# What is the mass?

Finds a mass from density and volume (m = ρV), from a force and an acceleration (m = F ÷ a), or from a weight and the gravity (m = W ÷ g), in kilograms, grams and pounds.

- Page: https://www.acalculator.org/physics/mass-calculator
- JSON spec: https://www.acalculator.org/physics/mass-calculator.json
- Version: c8852957e913

## Default answer

Example with the default inputs (Find the mass from Density × volume, Density 62.4279605761446 lb/ft³, Volume 0.528344104716297 gal): The mass is 4.40925 lb (2 kg).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| from | Find the mass from | Work out the mass from density and volume, from a force and an acceleration, or from a weight. |
| rho | Density | The density of the material: water is 1,000 kg/m³ (1 g/cm³). |
| V | Volume | The volume of the object. |
| F | Net force | The net force on the object. |
| a | Acceleration | The acceleration the force gives the object, in the unit chosen below. |
| au | Acceleration unit | The unit of the acceleration: m/s², ft/s² or g (standard gravity). |
| W | Weight | The weight of the object: the force of gravity on it, in newtons or pounds-force. |
| g | Gravity (m/s²) | The acceleration of gravity in m/s²: 9.80665 on Earth, about 1.62 on the Moon. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| lb | Mass (lb) | The mass in pounds (1 lb = 0.45359237 kg). |
| kg | Mass (kg) | The mass in kilograms. |
| g | Mass (g) | The mass in grams. |
| oz | Mass (oz) | The mass in ounces (1 oz = 1/16 lb). |

## Method

m = ρ × V; m = F ÷ a; m = W ÷ g.

## Assumptions

- Density × volume assumes the material is the same all through the object (an average density otherwise).
- Force ÷ acceleration uses the net force; weight ÷ gravity uses the gravity where the object is weighed.
- Exact unit sizes: 1 lb = 0.45359237 kg; 1 ft³ = 0.028316846592 m³; 1 gal = 3.785411784 L; 1 lbf = 4.4482216152605 N; 1 kgf = 9.80665 N.

## Worked examples

1. from = density, rho = 1,000, V = 0.002 gives kg = 2, g = 2,000, lb = 4.409245. Source: OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (ρ = m ÷ V), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure.
2. from = force, F = 10, a = 2, au = mps2 gives kg = 5. Source: OpenStax, University Physics Volume 1, §5.3 Newton’s Second Law (F = m a), https://openstax.org/books/university-physics-volume-1/pages/5-3-newtons-second-law.
3. from = weight, W = 4.448222, g = 9.80665 gives lb = 1, kg = 0.453592, oz = 16. Source: OpenStax, University Physics Volume 1, §5.4 Mass and Weight (w = m g), https://openstax.org/books/university-physics-volume-1/pages/5-4-mass-and-weight.
4. from = density, rho = 999.552115, V = 0.283168 gives lb = 624. Source: OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (ρ = m ÷ V), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure.

## FAQ

### How do you calculate mass from density and volume?

Multiply them: m = ρ × V. Two liters of water (0.002 m³) at 1,000 kg/m³ has a mass of 1,000 × 0.002 = 2 kg, or 4.41 lb.

### How do you find mass from force and acceleration?

Rearrange Newton’s second law F = m a to m = F ÷ a. A net force of 10 N that gives an acceleration of 2 m/s² acts on a mass of 5 kg.

### How do you find mass from weight?

Divide the weight by the acceleration of gravity: m = W ÷ g. On Earth g = 9.80665 m/s², so a weight of 98.0665 N is a mass of 10 kg. On the Moon (g ≈ 1.62 m/s²) the same mass weighs only about 16.2 N.

### What is the difference between mass and weight?

Mass is how much matter an object has, in kilograms; it is the same everywhere. Weight is the force of gravity on that mass, in newtons or pounds-force, and it changes with the gravity.

### Why does 1 lbf of weight give 1 lb of mass?

The pound-force is defined as the weight of 1 lb of mass at standard gravity: 0.45359237 kg × 9.80665 m/s² = 4.4482216152605 N. With g = 9.80665, any weight in lbf is the same number of pounds of mass.

## Sources

- OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (ρ = m ÷ V). https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure (retrieved 2026-10-03)
- OpenStax, University Physics Volume 1, §5.3 Newton’s Second Law (F = m a). https://openstax.org/books/university-physics-volume-1/pages/5-3-newtons-second-law (retrieved 2026-10-03)
- OpenStax, University Physics Volume 1, §5.4 Mass and Weight (w = m g). https://openstax.org/books/university-physics-volume-1/pages/5-4-mass-and-weight (retrieved 2026-10-03)
- NIST SP 811, Appendix B.8 Factors for Units Listed Alphabetically (pound, cubic foot, gallon, pound-force). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-03)