Circle Formula Calculator

Created by Luis Hoyos
Reviewed by Wojciech Sas, PhD candidate
Last updated: Mar 15, 2022

The circle formula calculator allows you to make circle calculations easily. Keep reading to learn things like:

  • What is the formula to calculate the diameter of a circle given its radius, or vice versa.
  • What is the formula for calculating the circumference of a circle.
  • What is the formula for the area of a circle.

Circle formulas

Although using the circle formula calculator is the fastest way to make circle calculations, it's crucial to know the formulas to understand the process better.

Formula to calculate the diameter of a circle given its radius, or vice versa

The formula of the diameter of a circle is the most straightforward of the equations and says that diameter (d) equals twice the radius (r):

d = 2r
r = d/2

The calculation of circumference and area of a circle formulas are more tricky. Look at the equations in the following sections.

Formula to calculate the circumference of a circle

The formula of the circle circumference (c) can be expressed in terms of radius, diameter, and area (A), as shown below:

c = 2πr
c = πd
c = 2√(πA)

Formula to calculate the area of a circle

We can express the formula to calculate the area of a circle in terms of the radius, diameter, and circumference:

A = πr²
A = πd²/4
A = c²/(4π)

How to use the area and circumference of a circle formula? An example

Suppose you have a circle of radius 3 cm. If you want to calculate its area and circumference, you can do it following these steps:

  1. Input the radius in the circle area formula:
    A = π × (3 cm)² = 28.2743 cm².
  2. Also, input the radius in the circumference formula:
    c = 2π × (3 cm) = 18.8496 cm.
  3. Check your results with the circle formula calculator. The results should also be 28.2743 cm² and 18.8496 cm for area and circumference.


What is the formula for the perimeter of a half-circle?

π (pi) times radius phalf = πr. The formula for the perimeter of a half-circle is the same formula for the circle circumference, divided by two. That results in the product of π (pi) and the radius.

What is the radius of a 3.65-inch diameter circle?

1.825 in. The formula for the diameter of a circle says diameter is twice the radius. To find the radius, simply divide the diameter by two: r = 3.65 in / 2 = 1.825 in.

Luis Hoyos
Image of a circle with radius, diameter, circumference and area marked.
Radius (r)
Diameter (d)
Circumference (c)
Area (A)
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