Free area calculator
Calculate the area of rectangles, triangles, circles, ellipses, and trapezoids — enter any dimensions to see the result, updated live, as you type.
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Results are in square units matching your input units. Standard geometry formulas.
Results are estimates. Consult a professional.
How the area calculator works
Area measures the amount of two-dimensional space enclosed by a shape, expressed in square units (cm², m², ft², etc.). Each shape has its own formula derived from its geometry — the calculator applies the correct one based on the shape you select.
Worked example: rectangle, circle, and triangle
Three common shapes solved using the core area formulas. All results are in square metres (m²).
Area formulas for common shapes
The table below lists six common 2D shapes with their area formulas, required inputs, and a brief description of each variable.
| Shape | Formula | Variables |
|---|---|---|
| Rectangle | A = l × w | l = length, w = width |
| Square | A = s² | s = side length |
| Circle | A = π r² | r = radius |
| Triangle | A = ½ b h | b = base, h = perpendicular height |
| Trapezoid | A = ½ (b₁ + b₂) h | b₁, b₂ = parallel sides, h = height |
| Ellipse | A = π a b | a = semi-major axis, b = semi-minor axis |
Source: standard Euclidean geometry formulas
Tips for calculating area accurately
A few habits prevent the most common area-calculation errors, whether you are tiling a floor, planning a garden, or solving a geometry problem.
- Use consistent units — if length is in metres and width is in centimetres, convert both to the same unit before multiplying or your answer will be wrong by a factor of 100.
- Height must be perpendicular — for triangles, trapezoids, and parallelograms, height (h) is the vertical distance between the two parallel sides, not the slant side length.
- Radius vs diameter — the circle formula uses radius (half the diameter); entering the diameter without halving it first produces a result four times too large.
- Break irregular shapes apart — for L-shapes, U-shapes, or any irregular polygon, split the figure into rectangles or triangles, calculate each sub-area, then add or subtract as needed.
- Double-check by estimation — a rough bounding rectangle (largest l × w that would contain the shape) should always be larger than the actual area; if your calculated area exceeds the bounding rectangle, recheck your inputs.
Accuracy and limitations
This calculator uses IEEE 754 double-precision arithmetic and the full value of π (not an approximation), giving results accurate to approximately 15 significant digits. For practical construction or landscaping purposes, rounding to two decimal places is sufficient. The formulas assume perfect geometric shapes; real-world surfaces may have curves, irregularities, or waste that require adding a 5–10 % buffer to material estimates. Very large inputs (side lengths above 10⁷ in the chosen unit) may accumulate minor floating-point rounding errors.
Key terms
About this calculator
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