Circle Calculator

Calculate area, circumference, and diameter of any circle from the radius or diameter.

What is a Circle?

A circle is a perfectly round, two-dimensional geometric shape defined as the set of all points in a plane that are equidistant from a fixed central point. That fixed distance from the center to any point on the circle is called the radius. The circle is one of the most fundamental and frequently encountered shapes in mathematics, engineering, physics, and everyday life - from wheels and coins to planets and orbits.

The key measurements of a circle are its radius (r), diameter (d), circumference (C), and area (A). The diameter is simply twice the radius and passes through the center, making it the longest straight line that can be drawn inside the circle. The circumference is the total distance around the circle - its perimeter. The area is the total space enclosed within the circle’s boundary.

All of these measurements are connected through the mathematical constant pi (π), which is the ratio of any circle’s circumference to its diameter. Pi is an irrational number that begins 3.14159265… and continues infinitely without repeating. No matter how large or small the circle, the circumference is always exactly π times the diameter. This remarkable consistency makes π one of the most important constants in all of mathematics.

Circles appear everywhere in engineering and design. Gears, wheels, pipes, tunnels, domes, and satellite dishes are all circular because the circle maximises the area enclosed for a given perimeter - a property known as the isoperimetric inequality. This property is why soap bubbles and planets tend toward spherical (three-dimensional circular) shapes.

Formula

Area of a Circle:

A = π × r²

A = Area (square units)

π = Pi ≈ 3.14159265

r = Radius (the distance from center to edge)

Circumference of a Circle:

C = 2 × π × r = π × d

C = Circumference (units)

d = Diameter = 2r

Diameter from Radius:

d = 2r

How to Use This Calculator

Choose your input mode - select “Enter Radius” if you know the radius, or “Enter Diameter” if you know the diameter. The calculator converts automatically.
Enter your measurement in the input field. You can use any unit (cm, m, inches, feet) - the results will be in the same unit (and square units for area).
Click Calculate to instantly see the area, circumference, and the derived third measurement (diameter or radius).
Read the results - each result card shows the formula used so you can verify the calculation manually if needed.
Switch modes at any time to check your answer from a different starting point.

Example Calculations

Example 1 - Circle with Radius 5 cm

A pizza has a radius of 5 cm. Find its area and circumference.

r = 5 cm, so diameter = 2 × 5 = 10 cm

Area = π × r² = 3.14159 × 25 = 78.54 cm²

Circumference = 2 × π × 5 = 31.42 cm

Area = 78.5398 cm² | Circumference = 31.4159 cm | Diameter = 10 cm

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Example 2 - Circle with Diameter 20 m

A circular fountain has a diameter of 20 m. What area of ground does it cover?

d = 20 m, so radius = 20 / 2 = 10 m

Area = π × 10² = π × 100 = 314.16 m²

Circumference = π × d = π × 20 = 62.83 m

Area = 314.1593 m² | Circumference = 62.8318 m | Radius = 10 m

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Frequently Asked Questions

What is the formula for the area of a circle?+

The area of a circle is A = π × r², where r is the radius. For example, a circle with radius 5 cm has area = π × 25 = 78.54 cm². If you know the diameter instead, the radius is half the diameter, so r = d / 2.

How do I calculate the circumference of a circle?+

The circumference (perimeter) of a circle is C = 2 × π × r, or equivalently C = π × d, where d is the diameter. For a circle with radius 7 cm, circumference = 2 × π × 7 = 43.98 cm.

What is the relationship between radius and diameter?+

The diameter is always exactly twice the radius: d = 2r. The radius is the distance from the center of the circle to any point on its edge, while the diameter is the distance across the circle through its center.

How do I find the radius if I only know the circumference?+

Rearrange the circumference formula: r = C / (2π). For example, if the circumference is 31.42 cm, then r = 31.42 / (2 × 3.14159) = 5 cm.

What is the area of a unit circle?+

A unit circle has radius = 1, so its area is π × 1² = π ≈ 3.14159 square units. Its circumference is 2π ≈ 6.28318 units. The unit circle is fundamental in trigonometry as a reference for defining sine and cosine.

How do you calculate the area of a circle?+

Area of a circle = pi x r^2, where r is the radius and pi is approximately 3.14159. Example: a circle with radius 7 cm has area = 3.14159 x 7^2 = 3.14159 x 49 = 153.94 cm^2. If you know the diameter instead, divide it by 2 to get the radius first. Area can also be written as pi x d^2 / 4 where d is the diameter.

What is the difference between circumference and perimeter?+

Circumference is the specific term for the perimeter of a circle - the total length around its boundary. Circumference = 2 x pi x r = pi x d. All shapes have a perimeter (total boundary length), but only circles have a circumference. Example: a circle with radius 5 cm has circumference = 2 x 3.14159 x 5 = 31.42 cm.

What is pi (pi) and why is it used for circles?+

Pi (pi) is the ratio of a circle's circumference to its diameter, equal to approximately 3.14159265. This ratio is the same for every circle regardless of size - it is a mathematical constant. Pi is irrational (it cannot be expressed as a simple fraction) and its decimal expansion never repeats. Pi appears in circle area, volume of cylinders and spheres, wave equations, probability theory, and many other areas of mathematics.