Area Calculator
Pick a shape and enter its measurements to get the area of a square, rectangle, triangle, circle, trapezoid, parallelogram, ellipse or regular polygon, with the formula worked out and the result in square metres and other units.
- FormulaA = a × b
- Substitution8 × 5 = 40
- In dunams (dönüm)0.04 dunam
- In hectares0.004 ha
In other area units
How it is calculated
Area is the size of the surface a flat shape covers, measured in squared units of length: a square with 1 m sides is 1 m². The formulas: square a², rectangle a × b, triangle base × height ÷ 2, a triangle from its three sides by Heron’s formula √(s(s − a)(s − b)(s − c)) (s is half the perimeter), circle π × r², circular sector π × r² × α ÷ 360, ellipse π × a × b (a and b are the semi-axes), trapezoid (bottom + top base) ÷ 2 × height, parallelogram base × height, rhombus and kite the product of the diagonals ÷ 2, regular polygon n × a² ÷ (4 × tan(180° ÷ n)).
A = a × b · A = a × h ÷ 2 · A = π × r² · A = (a + c) ÷ 2 × ha, b, c: sides or bases · h: height at right angles to the base · r: radius · π ≈ 3.14159. In order: rectangle, triangle, circle, trapezoid.- Pick the shape; the calculator asks only for the measurements it needs.
- Enter every measurement in the same unit (all cm or all m) and choose that unit.
- The area comes out in that unit squared (cm²), with the formula and the substitution shown.
- The table lists the area in other units (m², dunams, hectares, ft² …).
Example
A 4.2 m × 3.5 m room: 4.2 × 3.5 = 14.7 m². A circle of radius 7 cm: π × 7² ≈ 153.94 cm². A triangle with sides 13, 14 and 15 cm: s = (13 + 14 + 15) ÷ 2 = 21, area √(21 × 8 × 7 × 6) = 84 cm².
Frequently asked questions
How do I find a circle’s area from its diameter?
The radius is half the diameter: r = d ÷ 2. A circle 10 cm across has r = 5 cm and an area of π × 5² ≈ 78.54 cm². In one step: A = π × d² ÷ 4.
How do I find a triangle’s area without its height?
If you know all three sides, use “Triangle (three sides, Heron)”. Take half the perimeter s, then the area is √(s(s − a)(s − b)(s − c)). For sides 3, 4 and 5 cm, s = 6 and the area is √(6 × 3 × 2 × 1) = 6 cm². If one side is longer than the other two together, there is no triangle.
How many dunams is a square metre?
A dunam (dönüm) is taken as 1,000 m², the last statutory definition, in art. 5 of the since-repealed Law No. 4753 (Official Gazette 15.06.1945, No. 6032). Divide square metres by that number. This calculator also shows the area in dunams and hectares; for other land units, use the square metre, dunam and hectare converter.
How do I find the area of an irregular plot or room?
Split it into rectangles, triangles or trapezoids, find each part’s area and add them up. An L-shaped room split into 5 m × 4 m and 3 m × 2 m has 20 + 6 = 26 m².
How many cm² are in 1 m²?
10,000 cm². A metre is 100 cm, and area multiplies two lengths, so 100 × 100 = 10,000. For the same reason 1 cm² = 100 mm² and 1 km² = 1,000,000 m².
Is the height of a trapezoid or parallelogram its slanted side?
No. The height is the perpendicular distance between the bases. A slanted side is longer than the height, so using it instead overstates the area.
Source
- Wolfram MathWorld: Area
- Wolfram MathWorld: Heron’s formula
- Wolfram MathWorld: Regular polygon
- NIST SP 811, Appendix B.9: Conversion factors (ft², in²)
- NIST: Revised unit conversion factors after the US survey foot (acre = 43,560 ft² = 4,046.856 422 4 m²)
- Law No. 4753 on Providing Land to Farmers, art. 5 (Official Gazette 15.06.1945, No. 6032): the dönüm is 1,000 m²
- Law No. 3083, provisional art. 3 (Law No. 4753 repealed)
- TDV Encyclopaedia of Islam: “Dönüm” (traditional measures: evlek, old dönüm; Turkish)
- BIPM, The SI Brochure (9th ed.), Table 8: are and hectare