Force Calculator (F = ma)
Solve Newton’s second law for force, mass, or acceleration.
SI units: newtons, kilograms, m/s².
Newton’s second law is F = m × a: net force equals mass times acceleration. A 2 kg cart accelerating at 5 m/s² feels F = 2 × 5 = 10 N. Rearrange to m = F ÷ a or a = F ÷ m to find either of the other two.
Newton’s second law
The net force on an object equals its mass times its acceleration: F = ma. A bigger push produces more acceleration, while a heavier object resists being accelerated. Because it is one equation with three variables, knowing any two gives you the third. Once you have the acceleration, feed it into the kinematics solver to track the resulting motion.
F = force (N), m = mass (kg), a = acceleration (m/s²)
Worked example
A 2 kg cart accelerates at 5 m/s². What net force is acting on it?
- 1 Write Newton’s second law. F = m × a, with mass in kilograms and acceleration in m/s².
- 2 Substitute the known values. F = 2 kg × 5 m/s².
- 3 Compute the force. F = 10 N — that is the net (resultant) force on the cart.
Newton’s second law rearranged
One equation, three forms; weight is the special case F = mg.
| Solve for | Formula | SI unit |
|---|---|---|
| Force | F = m × a | newton (N) |
| Mass | m = F ÷ a | kilogram (kg) |
| Acceleration | a = F ÷ m | m/s² |
| Weight | W = m × g (g = 9.81 m/s²) | newton (N) |
Units, weight, and common mistakes
One newton is the force that accelerates a 1 kg mass at 1 m/s². Stick to SI units — newtons, kilograms, and m/s² — or the answer will be off by a factor you have to chase down.
Mass is not weight. Mass (kg) is the amount of matter; weight (N) is the gravitational force on it, W = mg. A 10 kg bag has the same mass on the Moon but weighs about a sixth as much.
F is the net force. If several forces act at once, add them as vectors first. When the net force is zero, the object is in equilibrium — at rest or moving at constant velocity.