How do I calculate the area of a circle?

Area = π × r², where r is the radius. For a circle with radius 5, area = π × 25 ≈ 78.54 sq units.

What is the difference between area and perimeter?

Area measures the space inside a shape (in square units). Perimeter measures the distance around the outside (in linear units).

Area Calculator - Free Online Calculator

Calculate the area of common shapes: rectangle, triangle, circle, trapezoid, and ellipse.

How to Use This Calculator

Enter the dimensions for your shape and click "Calculate" to get instant results with step-by-step explanations. Enter length and width for rectangles and triangles; for circles, enter the radius as the "Length" field.

Area Formulas by Shape

Rectangle: A = l × w | Triangle: A = ½ × b × h | Circle: A = π × r²

Complete Shape Reference

Rectangle / Square: A = length × width. A square is a special case where length = width.
Triangle: A = ½ × base × height. Height must be perpendicular to the base.
Circle: A = π × r² ≈ 3.14159 × r². Remember: radius = diameter ÷ 2.
Trapezoid: A = ½ × (a + b) × h, where a and b are the parallel sides.
Parallelogram: A = base × height (same as rectangle when height is perpendicular).
Ellipse: A = π × a × b, where a and b are the semi-major and semi-minor axes.

Practical Examples

Room floor (rectangle) 12 ft × 15 ft = 180 sq ft (to find carpet needed)
Circular pool with radius 8 ft: A = π × 64 ≈ 201.1 sq ft
Triangle sail with base 6 m and height 10 m: A = ½ × 6 × 10 = 30 sq m

Area vs. Perimeter

Area measures the two-dimensional space inside a shape, expressed in square units (sq ft, m², cm²). Perimeter measures the total length around the outside of a shape, expressed in linear units. For flooring or painting, you need area. For fencing or framing, you need perimeter. A shape can have a large area with a small perimeter (like a circle, which is the most "efficient" shape) or a small area with a large perimeter (like a very thin rectangle).

Unit Conversions for Area

1 square foot = 144 square inches | 1 square yard = 9 square feet | 1 acre = 43,560 square feet | 1 hectare = 10,000 square meters | 1 square meter ≈ 10.764 square feet. When converting areas, remember that linear conversion factors must be squared: 1 ft = 0.3048 m, so 1 sq ft = 0.3048² = 0.0929 sq m.

Area Calculator