Newton's second law
F = m·a is Newton's second law: the net force on an object equals its mass times its acceleration. A 10 kg mass accelerating at 9.8 m/s² feels a force of 98 N (newtons). Using a = 9.8 m/s² gives the object's weight under gravity. Find the acceleration with the acceleration calculator.
The word net matters. If several forces act at once, F in the equation is their vector sum, not any single push or pull. An object sliding at constant velocity has zero net force even though friction and thrust are both present — they cancel.
How to use this calculator
Enter the mass in kilograms and the acceleration in meters per second squared. The result is in newtons (N), where 1 N = 1 kg·m/s². To find an object's weight, use the acceleration due to gravity (about 9.8 m/s²).
Convert grams to kilograms before entering a value, since 500 g is 0.5 kg and entering 500 would inflate the force a thousandfold. Negative accelerations are valid and simply mean the net force points opposite to the direction you chose as positive — braking, for instance, produces a negative force in the direction of travel. The force gravity exerts on a mass is its weight, which uses the same equation with g in place of a.
Force, mass and motion
The same force produces less acceleration on a heavier object. Rearranged, the law gives a = F / m and m = F / a. Force is closely related to torque, which is force applied at a distance — see the torque calculator.
This inverse relationship explains why pushing an empty trolley speeds it up far faster than pushing a loaded one.
Frequently asked questions
- How do I calculate force?
- Multiply mass by acceleration: F = m·a. A 10 kg mass at 9.8 m/s² gives 98 N.
- What is a newton?
- The SI unit of force; 1 N is the force that accelerates 1 kg at 1 m/s² (1 N = 1 kg·m/s²).
- How do I find an object's weight?
- Use F = m·a with a = 9.8 m/s², the acceleration due to gravity. A 10 kg mass weighs about 98 N.
- What is Newton's second law?
- It states that the net force on an object equals its mass times its acceleration, F = m·a.
- What is the difference between mass and weight?
- Mass is the amount of matter in an object, measured in kilograms, and never changes. Weight is the force gravity exerts on that mass, measured in newtons, and depends on location — the same 10 kg mass weighs about 98 N on Earth but only around 16 N on the Moon.