# Sphere Density Calculator

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:

where:

- $\rho$ — density,
- $m$ — mass, and
- $V$ — 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:

where:

- $V$ — volume,
- $r$ — radius of a sphere.

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

## How to use sphere density calculator?

To calculate the desired values using our calculator:

- Take a look at the left side of the page on the calculator panel.
- Input the mass (weight) of a sphere. You can choose whichever unit you want.
- Input one of the two — either
**volume**of a sphere or simply its**radius**. - You can look at the picture above the sphere density calculator if needed.
- 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:

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

### 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:

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

- Count the volume of a sphere, using the equation
**volume = (4/3) × π × r**^{3} - In our case: volume = (4/3) × π × 3
^{3}=**113.1 cu in (cubic inches)** - Then let's consider the formula for density, which is
**density = mass/volume**. - We've already got all the data needed!
- Let's put that into practice. density = 0.5 lb / 113.1 cu in =
**0.004421 lb/cu in**