Area of a Circle Calculator

Use the this circle area calculator below to find the area of a circle given its radius, or other parameters. To calculate the area, you just need to enter a positive numeric value in one of the 3 fields of the calculator. You can also see at the bottom of the calculator, the step-by-step solution.

Area of a Circle Calculator

Formulas:

Inputs:

Radius:		or
Diameter:		or
Circumference:
Unit:

Result:

The area of a circle with radius 5 is 78.54

Solution Steps:

Area of a cicle in terms of radius:

Area = π . r² = 3.14 × 5² = 78.54 square meters.

In terms of diameter:

Area = π . (d/2)² = 3.14 × (10/2)² = 3.14 × (5)² = 78.54 square meters.

In terms of circumference:

Area = ^C²/_(4π) = ^31.42²/_4π = ^987.22/_{(4 × 3.14)} = 987.22/(12.56) = 78.54 square meters.

Note: for simplicity, some results may be rounded to nearest hundredth and π was rounded to 3.14. See formula details below in this page.

A circle of radius = 5 or diameter = 10 or circunference = 31.42 meters has an area of 78.54 square meters which is equal to:

7.854E-5 square kilometers (km²)

785400 square centimeters (cm²)

0.01941 acres (ac)

0.007854 hectares (ha)

3.032E-5 square miles (mi²)

93.93 square yards (yd²)

845.4 square feet (ft²)

121700 square inches (in²)

Formula for area of a circle

Here a three ways to find the area of a circle (formulas):

Circle area formula in terms of radius

Circle area formula in terms of diameter

Circle area formula in terms of circumference

See below some definitions related to the formulas:

Circumference

Circumference is the linear distance around the circle edge.

Radius

The radius of a circle is any of the line segments from its center to its perimeter. The radius is half the diameter or r = ^d/₂.

Diameter

The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. The diameter is twice the radius or d = 2r.

The Greek letter π

π represents the number Pi which is defined as the ratio of the circumference of a circle to its diameter or π = ^C / _d. For simplicity, you can use Pi = 3.14 or Pi = 3.1415. Pi is an irrational number. The first 100 digits of Pi are: 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 ...

Note:

If you input the radius in centimeters, you will get the answer in square centimeters (cm²), if in inches, will get the answer in square inches (in²) and so on ...

Circumference is often misspeled as circunference.

You can use our area unit converter to see the results in other units.

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Area of a Circle Calculator