# What is the density?

Computes density from mass and volume (ρ = m ÷ V), or the mass or volume from the other two, in metric or US units.

- Page: https://www.acalculator.org/physics/density-calculator
- JSON spec: https://www.acalculator.org/physics/density-calculator.json
- Version: 41113b7c4ff9

## Default answer

Example with the default inputs (Mass 22.0462262184878 lb, Volume 0.141258666885954 ft³): A mass of 10 kg in a volume of 0.1413 ft³ has a density of 156.07 lb/ft³.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| m | Mass | The mass of the object or sample. |
| v | Volume | The volume the object or sample takes up. |
| rho | Density | The density: mass per unit of volume. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| mass | Mass | The mass of the object or sample. |
| volume | Volume | The volume the object or sample takes up. |
| density | Density | The density: mass per unit of volume. |

## Method

ρ = m ÷ V; m = ρ × V; V = m ÷ ρ.

## Assumptions

- The density is the average over the whole object: mass divided by the total volume it takes up.
- Units are converted exactly: 1 lb = 0.45359237 kg, 1 ft³ = 0.028316846592 m³, 1 L = 0.001 m³ (NIST SP 811).

## Worked examples

1. m = 10, v = 0.004 gives rho = 2,500. Source: hand calculation in content.mdx: 10 kg ÷ 0.004 m³ = 2,500 kg/m³ = 2.5 g/cm³.
2. rho = 19,300, v = 0.000001 gives m = 0.0193. Source: hand calculation in content.mdx: 19,300 kg/m³ × 1e-6 m³ = 0.0193 kg = 19.3 g.
3. m = 28.304164, rho = 999.552115 gives v = 0.028317. Source: hand calculation in content.mdx: 62.4 lb ÷ 62.4 lb/ft³ = 1 ft³ = 0.028316846592 m³ (NIST SP 811).

## FAQ

### What is the formula for density?

Density = mass ÷ volume, written ρ = m ÷ V. The SI unit is the kilogram per cubic meter (kg/m³). For example, 10 kg in 4 liters is 10 ÷ 0.004 m³ = 2,500 kg/m³.

### How do I find mass from density and volume?

Multiply them: m = ρ × V. One cubic centimeter of gold (about 19.3 g/cm³) has a mass of 19.3 × 1 = 19.3 g.

### How do I find volume from mass and density?

Divide the mass by the density: V = m ÷ ρ. 62.4 lb of water at 62.4 lb/ft³ takes up 1 cubic foot.

### How do g/cm³, g/mL and kg/m³ compare?

1 g/cm³ = 1 g/mL = 1 kg/L = 1,000 kg/m³, because 1 mL = 1 cm³ and 1 m³ = 1,000 L. Water near room temperature is about 1 g/cm³.

### Does density change with temperature?

Yes, a little for liquids and solids and a lot for gases, because most materials expand as they warm. Use a mass and volume measured at the same temperature.

## Sources

- NIST Special Publication 811 (2008), Guide for the Use of the International System of Units, section 8.6.5 (mass density) and Appendix B.8 (1 lb = 0.45359237 kg, 1 ft³ = 0.028316846592 m³, 1 gal = 3.785411784 L). https://www.nist.gov/pml/special-publication-811
- BIPM, The International System of Units (SI Brochure), 9th edition (2019), Table 5: mass density in kg/m³. https://www.bipm.org/en/publications/si-brochure