Density Calculator
Calculate density by entering the mass and volume in the calculator below. Alternatively, solve mass or volume using the density.
Density:
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How to Calculate Density
Density is the measure of a unit’s mass to its volume, or essentially how compact an object’s mass is. It is expressed as the unit of mass over the unit of volume, for example, lbs/cu ft.
Density is expressed using the Greek letter ρ (rho), and you can calculate it using a standard formula.
Density Formula
To calculate density, divide the mass of an object or substance by its volume.
ρ = m / V
where:
ρ = density
m = mass or weight
V = volume
For example, let’s find the density of an object that weighs 5 pounds and has a volume of 2 cubic feet.
density = 5 lbs ÷ 2 cu. ft.
density = 2.5 lbs / cu. ft.
Tip: use our shape volume calculator to find the volume of an object.
How to Calculate in Different Units
The formula above makes the assumption that the resulting density value should be expressed in the same units of measure as mass and volume. It’s possible to find the density of an object when the mass and volume are not in the same units of measure.
The key to finding the density in the desired unit of measure is to convert the mass unit and the volume unit to the right measurements before using the formula above.
For example, let’s find the density of an object in pounds per cubic foot for an object that weighs 80 ounces and has a volume of 3,456 cubic inches.
First, convert the mass to pounds.
mass(oz) = 80 oz
mass(lb) = 80 oz ÷ 16 oz per pound
mass(lb) = 5 lbs
Second, convert the volume to cubic feet.
volume(cu. in.) = 3,456 cu. in.
volume(cu.ft.) = 3,456 cu. in. ÷ 1,728 cu. in. per cu. ft.
volume(cu.ft.) = 2 cu. ft.
Now that that mass and volume are in the correct output unit, enter them in the formula above to find density.
How to Calculate Mass From Density and Volume
Using the formula above, it’s also possible to calculate mass if the density and volume are known. Using algebra, we can rewrite the formula above to allow finding mass.
m = ρ × V
where:
m = mass or weight
ρ = density
V = volume
For example, let’s find the mass of an object with a density of 4 pounds per cubic foot and a volume of 3 cubic feet.
mass = 4 lbs / cu. ft. × 3 cu. ft.
mass = 12 lbs
Here’s a tip: if you aren’t sure what the volume is, use a tool such as our cubic feet calculator to find it.
How to Calculate Volume using Mass and Density
It’s also possible to calculate volume if both mass and density are known. Rewriting the original formula like this will allow solving for volume.
V = m / ρ
where:
V = volume
m = mass or weight
ρ = density
For example, let’s find the volume of an object with a density of 2 pounds per cubic foot and a mass of 6 pounds.
volume = 6 lbs ÷ 2 lbs / cu. ft.
volume = 3 cu. ft.
Common Material Densities
| Material | Density |
|---|---|
| water (at 4 °C) | 1.0 g/cm³ |
| isopropyl alcohol | 0.786 g/cm³ |
| gasoline | 0.77 g/cm³ |
| milk | 1.026 g/cm³ |
| latex paint | 1.34 g/cm³ |
| aluminum | 2.7 g/cm³ |
| brass | 8.73 g/cm³ |
| copper | 8.96 g/cm³ |
| iron | 7.86 g/cm³ |
| steel | 8.050 g/cm³ |
| platinum | 21.45 g/cm³ |
| air | 0.001225 g/cm³ |
| carbon dioxide | 0.001977 g/cm³ |
| helium | 0.000179 g/cm³ |
You might also find our water weight calculator and hardwood lumber calculator interesting, which use these same principles of density to determine the weight of these materials.