Universal Area Calculator
Calculate the area of common geometric shapes in seconds. Choose a shape, enter its dimensions, and get the result, formula, step-by-step working and converted units—all in one place.
Area formulas for common shapes
Area measures the two-dimensional space inside a boundary. Select the shape that matches your measurements: different shapes require different formulas, and lengths must be measured in consistent units.
A = length × widthMultiply the two perpendicular sides.A = side²Multiply one side by itself.A = ½ × base × heightHeight is perpendicular to the base.A = πr²Use the radius, which is half the diameter.A = πaba and b are the semi-major and semi-minor axes.A = ½(a + b)ha and b are the parallel sides.A = base × perpendicular heightDo not substitute the slanted side for height.A = ½ × d₁ × d₂d₁ and d₂ are the diagonals.A = ½ × perimeter × apothemThe apothem is the perpendicular distance from the centre to a side.Area unit conversions
The calculator converts your result from the selected input length unit. Area conversion factors are squared: for example, one metre equals 100 centimetres, but one square metre equals 10,000 square centimetres.
| Area unit | Equivalent in square metres | Typical use |
|---|---|---|
| 1 mm² | 0.000001 m² | Small components |
| 1 cm² | 0.0001 m² | Small surfaces |
| 1 m² | 1 m² | Rooms and floors |
| 1 km² | 1,000,000 m² | Large land areas |
| 1 ft² | 0.09290304 m² | Floor area in imperial units |
| 1 in² | 0.00064516 m² | Small imperial measurements |
| 1 acre | 4,046.8564224 m² | Land and plots |
| 1 hectare | 10,000 m² | Agricultural land |
How to use the universal area calculator
- Choose the shape. Select a rectangle, circle, triangle, ellipse, polygon or another supported figure.
- Choose your length unit. Use metres, centimetres, millimetres, kilometres, inches, feet, yards or miles.
- Enter the dimensions. Only the fields needed for the selected shape will be shown. For a circle, enter the radius; for a triangle, make sure the height is perpendicular to its base.
- Choose the output unit. View the result in the square unit that makes sense for your project, or use the default square of your input unit.
- Read the formula and working. The result panel shows the equation used and the values substituted into it.
Calculations are performed locally in your browser. The dimensions you enter are not submitted to this PHP page or stored by this calculator.
Frequently asked questions
What is area?
Area is the amount of two-dimensional space enclosed by a shape. It is expressed in square units, such as cm², m² or ft².
What is the difference between area and perimeter?
Area measures the inside of a shape in square units. Perimeter measures the length around its boundary in linear units. They describe different properties and cannot be directly compared.
Can I calculate the area of a circle using its diameter?
Yes. Divide the diameter by two to get the radius, then use A = πr². This calculator asks for the radius to make that distinction explicit.
How do I calculate an irregular polygon?
Enter its vertices in order around the outline, one x,y coordinate pair per line. The calculator applies the shoelace formula. The polygon should not cross itself, and all coordinates must use the same length unit.
Why does the area unit change by a squared factor?
Area uses two dimensions. If every length is multiplied by 100 when converting metres to centimetres, the area is multiplied by 100 × 100 = 10,000.
Is the result suitable for construction or surveying?
This tool is intended for general calculations and estimates based on the dimensions you enter. For legal land boundaries, structural work or regulated surveying, verify measurements and calculations with the relevant professional.
Explore more geometry calculators
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