Calculate weight per volume or density from mass and volume, or convert volume to weight and weight to volume using typical material densities or your own.
Weight Per Volume Formula
The weight per volume calculator uses mass, volume, and weight per unit volume. In SI units, the base calculation uses kilograms for mass, cubic meters for volume, and newtons per cubic meter for weight per volume.
To solve for mass:
To solve for volume:
- WPV = weight per volume, usually in N/m³
- m = total mass, in kg after unit conversion
- V = total volume, in m³ after unit conversion
- 9.80665 = standard gravitational acceleration in m/s²
If you enter mass and volume, the calculator finds weight per volume. If you pick a material (or enter weight per volume) and volume, it finds total mass. If you enter mass and pick a material (or enter weight per volume), it finds total volume. Unit selections are converted to base units first, then the result is converted back to the unit you selected for the missing value.
Supported Units and Base Conversions
The calculator uses kilograms, cubic meters and kg/m³ internally. N/m³ is converted using standard gravity. The second table uses illustrative density inputs rather than material specifications.
| Quantity | Unit | Conversion to Base Unit |
|---|---|---|
| Mass | g | 1 g = 0.001 kg |
| Mass | lb | 1 lb = 0.45359237 kg |
| Volume | L | 1 L = 0.001 m³ |
| Volume | ft³ | 1 ft³ = 0.028316846592 m³ |
| Volume | US gallon | 1 US liquid gal = 0.003785411784 m³ |
| Illustrative input | Example density | Calculated weight per volume |
|---|---|---|
| Example A | 1000 kg/m³ | 9806.65 N/m³ |
| Example B | 1.2 kg/m³ | 11.8 N/m³ |
| Example C | 2400 kg/m³ | 23535.96 N/m³ |
| Example D | 7850 kg/m³ | 76982.2025 N/m³ |
Example
Example 1: Find weight per volume
You have a material with a mass of 50 kg and a volume of 0.02 m³.
The weight per volume is 24,516.625 N/m³. If expressed as kg/m³ in the calculator, the equivalent value is 2,500 kg/m³.
Example 2: Find mass
A substance has a weight per volume of 9806.65 N/m³ and occupies 3 m³.
The total mass is 3000 kg.
FAQ
Is weight per volume the same as density?
Not exactly. Density is mass per volume, such as kg/m³. Weight per volume is force per volume, such as N/m³. They are related by gravity:
For example, water has a density of about 1000 kg/m³ and a weight per volume of about 9806.65 N/m³.
Why does the formula use 9.80665?
The value 9.80665 m/s² is the standard acceleration due to gravity on Earth. It converts mass in kilograms into weight force in newtons. If you are doing a calculation for a location with different gravity, such as another planet, the result would be different.
How do I choose what to calculate?
Select the quantity to solve for, then enter the two requested quantities and their units. Volume must be positive. Zero mass is allowed in forward calculations; zero mass and zero density do not determine a unique volume.
