What Newton's second law says
A force changes how an object moves. Newton's second law puts a number on it: the net force equals the mass times the acceleration it produces. A heavier object needs more force to speed up at the same rate, which is why a loaded truck accelerates more slowly than an empty one with the same engine.
Weight is a special case. Gravity accelerates every falling object at about 9.81 m/s², so the force of gravity on a mass, its weight, is m × g. This calculator uses standard gravity, g = 9.80665 m/s².
The formula
m = F ÷ a
a = F ÷ m
weight W = m × g, with g = 9.80665 m/s²
Use kilograms and m/s² to get newtons. Conversions: 1 lb = 0.45359237 kg, 1 lbf = 4.448222 N, 1 ft/s² = 0.3048 m/s².
Example: pushing a 1,500 kg car to 3 m/s²
What net force does it take to accelerate a 1,500 kg car at 3 m/s²? These are the default values.
| Step | Result |
|---|---|
| F = 1,500 × 3 | 4,500 N |
| In kilonewtons: 4,500 ÷ 1,000 | 4.5 kN |
| In pound-force: 4,500 ÷ 4.448222 | 1,012 lbf |
| Acceleration in g: 3 ÷ 9.80665 | 0.3059 g |
| Car's weight: 1,500 × 9.80665 | 14,710 N (3,307 lbf) |
Notice that the force needed to accelerate the car at 3 m/s² is less than a third of its weight. That's why you can't lift a car, but a few people can push one along a flat road (slowly, since friction also pushes back).
Common mistakes
- Using pounds as force and mass interchangeably. In US units, "pound" can mean mass (lb) or force (lbf). A 1 lb mass weighs 1 lbf on Earth, but F = ma only works directly in newtons with kilograms.
- Forgetting other forces. F = ma uses the net force. Subtract friction, drag or anything pushing the other way first.
- Using grams. 500 g × 2 m/s² is 1 N, not 1,000 N. Convert grams to kilograms first.
- Calling weight mass. Bathroom scales show kilograms or pounds of mass, but they actually measure the force your weight puts on them.
Frequently asked questions
What is Newton's second law?
The net force on an object equals its mass times its acceleration: F = m × a. Push twice as hard and the acceleration doubles; push the same on something twice as heavy and the acceleration halves. With mass in kilograms and acceleration in m/s², the force comes out in newtons.
What is a newton?
One newton is the force that gives a 1 kg mass an acceleration of 1 m/s². It's a small force: holding a medium apple (about 100 grams) against gravity takes roughly 1 newton.
What is the difference between mass and weight?
Mass is how much matter an object has, in kilograms, and it's the same everywhere. Weight is the force gravity pulls it with, in newtons: weight = m × g. On Earth, a 70 kg person weighs about 686 N; on the Moon the same person still has 70 kg of mass but weighs only about 113 N.
How do I convert newtons to pound-force?
Divide newtons by 4.448222. So 4,500 N is about 1,012 lbf. One pound-force is the weight of a 1-pound mass under standard gravity, which is why a 1,500 kg car (3,307 lb) weighs 3,307 lbf.
Is F = ma the net force or any force?
It's the net force, the total of all forces acting on the object added up with their directions. If you push a box with 100 N and friction pushes back with 60 N, only the 40 N difference accelerates the box.
Rates and figures last checked October 2026.
This calculator gives estimates for planning. Check current rates and product labels before you buy, list or file.