What this calculator does
Newton's second law says force equals mass times acceleration. It is the most quoted equation in physics and the most commonly misapplied, because the acceleration it wants is the net acceleration produced by all forces together, not the force you happen to be thinking about.
This calculator also separates two things that get confused constantly: mass and weight. Mass is how much matter there is and does not change. Weight is the force gravity exerts on that mass, and it changes with where you are standing.
The formula
Multiply mass in kilograms by acceleration in metres per second squared to get force in newtons. Weight is the same calculation with gravity as the acceleration, using 9.80665 m/s² for Earth and about 1.62 for the Moon.
| Term | Meaning |
|---|---|
| Newton (N) | The force that accelerates one kilogram at one metre per second squared. |
| Mass | The amount of matter in an object, in kilograms. Identical everywhere in the universe. |
| Weight | The force gravity exerts on a mass. A 10 kg object weighs about 98 N on Earth and about 16 N on the Moon. |
The inputs explained
| Field | What to enter |
|---|---|
| Mass (kg) | The mass of the object in kilograms. This is mass, not weight, so it is the same figure regardless of where the object is. |
| Acceleration (m/s²) | The acceleration in metres per second squared. For an object in free fall near Earth this is about 9.81. |
When to use it
Working out the force to accelerate something
Getting a known mass up to speed in a given time needs a specific force, which is the starting point for sizing a motor or an actuator.
Converting between mass and weight
Scales read in kilograms but structural work needs newtons, and the conversion is multiplication by gravity.
Checking a physics problem
Most introductory mechanics questions reduce to this equation once the net force has been identified correctly.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does force scale with mass at a fixed acceleration?
A range of masses accelerated at the same rate.
| Mass | Force | Weight on Earth |
|---|---|---|
| 1 kg | 3.000 N | 9.807 N |
| 10 kg | 30.000 N | 98.066 N |
| 50 kg | 150.000 N | 490.333 N |
| 100 kg | 300.000 N | 980.665 N |
Questions
Is weight the same as mass?
No. Mass is measured in kilograms and never changes. Weight is a force measured in newtons and depends on local gravity, which is why the same object weighs about six times less on the Moon while its mass is identical.
Why do bathroom scales show kilograms then?
They measure the force you exert on them and divide by Earth's gravity to display a mass. The same scales on the Moon would read about a sixth of your actual mass, because the conversion assumes Earth gravity.
What acceleration should I use?
The net acceleration of the object. If several forces act, the equation applies to their resultant, not to any single one of them. A box pushed across a floor at constant speed has zero acceleration and therefore zero net force, even though you are clearly pushing it.
What is a kilogram-force?
The force exerted by one kilogram under Earth gravity, about 9.81 newtons. It is an older unit still seen on some equipment, and it exists precisely because people wanted to talk about force in familiar mass units.
For what that force does over a distance, see the work, power and efficiency calculator. For the momentum it builds, see the momentum and impulse calculator.