The mass formula physics problems use most often is : divide the net force on an object by the acceleration it produces. This is the second law of motion, , solved for m instead of F. A trolley that accelerates at 2 m/s² under a net force of 10 N has a mass of 5 kg.
Think of mass as the quantity of matter an object holds, and also as a measure of its inertia: the bigger the mass, the harder it is to speed up, slow down or turn. There is no single definition formula for it, because the kilogram is an SI base unit. Instead you find mass from whatever the question gives: force and acceleration, density and volume (), or weight and gravity ().
Quick facts
From force
From density
From weight
SI unit
kilogram (kg), a base unitDimensional formula
[M¹ L⁰ T⁰]Type
Scalar, the same everywhere in the universe
Mass formula physics: what is the formula of mass?
| Formula | You need | Units in, unit out |
|---|---|---|
| Net force and acceleration | N ÷ m/s² = kg | |
| Density and volume | kg/m³ × m³ = kg | |
| Weight and gravitational field strength | N ÷ m/s² = kg | |
| Momentum and velocity | kg m/s ÷ m/s = kg |
The first form measures inertial mass, the resistance to acceleration. The weight form measures gravitational mass, the response to gravity. Experiments show the two are equal, and that equality is the reason a hammer and a feather would land together in a vacuum.
Worked examples for each form
Example 1: Newton's second law
A net force of 30 N gives a box an acceleration of 1.5 m/s². Find its mass.
Example 2: from density, with a volume conversion
An aluminium block has a volume of 250 cm³. The density of aluminium is 2700 kg/m³. Find the mass.
Convert: 250 cm³ = 250 × 10⁻⁶ m³ = 2.5 × 10⁻⁴ m³.
Example 3: from weight
A bathroom scale shows a weight of 588 N. What is the person's mass? Use g = 9.8 m/s².
On the Moon the same person would weigh about 98 N, but the mass would still be 60 kg.
Mass versus weight
| Property | Mass | Weight |
|---|---|---|
| What it measures | Inertia, the reluctance to speed up or slow down | The pull of gravity on the body |
| Measured in | kg | N |
| Direction | None | Toward the centre of the Earth |
| Same on the Moon | Yes | No, about one sixth |
| Formula link |
Everyday language uses weight for mass, but physics never does. The weight formula page covers W = mg in detail, and the density formula page covers ρ = m / V.
Units and the dimensional formula of mass
The kilogram is one of the seven SI base units, so mass is a base quantity with dimensional formula [M¹ L⁰ T⁰], written [M]. Every other mechanical quantity is built from M, L and T. Force, for example, is [M L T⁻²] because it is mass times acceleration. The dimensional formula of mass page shows how this is used to check equations.
Useful conversions: 1 g = 10⁻³ kg, 1 tonne = 1000 kg, and 1 mg = 10⁻⁶ kg. Always convert to kilograms before using SI formulas.
Slips with mass questions
- Using the applied force instead of the net force in m = F/a when friction acts.
- Grams in SI formulas. Convert to kg first.
- Confusing kg and N. Writing a mass in newtons, or a weight in kilograms, loses the unit mark at once.
- cm³ to m³. Divide by 10⁶, not 10² or 10³.
Mass appears all through motion and force problems. The force formula page uses it with F = ma, and kinematics formulas covers the motion that the force produces.
Frequently asked questions
Which mass formula is used most in physics?
The most used one is m = F / a from Newton's second law. You can also use m = ρV with density and volume, or m = W / g with weight.
What is the SI unit of mass?
The kilogram (kg). It is one of the seven SI base units.
Is mass a scalar or a vector?
A scalar. A 2 kg bag is 2 kg whichever way it moves and wherever it sits, so no direction is attached.
Does mass change on the Moon?
No. Mass stays the same everywhere. Weight changes, because the Moon's gravitational field is about one sixth of Earth's.
How do you find mass from density?
Multiply density by volume: m = ρV. Use kg/m³ and m³ to get kilograms.