Force Calculator
Calculate force, mass or acceleration using Newton’s second law, F = ma.
About
Force Calculator
Force is F = m × a: mass multiplied by acceleration. Pick which of the three you want above and the calculator rearranges the equation, shows the substitution, and converts the answer between newtons, kilonewtons, pounds-force and kilograms-force.
What the equation says
Newton's second law states that the acceleration of an object is proportional to the force on it and inversely proportional to its mass. Push twice as hard and it accelerates twice as fast. Make it twice as heavy and the same push produces half the acceleration.
The equation defines the newton. One newton is the force that accelerates one kilogram at one metre per second squared, which is why the unit has no separate definition of its own. It is a derived unit, kg·m/s² written shorter.
Mass and weight are different things
Mass is how much matter something contains and does not change. Weight is the force gravity exerts on that mass, and it changes with where you are.
A 70 kg person has a weight on Earth of 70 × 9.80665 = 686.4655 N. On the Moon, where g is about 1.62 m/s², the same person weighs 113.4 N while still having a mass of 70 kg. Bathroom scales are calibrated to divide the force they measure by Earth's gravity and show you a mass, which is why they would read wrong on the Moon.
A worked example
A 70 kg person standing still on Earth.
- Mass: 70 kg
- Acceleration: 9.80665 m/s², the standard value for gravity
- Force: 70 × 9.80665 = 686.4655 N
That is 154.3 pounds-force, or 70 kilograms-force. The kilogram-force is a unit that exists precisely because people wanted weight expressed as a number matching their mass, and it equals 9.80665 N by definition.
Acceleration is a rate of change, not a speed
The most common confusion here is treating acceleration as though it were velocity. Acceleration is how quickly velocity changes, measured in metres per second per second.
A car reaching 100 km/h, which is 27.78 m/s, from rest in 8 seconds has an acceleration of 27.78 / 8 = 3.47 m/s². If the car has a mass of 1500 kg, the force driving it is 1500 × 3.47 = 5209 N, about 5.2 kN. That is the net force at the wheels after drag and rolling resistance have taken their share, which is why engine output has to be larger.
Why crumple zones and airbags work
The same equation explains why modern cars are designed to fall apart in a crash. Force depends on how quickly velocity changes, so stretching the change over more time reduces the force.
A 70 kg occupant going from 15 m/s to rest in 0.3 seconds experiences an acceleration of 50 m/s² and a force of 3500 N. Stopped in 0.03 seconds instead, by hitting a rigid dashboard rather than an inflating bag, the acceleration is 500 m/s² and the force is 35,000 N. Ten times longer to stop means a tenth of the force, and that ratio is the entire principle behind crumple zones, airbags, helmets and crash mats.
Net force is what counts
The F in the equation is the resultant of every force acting, not any single one. A box sitting on a table has gravity pulling it down and the table pushing it up with an equal force, so the net force is zero and it does not accelerate.
An object moving at constant speed also has zero net force, which surprises people. A car cruising at a steady 100 km/h has its driving force exactly balanced by drag and friction. The force has not disappeared; it has cancelled.
Units
| Unit | Equals | Used for |
|---|---|---|
| newton (N) | 1 kg·m/s² | the SI unit, used everywhere in science |
| kilonewton (kN) | 1000 N | structural loads, vehicle forces |
| pound-force (lbf) | 4.4482 N | US engineering |
| kilogram-force (kgf) | 9.80665 N | older European specifications |
Mass must be in kilograms and acceleration in metres per second squared before multiplying, or the answer will not be in newtons. Entering a mass in grams and expecting newtons is out by a factor of a thousand.
Where it gets used
Structural engineering. Loads on beams, foundations and fixings are forces, and they are the starting point of every structural calculation.
Vehicle design. Acceleration, braking and cornering all come from forces at the tyre contact patches, and the mass of the vehicle sets what each force achieves.
Rocketry. Thrust is a force, and the acceleration it produces rises through the flight as fuel burns off and mass falls, which is why a rocket accelerates hardest near the end of a stage.
Everyday physics problems. Most introductory mechanics coursework is this equation applied with different labels on the quantities.
The third law, and why forces come in pairs
Every force is one half of a pair. Push on a wall and the wall pushes back on you with an equal force in the opposite direction. The two act on different objects, which is why they do not cancel each other out.
That last point is where the law is usually misunderstood. If action and reaction cancelled, nothing could ever accelerate. A rocket works because the engine pushes gas backwards and the gas pushes the rocket forwards; those two forces act on different bodies, so each one accelerates its own.
Walking is the same arrangement. Your foot pushes backwards on the ground and the ground pushes forwards on you. On ice the ground cannot supply that reaction because there is too little friction, so no matter how hard you push you go nowhere.
Friction, and the force you have to overcome
Most real problems include friction, which resists motion and is proportional to the force pressing the surfaces together rather than to the contact area. It is written F = μN, where N is the normal force and μ is the coefficient of friction.
| Surfaces | Approximate μ | Force to slide 70 kg |
|---|---|---|
| Rubber on dry asphalt | 0.8 | 549 N |
| Steel on steel | 0.6 | 412 N |
| Wood on wood | 0.35 | 240 N |
| Ice on ice | 0.05 | 34 N |
The last row explains a great deal about winter driving. A car that needs 5000 N to accelerate briskly on dry asphalt can only call on a fraction of that on ice, and no amount of engine power changes it. The limit is set by what the surface can supply.
Working in the other direction
The equation is used to find mass and acceleration at least as often as force. A known force acting on an object of unknown mass reveals the mass once the acceleration is measured, which is how mass is determined in orbit where scales cannot work.
Astronauts on the International Space Station measure their mass by strapping into a device that applies a known force and records the resulting acceleration. Dividing one by the other gives the mass, since weight is unavailable as a proxy.
Common mistakes
Using weight where mass belongs. If a figure is given in newtons or pounds-force, it is already a force. Divide by gravity to recover the mass.
Confusing acceleration with speed. Acceleration is the rate at which speed changes. A steady 100 km/h is zero acceleration.
Forgetting other forces. The equation needs the net force. Friction, drag and gravity all count.
Mixing units. Kilograms and metres per second squared, or the answer is not in newtons.
Common questions
Frequently asked questions
Force equals mass times acceleration, F = ma. A 70 kg mass under Earth gravity of 9.80665 m/s squared experiences 686.4655 newtons.
Mass is the amount of matter and never changes. Weight is the force gravity applies to that mass. A 70 kg person weighs 686 N on Earth and 113 N on the Moon, with the same mass in both places.
Divide the force by the acceleration. A 686.5 N weight under Earth gravity corresponds to a mass of 686.5 divided by 9.80665, which is 70 kg.
The force that accelerates one kilogram at one metre per second squared. It is a derived unit, kg times m per second squared written more briefly.
They stretch the stop over more time. Going from 15 m/s to rest in 0.3 seconds needs 3500 N for a 70 kg person; doing it in 0.03 seconds needs 35,000 N.
No. The driving force is exactly balanced by drag and friction, so the net force is zero even though the engine is working hard.
Divide by 4.4482. 686.5 N is about 154.3 lbf.
100 km/h is 27.78 m/s, so the acceleration is 3.47 m/s squared. For a 1500 kg car that needs a net force of about 5209 N.