. Both are options in the shape list.
What is the formula for the area of a trapezoid?
Add the two parallel sides, halve the total, and multiply by the height between them: A = (a + b) / 2 x h. A trapezoid with parallel sides of 6 and 10 and a height of 4 has an area of 8 x 4 = 32 square units.
How many square feet are in a square metre?
10.7639 - because a metre is 3.28084 feet and both sides are converted, 3.28084² = 10.7639. Going the other way, one square foot is exactly 0.09290304 m², so 120 ft² is 11.15 m². The calculator lists the area in both, plus acres, hectares and other units.
How do I work out the area of an L-shaped room?
Split it into two rectangles along one wall, calculate the area of each with length x width, and add them together. Measure both parts in the same unit so the two areas can be added directly.
What is the area of a regular hexagon?
For side length s, the area is (3√3 / 2) x s², about 2.598 x s². A hexagon with 2 cm sides has an area of 10.39 cm². Choose Regular polygon with 6 sides for any side length.
Why is the area of a shape in square units?
Area counts how many unit squares fit inside the shape. A 3 m by 2 m rectangle holds six squares each 1 m by 1 m, so its area is 6 square metres, written 6 m².
Last reviewed by the A2Z.Tools team against the sources listed above.
