Newton’s second law
Force, mass and acceleration are linked by Newton’s second law: the net force on an object equals its mass times its acceleration, F = ma. Push twice as hard and the object accelerates twice as fast; push the same on something twice as heavy and it accelerates half as fast. The calculator solves the law for whichever of the three values you are missing.
The formulas
- Force = mass × acceleration
- Mass = force ÷ acceleration
- Acceleration = force ÷ mass
- Acceleration in g = acceleration ÷ 9.80665 m/s²
The calculator works in SI units internally (kilograms, meters per second squared, newtons) and converts the results to the unit you pick, including pounds-force (lbf) and kilograms-force (kgf).
Worked example
A 3,300 lb car accelerates at 10 ft/s².
- In SI units, that is 1,497 kg and 3.05 m/s².
- Force = 1,497 × 3.05 = 4,562 N, or about 1,026 lbf.
- The acceleration is 0.31 g: the driver is pushed into the seat with about a third of their own weight.
- For comparison, the car’s weight on Earth is 3,300 lbf, or 14,679 N.
Units of force
| Unit | Value in newtons |
|---|---|
| 1 newton (N) | 1 |
| 1 kilonewton (kN) | 1,000 |
| 1 pound-force (lbf) | 4.448 |
| 1 kilogram-force (kgf) | 9.807 |
A newton is small: it is roughly the weight of a medium apple. One pound-force is the weight of a one-pound mass under standard gravity.
Net force, not any single force
F = ma applies to the net force, the sum of every force acting on the object. A car’s tires may push forward with 5,000 N while air drag and rolling resistance push back with 1,000 N: the car accelerates as if a single 4,000 N force acted on it. When the net force is zero, the object keeps a constant speed, which is Newton’s first law.
Mass versus weight
Mass, in kilograms or pounds, measures the amount of matter and does not change from place to place. Weight is a force, the pull of gravity on that mass, W = mg. That is why the calculator shows the weight of the mass on Earth as a separate result, and why the same mass weighs much less on the Moon.
Where it is used
Engineers use F = ma to size brakes, engines, cables and supports. Physics students use it in nearly every mechanics problem, from blocks on slopes to rockets, often together with the formulas for acceleration, kinetic energy and torque.