Area of Shapes Calculator
Calculate the area of any 2D shape — circle, rectangle, triangle, trapezoid, parallelogram, ellipse, and more.
Supports metric and imperial units.
Area Formulas for Common 2D Shapes
Area is the amount of two-dimensional space enclosed within a flat shape. All area results are in square units (e.g., cm², m², in², ft²).
Rectangle
A = length × width
The most fundamental area formula. A square is a special rectangle where length = width.
Square
A = side²
Circle
A = π × r²
The area of a circle grows with the square of the radius — doubling the radius quadruples the area. The connection between π and the circle area was known to the ancient Egyptians and Babylonians, though Archimedes provided the first rigorous mathematical proof around 250 BC.
Triangle
A = (1/2) × base × height
The height must be perpendicular to the base. For any triangle (including obtuse), you can always drop a perpendicular from the opposite vertex.
Trapezoid (Trapezium)
A = (1/2) × (a + b) × height
Where a and b are the lengths of the two parallel sides. Think of it as averaging the two parallel sides, then multiplying by height.
Parallelogram
A = base × height
The height is the perpendicular distance between the parallel sides — not the slant side length.
Ellipse
A = π × a × b
Where a and b are the semi-major and semi-minor axes. A circle is a special case of an ellipse where a = b = r.
Regular Hexagon
A = (3√3 / 2) × side²
A regular hexagon can be divided into 6 equilateral triangles, each with area (√3/4) × s².
Regular Pentagon
A = (√(25 + 10√5) / 4) × side²
Approximately A ≈ 1.720 × s².
Rhombus
A = (d₁ × d₂) / 2
Where d₁ and d₂ are the lengths of the two diagonals.
Mnemonic Tips
- Rectangle: “Length times width”, think of counting tiles
- Triangle: “Half of a rectangle”, a triangle is exactly half a rectangle with the same base and height
- Circle: “Apple pie are squared”, a popular mnemonic for A = πr²
- Trapezoid: “Average the parallel sides, multiply by height”
Unit Conversion Reference
| Unit | Square Conversion |
|---|---|
| 1 ft² | 144 in² |
| 1 m² | 10,000 cm² |
| 1 acre | 43,560 ft² |
| 1 hectare | 10,000 m² |
Real-World Applications
- Flooring: Calculate square footage needed for hardwood or tile
- Paint: One gallon covers approximately 350 ft², how many gallons to paint a room?
- Landscaping: Sod, mulch, and seed are sold by area
- Real estate: Land plots and building footprints measured in square meters or acres
- Fabric: Pattern cutting in dressmaking requires accurate area calculations
- Solar panels: Panel output and installation cost scale directly with roof area
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
SuperGlobalCalculator is independently built and maintained. See how we build and verify our calculators.