Force Calculator
Newton's second law ties force, mass and acceleration together. Give this calculator any two and it returns the third.
Formula
F = m × a
- F in newtons, m in kilograms, a in metres per second squared
- Weight is a force: W = m × 9.81 on Earth
1,200 kg accelerating at 3 m/s²: 1,200 × 3 = 3,600 N
Newton's Second Law
F = m × a
Force in newtons, mass in kilograms, acceleration in metres per second squared.
A 1,500 kg car accelerating at 3 m/s² needs 1,500 × 3 = 4,500 N.
One newton is the force that accelerates one kilogram at one metre per second squared — roughly the weight of a medium apple, which is a pleasing coincidence given the mythology.
Weight Is a Force, Mass Is Not
Everyday speech treats them as the same; physics does not. Mass is how much matter something contains, measured in kilograms and unchanged by location. Weight is the force gravity exerts on that mass:
Weight = mass × g, where g is 9.81 m/s² on Earth.
A 70 kg person weighs about 687 N on Earth and roughly 114 N on the Moon. Their mass is 70 kg in both places.
Net Force Is What Matters
F = ma refers to the resultant force, once everything acting on the object is added together. A car at constant motorway speed has substantial engine thrust and equally substantial drag and friction, summing to zero — which is why it does not accelerate.
This is also why seatbelts and crumple zones work: they extend the time over which momentum changes, and since force is the rate of change of momentum, a longer stop means a smaller force.
Quick Reference
| Body | Gravity (m/s²) | Weight of 70 kg |
|---|---|---|
| Earth | 9.81 | 687 N |
| Moon | 1.62 | 113 N |
| Mars | 3.72 | 260 N |
| Jupiter | 24.79 | 1,735 N |
| Sun | 274 | 19,180 N |
Frequently Asked Questions
- What is the formula for force?
- Force equals mass times acceleration, F = ma. A 1,500 kg car accelerating at 3 m/s² requires 4,500 newtons.
- What is the difference between mass and weight?
- Mass is the amount of matter, measured in kilograms and constant everywhere. Weight is the gravitational force on that mass, measured in newtons and dependent on local gravity.
- How much is one newton?
- The force needed to accelerate one kilogram at one metre per second squared, roughly the weight of a small apple on Earth.
- Why does a car not accelerate at constant speed?
- Because the net force is zero. Engine thrust is exactly balanced by drag and friction, so there is nothing left over to produce acceleration.