Calculator Soup^{®}

r = radius

V = volume

A = surface area

C = circumference

π = pi = 3.14159

√ = square root

This online calculator will calculate the 3 unknown values of a sphere given any 1 known variable including radius r, surface area A, volume V and circumference C. A sphere is a set of points in three dimensional space that are located at an equal distance r (the radius) from a given point (the center point).

* **Units:** Note that units are shown for convenience but 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}. For example, if you are starting with mm and you know a and r in mm, your calculations will result with S in mm^{2}, V in mm^{3} and C in mm.

- Volume of a sphere:
**V = (4/3)πr**^{3}

- Circumference of a sphere:
**C = 2πr**

- Surface area of a sphere:
**A = 4πr**^{2}

in terms of radius |
\[ V = \frac{4}{3}\pi r^3 \] | \[ V \approx 4.1888r^3 \] |
---|---|---|

in terms of surface area |
\[ V = \frac{A^{3/2}}{6\sqrt{\pi}} \] | \[ V \approx 0.09403A^{3/2} \] |

in terms of circumference |
\[ V = \frac{C^3}{6\pi^2} \] | \[ V \approx 0.01689C^3 \] |

in terms of radius |
\[ A = 4 \pi r^2 \] | \[ A \approx 12.5664r^2 \] |
---|---|---|

in terms of volume |
\[ A = \pi^{1/3} (6V)^{2/3} \] | \[ A \approx 4.83598V^{2/3} \] |

in terms of circumference |
\[ A = \frac{C^2}{\pi} \] | \[ A \approx 0.3138C^2 \] |

in terms of volume |
\[ r = \left(\frac{3V}{4 \pi}\right)^{1/3} \] | \[ r \approx 0.62035V^{1/3} \] |
---|---|---|

in terms of surface area |
\[ r = \sqrt{\frac{A}{4 \pi}} \] | \[ r \approx 0.2821 \sqrt{A} \] |

in terms of circumference |
\[ r = \frac{C}{2 \pi} \] | \[ r \approx 0.1592C \] |

in terms of radius |
\[ C = 2 \pi r \] | \[ C \approx 6.2832r \] |
---|---|---|

in terms of volume |
\[ C = \pi^{2/3} (6V)^{1/3} \] | \[ C \approx 3.89778V^{1/3} \] |

in terms of surface area |
\[ C = \sqrt{\pi A} \] | \[ C \approx 1.77245\sqrt{A} \] |

Use the following additional formulas along with the formulas above.

- Given the radius of a sphere calculate the volume, surface area and circumference

Given r find V, A, C- use the formulas above

- Given the volume of a sphere calculate the radius, surface area and circumference

Given V find r, A, C- r = cube root(3V / 4π)

- Given the surface area of a sphere calculate the radius, volume and circumference

Given A find r, V, C- r = √(A / 4π)

- Given the circumference of a sphere calculate the radius, volume and surface area

Given C find r, V, A- r = C / 2π

**Cite this content, page or calculator as:**

Furey, Edward "Sphere Calculator" From *http://www.CalculatorSoup.com* - Online Calculator Resource.