Sphere Density Calculator

Created by Gabriela Diaz
Last updated: Nov 05, 2022

With the sphere density calculator, you can instantly find the density of a sphere by giving its mass and radius.

Density is one of the most important properties of matter. It represents the amount of mass that is contained in a particular volume. In this article, we'll go through the specific case of sphere density and how to calculate it. Keep reading to also learn:

  • How to obtain the sphere density formula;

  • How to find the radius of a sphere, given its density and mass; and

  • How to calculate the mass of a sphere, given its density and radius.

Calculating the density of a sphere

Sphere density is a measure of mass per unit volume of a sphere. If we recall the general formula for calculating the density of any substance, all you need to know is the mass and volume:

density =massvolume\small \text{density =} \cfrac{\text{mass}}{\text{volume}}

or

ρ=mV\small \rho = \cfrac{m}{V}

where:

  • ρ\rho – Density of the substance;
  • mm – Amount of mass of the substance; and
  • VV – Volume occupied by the substance.

💡 If you'd like to learn more about density, you can visit the density calculator or the density altitude calculator to read how density changes with height!

We can customize this expression to the specific case of a sphere by using the formula to find the volume VV of a sphere or radius rr:

V=43πr3\small V = \cfrac{4}{3}\pi r^3

Check out our sphere volume calculator for a detailed explanation of how to find the volume of a sphere

If we replace this in the general formula for density, we get the following expression:

ρ=m43πr3\small \rho = \cfrac{m}{\cfrac{4}{3}\pi r^3}

This is the sphere density formula. Notice that if we know the mass and radius of a sphere, we can easily determine its density by using this expression.

We can also use this formula to calculate the mass of a sphere if we know its density and radius. By rearranging the previous formula:

m=43πr3ρ\small m = \cfrac{4}{3}\pi r^3 \rho

Another possibility is that you need to find the radius of the sphere, given its density and mass. In that case, you can use this variant of the sphere density formula:

r=(m43πr3)1/3\small r = \left(\cfrac{m}{\cfrac{4}{3} \pi r^3}\right)^{1/3}

💡 What about finding the density of the Earth? You can do so with the volume to mass calculator, where we've included some astronomy-related materials 🌎

How to use the sphere density calculator

You can use this sphere density calculator to determine a sphere's density, mass, or radius. To find the density of a sphere with this tool:

  1. Input the mass in the Weight/mass field.

  2. Next, enter either the Radius or the Mass of the sphere.

  3. The calculator will display its Density.

  4. That's it! 😉

Remember, you can use any of our tools in any direction. Then, it's also possible to use this calculator to find the mass of a sphere given its density and radius, or the radius of a sphere given its density and mass. Go test it yourself!

Gabriela Diaz
Sphere with radius marked. Sphere volume
Weight/mass
lb
Volume
cu ft
Radius
ft
Density
lb/cu ft
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