Force Calculator (F = ma)
Calculate force, mass, or acceleration with Newton's second law F = ma — enter any two and get the third, in newtons.
Force and Newton's second law
Newton's second law says the force on an object equals its mass times its acceleration. It's the rule that connects a push or pull to the motion it produces.
F = m · a · m = F / a · a = F / m
Force is measured in newtons (N): one newton accelerates one kilogram at one metre per second squared. This calculator solves for whichever of force, mass, or acceleration you leave out, and also shows the force in kilograms-force — a handy everyday feel, since 1 kgf is the weight of 1 kg under gravity (9.81 N).
Worked example
Accelerating a 1000 kg car at 3 m/s² needs F = 1000 × 3 = 3000 N (about 306 kgf). To find the acceleration a 500 N force gives a 20 kg cart, rearrange to a = F / m = 500 / 20 = 25 m/s².
Weight is a force
An object's weight is just the force of gravity on it: W = m · g, with g ≈ 9.81 m/s². So a 10 kg mass weighs about 98.1 N. Set acceleration to 9.81 in this calculator to get any mass's weight in newtons.
Common questions
- What is one newton, in something I can picture?
- Roughly the weight of a small apple. Formally it is the force that accelerates one kilogram at one metre per second squared, which works out to about 102 grams held against Earth's gravity. If you want a feel for the scale: a bag of sugar weighs about 10 N, an adult about 700 N.
- Is weight the same thing as mass?
- No, and this calculator keeps them apart deliberately. Mass is how much matter there is, measured in kilograms, and it does not change wherever you go. Weight is the force gravity exerts on that mass, measured in newtons, and it does change — the same 70 kg person weighs about 687 N on Earth and 114 N on the Moon. Bathroom scales are calibrated to show mass, which is why they read the same everywhere on Earth.
- What is a kilogram-force, and why does this page show it?
- A kilogram-force is the weight of one kilogram under standard gravity: exactly 9.80665 N. It is not an SI unit and it is discouraged in technical work, but it survives because it is intuitive — saying a fixing is rated at 50 kgf immediately tells you it holds a 50 kg load. The page shows it alongside newtons for exactly that reason.
- How much force do I need to lift something?
- To hold it still, exactly its weight: mass × 9.81. To actually accelerate it upwards you need more, and the excess is what produces the acceleration — F = m(g + a). This is why a lift feels heavy as it starts moving up and light as it starts moving down, and why a crane rated for a static load must be derated for a fast lift.