# Circle Calculator

## Circle Shape

r = radius

d = diameter

C = circumference

A = area

π = pi = 3.1415926535898

√ = square root

## Calculator Use

Use this circle calculator to find the area, circumference, radius or diameter of a circle. Given any one variable A, C, r or d of a circle you can calculate the other three unknowns.

**Units:** Note that units of length are shown for convenience. They do not affect the calculations. The units are in place to give an indication of the order of the results such as ft, ft^{2} or ft^{3}. Any other base unit can be substituted.

## Circle Formulas in terms of Pi π, radius r, and diameter d

## Radius and Diameter:

r = d/2

d = 2r## Area of a circle:

A = πr

^{2}= πd^{2}/4## Circumference of a circle:

C = 2πr = πd

## Circle Calculations:

Using the formulas above and additional formulas you can calculate properties of a given circle for any given variable.

**Calculate A, C and d | Given r**

Given the radius of a circle calculate the area, circumference and diameter. Putting A, C and d in terms of r the equations are:

\[A = \pi r^2 \]

\[C = 2 \pi r \]

\[d = 2r \]

**Calculate r, C and d | Given A**

Given the area of a circle calculate the radius, circumference and diameter. Putting r, C and d in terms of A the equations are:

\[r = \sqrt{\frac{A}{\pi}} \]

\[C = 2 \pi r = 2 \pi \sqrt{\frac{A}{\pi}} \]

\[ d = 2r = 2 \sqrt{\frac{A}{\pi}} \]

**Calculate A, r and d | Given C**

Given the circumference of a circle calculate the radius, area and diameter. Putting A, r and d in terms of C the equations are:

\[r = \frac{C}{2 \pi} \]

\[A = \pi r^2 = \pi \left(\frac{C}{2 \pi}\right)^2 = \frac{\pi C^2}{4 \pi^2} = \frac{C^2}{4 \pi} \]

\[d = 2r = \frac{2C}{2 \pi} = \frac{C}{\pi} \]

**Calculate A, C and r | Given d**

Given the diameter of a circle calculate the radius, area and circumference. Putting A, C and r in terms of d the equations are:

\[r = \frac{d}{2} \]

\[A = \pi r^2 = \pi \left(\frac{d}{2}\right)^2 = \frac{\pi d^2}{4} \]

\[C = 2 \pi r = 2 \pi \frac{d}{2} = \pi d \]