# Sphere Calculator

Sphere
 Solve for: A, V, C | Given r r, C, A | Given V r, C, V | Given A r, A, V | Given C r = in ft m cm mm Significant Figures: auto 3 4 5 6 7 8 9 Answer: r = m V = m3 A = m2 C = m

## Sphere Shape

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, ft2 or ft3.  For example, if you are starting with mm and you know a and r in mm, your calculations will result with S in mm2, V in mm3 and C in mm.

## Sphere Formulas in terms of radius r:

• Volume of a sphere:
• V = (4/3)πr3
• Circumference of a sphere:
• C = 2πr
• Surface area of a sphere:
• A = 4πr2
in terms of in terms of radius surface area $V = \frac{4}{3}\pi r^3$ $V \approx 4.1888r^3$ $V = \frac{A^{3/2}}{6\sqrt{\pi}}$ $V \approx 0.09403A^{3/2}$ $V = \frac{C^3}{6\pi^2}$ $V \approx 0.01689C^3$
in terms of in terms of radius volume $A = 4 \pi r^2$ $A \approx 12.5664r^2$ $A = \pi^{1/3} (6V)^{2/3}$ $A \approx 4.83598V^{2/3}$ $A = \frac{C^2}{\pi}$ $A \approx 0.3138C^2$
in terms of in terms of volume surface area $r = \left(\frac{3V}{4 \pi}\right)^{1/3}$ $r \approx 0.62035V^{1/3}$ $r = \sqrt{\frac{A}{4 \pi}}$ $r \approx 0.2821 \sqrt{A}$ $r = \frac{C}{2 \pi}$ $r \approx 0.1592C$
in terms of in terms of radius volume $C = 2 \pi r$ $C \approx 6.2832r$ $C = \pi^{2/3} (6V)^{1/3}$ $C \approx 3.89778V^{1/3}$ $C = \sqrt{\pi A}$ $C \approx 1.77245\sqrt{A}$

### Sphere Calculations:

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.