Area Calculator
Calculate the area of common 2D shapes with this free online area calculator. It supports rectangles, squares, circles, triangles, ellipses, trapezoids, and sectors, and also includes formulas, examples, and area unit references.
Enter Dimensions
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.
How to Use This Area Calculator
The calculator is designed to help you move quickly from shape selection to a final area result without having to memorize each formula.
- Choose the shape you want to calculate, such as a rectangle, circle, triangle, ellipse, trapezoid, or sector.
- Enter the required dimensions for that shape using the same unit for every input, such as meters, centimeters, feet, or inches.
- Select the square unit you want the result displayed in, then click the calculate button.
- Review the result and compare it with the formula section below if you want to understand how the number was produced.
For accurate results, make sure your dimensions use the same base unit before calculating. Mixing centimeters with meters or feet with inches can produce the wrong area value.
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.
Example Area Calculations
Rectangle Example
A rectangle with a length of 8 meters and a width of 5 meters is a common example used in room planning.
Area = 8 × 5
Result: 40 m²
Circle Example
If a circle has a radius of 3 meters, use π multiplied by the radius squared.
Area = π × 3²
Result: about 28.27 m²
Triangle Example
For a triangle with a base of 10 meters and a height of 4 meters, use half of base times height.
Area = 1/2 × 10 × 4
Result: 20 m²
Sector Example
If a sector has a radius of 6 meters and a central angle of 60 degrees, it represents one-sixth of the full circle.
Area = (60/360) × π × 6²
Result: about 18.85 m²
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)
Area Calculator FAQ
What shapes can this area calculator handle?
This page supports rectangles, squares, circles, triangles, ellipses, trapezoids, and sectors. Each shape uses the standard geometry formula for area.
Do all dimensions need to use the same unit?
Yes. You should enter all dimensions in the same base unit before calculating. For example, if one value is in meters and another is in centimeters, convert them first.
What is the difference between area and perimeter?
Area measures the amount of surface inside a 2D shape, while perimeter measures the total distance around the outside edge of the shape.
Can I use this calculator for square feet and square meters?
Yes. The calculator lets you display the result in several common area units, including square feet and square meters.