Sphere Density Calculator

Created by Aleksandra Zając, MD
Reviewed by Rijk de Wet
Last updated: Apr 22, 2022

If you're struggling with questions about spheres, you've come to the right place — the sphere density calculator will help you with all the issues referring to spheres and the density formula of a sphere. Read on and find out more about calculating the density of a sphere and more, e.g., 'how to find the mass of a sphere given density and radius'?

Density and density formula of a sphere

Density is a physical term to define mass per unit volume of space.

The formula for density is:

ρ=mV\rho = \frac{m}{V}

where:

  • ρ\rho — density,
  • mm — mass, and
  • VV — volume.

If we've got two objects (let's say watermelons) that are the same size, but one of them is heavier (i.e., its mass is greater), then it means this one has the greater density than the other.

If we are interested in the density of a sphere, we need to use the volume of the sphere in the main equation.

The volume of a sphere is defined as:

V=43×π×r3V = \frac{4}{3} \times \pi \times r^3

where:

  • VV — volume,
  • rr — radius of a sphere.

Combining the two formulas, we get the density formula of a sphere:

ρ=m43×π×r3\rho = \frac{m}{\frac{4}{3} \times \pi \times r^3}

How to use sphere density calculator?

To calculate the desired values using our calculator:

  1. Take a look at the left side of the page on the calculator panel.
  2. Input the mass (weight) of a sphere. You can choose whichever unit you want.
  3. Input one of the two — either volume of a sphere or simply its radius.
  4. You can look at the picture above the sphere density calculator if needed.
  5. The result is ready immediately. You'll also see that the rest of the data was automatically calculated.

More relevant calculators

If you want to know more about density and various shapes, check out our collection:

FAQ

How do I calculate the radius of a sphere given density and mass?

To calculate the radius of a sphere with a given density and mass:

  1. Recalculate the data to the same units. For example, if your mass comes in kg, make sure the density refers to kgs as well.
  2. Calculate the volume of a sphere with the formula volume = mass/density.
  3. Knowing that the volume of a sphere is defined with (4/3) × π × r3, calculate the radius.
  4. That's it! You can also use a combined formula right away: mass/density = (4/3) × π × r3

How do I find the mass of a sphere given density and radius?

To count the mass of a sphere with known density and radius:

  1. Convert the units so that they're consistent. If your radius comes in cm, density should also refer to centimeters.
  2. Knowing radius, you can count the volume of a sphere with the equation volume = (4/3) × π × r3.
  3. Then, using the density formula density = mass/volume, you can count the mass by multiplying density and volume: mass = volume × density.
  4. You can also use a combined formula: mass = (4/3) × π × r3 × density

How do I find density of a sphere which radius is 3 in and mass 0.5 lb?

To find the density of a sphere with a known radius and mass:

  1. Count the volume of a sphere, using the equation volume = (4/3) × π × r3
  2. In our case: volume = (4/3) × π × 33 = 113.1 cu in (cubic inches)
  3. Then let's consider the formula for density, which is density = mass/volume.
  4. We've already got all the data needed!
  5. Let's put that into practice. density = 0.5 lb / 113.1 cu in = 0.004421 lb/cu in
Aleksandra Zając, MD
Sphere with radius marked. Sphere volume
Weight/mass
lb
Volume
cu ft
Radius
ft
Density
lb/cu ft
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