Area is the measure of the amount of two-dimensional space taken up by a shape. It is typically measured in square units, such as square meters (m²), square feet (ft²), or square centimeters (cm²).

How do you calculate the area of a circle?

The area of a circle is calculated using the formula A = πr², where 'r' is the radius of the circle and π (pi) is approximately 3.14159.

What is the difference between area and perimeter?

Area measures the space inside a shape, while perimeter measures the distance around the outside edge of a shape. For example, the area of a square is side × side, while its perimeter is 4 × side.

Area Calculator (Rectangle, Circle, Triangle, etc.)

How Does This Calculator Work?

This calculator uses standard geometric formulas to find the area of the shape you select. Area is the measure of the two-dimensional space inside a shape's boundary.

Rectangle: Area = Length × Width
Circle: Area = π × radius² (where π is approx. 3.14159)
Triangle: Area = ½ × Base × Height
Square: Area = Side × Side
Trapezoid: Area = ½ × (Base 1 + Base 2) × Height

You simply select your shape, enter the required dimensions, and the calculator applies the correct formula to give you the result.

The Surprising History of Area Measurement

The need to measure area is one of the oldest practical problems in mathematics. It arose in ancient civilizations like Egypt and Babylon for very practical reasons: farming and taxation. After the annual flooding of the Nile River, property boundaries would be washed away.

Surveyors, known as "rope-stretchers," would use ropes with knots at regular intervals to re-measure and partition the land. They developed surprisingly sophisticated methods for calculating the area of rectangles and triangles. The Greeks, particularly Euclid and Archimedes, later formalized these concepts, moving from practical measurement to rigorous, proof-based geometry. Archimedes famously developed the "method of exhaustion" to find the area of a circle, a technique that was a precursor to modern calculus.

Explore More Related Tools

While you're here, check out some of our other popular math and science calculators:

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Standard Deviation Calculator: A key tool for statistics.
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Frequently Asked Questions (FAQ)

What units should I use?

You can use any unit of measurement (e.g., cm, meters, feet, inches), as long as you are consistent for all dimensions of a shape. The resulting area will be in the square of that unit (e.g., cm², m², ft², in²).

What is the difference between radius and diameter?

The radius of a circle is the distance from the center to any point on its edge. The diameter is the distance across the circle passing through the center. The diameter is always twice the length of the radius (Diameter = 2 × Radius).

How do you find the area of an irregular shape?

This calculator is for standard geometric shapes. To find the area of an irregular shape, a common method is to break it down into smaller, standard shapes (like rectangles and triangles), calculate the area of each part, and then add them together.

Area Calculator

Area: