Force Calculator
Choose the law: F = ma, momentum, impulse, centripetal force, gravity between two masses, or Coulomb's law. Fill in all but one box and the missing one is worked out.
Fill in all the boxes but one and leave the one you want to find empty. The answer appears as you type, in the unit shown next to its box. The gravity example is the Earth and the Moon (5.972e24 kg and 7.342e22 kg). Enter a negative charge in Coulomb's law to see attraction.
Worked examples
Second law
Mass 10 kg, acceleration 2 m/s squared
20 N
F = m x a.
Earth and Moon
5.972e24 kg, 7.342e22 kg, 384,400 km
About 1.98e20 N
F = G m1 m2 / r squared.
About Force Calculator
Most forces in school and college physics come from a handful of laws, and each one links four or fewer quantities. This calculator puts six of them in one place. Newton's second law says force equals mass times acceleration. Momentum is mass times velocity, and impulse, the force multiplied by the time it acts, equals the change in momentum. Centripetal force is the inward force that holds an object on a circle: mass times speed squared over the radius.
The last two laws work at the largest and smallest scales. Newton's law of gravitation gives the pull between two masses from the gravitational constant, and Coulomb's law gives the push or pull between two electric charges from the Coulomb constant. Both fall with the square of the distance. Choose the law, fill in all the boxes but one, and the missing value appears along with extras such as the acceleration as a multiple of g or the time for one turn.
How to use Force Calculator
- Choose the law from the menu.
- Fill in all the boxes except the one you want to find, choosing units where there is a menu.
- Read the answer in the box you left empty, with its unit.
- Use the extra rows for related figures, and change the law to solve another type of problem.
Common uses
- Finding the push needed to accelerate a trolley or a car
- Working out the average force of a collision from the stopping time
- Checking the grip needed to take a bend at a speed
- Calculating the gravitational pull between planets or the force between charges
Frequently asked questions
What is Newton's second law?
The resultant force on an object equals its mass multiplied by its acceleration. One newton gives one kilogram an acceleration of one metre per second squared.
What is the difference between momentum and impulse?
Momentum is mass times velocity of a moving object. Impulse is force times time and equals the change in momentum, so a longer stopping time means a smaller force.
What constants does it use?
The gravitational constant is 6.67430e-11 N m squared per kg squared, the Coulomb constant is 8.9875517923e9 N m squared per C squared, and g is 9.80665 metres per second squared.
What does centripetal force mean?
It is the name for the net inward force needed for circular motion, such as friction on a car's tyres, tension in a string or gravity on a satellite.
Why do I have to leave one box empty?
The page solves for the missing value, so it needs exactly one box blank. Clear a different box to solve for another quantity.