Area Calculator
The universal geometric solver for calculating two-dimensional surface areas of standard polygons, circles, ellipses, and irregular shapes with interactive diagrams and formulas.
Calculate Area
How to Calculate Geometric Area
Area measures the continuous 2D surface space enclosed by a shape's perimeter, expressed in square units. Select your shape to apply the corresponding geometric formula.
Area Formulas for Common 2D Geometric Shapes
Every two-dimensional geometric figure relies on dedicated dimensional formulas derived from Euclidean geometry:
Multiply length by width. For a square with side s: Area = s².
Multiply half the base by the perpendicular altitude.
Multiply Pi by the square of the radius (r = d ÷ 2).
Average the parallel bases (a and b), then multiply by height.
Multiply Pi by semi-major axis (a) and semi-minor axis (b).
Multiply base length by perpendicular height (h).
Heron's Formula for Triangles with 3 Known Sides
When the perpendicular height of a triangle is unknown but all three side lengths (a, b, c) are measured, Heron's Formula provides the exact area without requiring trigonometry:
Example: For side lengths a = 5, b = 6, c = 7 → s = (5 + 6 + 7)/2 = 9 → Area = √(9 · 4 · 3 · 2) = √216 ≈ 14.70.
Total Surface Area of 3D Geometric Solids
Surface area computes the cumulative outer area covering the exterior faces of a 3D solid:
| 3D Shape | Surface Area Formula | Key Parameters |
|---|---|---|
| Cube | A = 6s² | s = side edge length |
| Rectangular Prism | A = 2(lw + lh + wh) | l = length, w = width, h = height |
| Cylinder | A = 2πrh + 2πr² | r = radius, h = height |
| Cone | A = πr(r + √(h² + r²)) | r = radius, h = cone height |
| Sphere | A = 4πr² | r = radius |
Sibling Calculators in the Geometry Ecosystem
Navigate directly to specialized geometric calculators across our knowledge graph:
Area vs. Perimeter: The Fundamental Difference
Measures the amount of interior flat surface enclosed inside the boundary. Expressed in square units (m², ft², in²). Critical for flooring, paint, roofing, and turf estimation.
Measures the total linear distance around the outer edge of the shape. Expressed in linear units (m, ft, in). Critical for fencing, baseboards, framing, and perimeter lighting.
Key Square Unit Conversion Standards
Common Calculation Pitfalls to Avoid
In triangles and parallelograms, area requires the perpendicular height (at 90° to the base), NOT the slanted side edge length.
Circles and cylinders use radius (r = d / 2). Squaring the diameter instead of the radius yields an answer 4 times too large.