Area Calculator

Calculate the area of various shapes with our simple and free area calculator. Supports rectangles, squares, circles, triangles, and more.

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What is Area?

Area is a measure of the amount of space inside a two-dimensional shape. It is calculated in square units, such as square meters (m²) or square feet (ft²). Area is a fundamental concept in geometry, mathematics, science, and everyday life.

Area Formulas for Common Shapes

Rectangle

Area = Length × Width

The area of a rectangle is calculated by multiplying its length by its width. Both dimensions must be in the same unit of measurement.

Square

Area = Side² (Side × Side)

The area of a square is calculated by multiplying the length of one side by itself, or squaring the side length.

Circle

Area = π × Radius²

The area of a circle is calculated using the formula π (approximately 3.14159) multiplied by the square of the radius. The radius is the distance from the center of the circle to its edge.

Triangle

Area = ½ × Base × Height

The area of a triangle is calculated by multiplying the base length by the height, and then dividing by 2. The height must be measured perpendicular to the base.

Ellipse

Area = π × a × b

The area of an ellipse is calculated by multiplying π by the product of the semi-major axis (a) and semi-minor axis (b).

Trapezoid

Area = ½ × (a + b) × h

The area of a trapezoid is calculated by taking the average of the parallel sides (bases) and multiplying by the height.

Sector

Area = (θ/360) × π × r²

The area of a sector is calculated as a fraction of a circle. θ represents the angle in degrees, and r is the radius.

Applications of Area Calculation

Area calculations are important in many fields and everyday situations:

  • Construction and architecture – calculating flooring, roofing, wall space, and land areas
  • Agriculture – determining crop yields, irrigation requirements, and land management
  • Manufacturing – measuring material requirements for production
  • Real estate – property valuation and space planning

Area Unit Conversion

When working with areas, it's often necessary to convert between different units. Here are some common conversions:

  • 1 square meter (m²) = 10.764 square feet (ft²)
  • 1 square kilometer (km²) = 0.386 square miles (mi²)
  • 1 acre = 4,047 square meters (m²) = 43,560 square feet (ft²)