Newton's second law calculator
Enter two of the three quantities and get the third. Find the force needed to accelerate a car, the acceleration a push gives to a cart, or the mass that a known force speeds up at a known rate. Units can be mixed freely; the calculator converts them for you.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose what to find: force, mass or acceleration.
- Enter the other two quantities and pick their units.
- Read the answer in your unit, plus the force in newtons and the acceleration in g.
- Force: F = m × a.
- Mass: m = F ÷ a. Acceleration: a = F ÷ m.
- In g: a ÷ 9.80665 m/s².
Before the calculation every value is converted to SI: grams and pounds to kilograms (1 lb = 0.45359237 kg), ft/s² and g to m/s², kN and lbf to newtons.
Worked example
A 1200 kg car speeds up at 3 m/s². The net force is 1200 × 3 = 3,600 N, and the acceleration is 3 ÷ 9.80665 = 0.3059 g.
A 10 N push on a 2 kg cart with no friction gives a = 10 ÷ 2 = 5 m/s², or 0.5099 g.
Common mistakes
- Using one force instead of the sum. Subtract friction, drag and any opposing pull first.
- Mixing weight and mass. A mass of 70 kg weighs about 686 N; enter the mass in kg, not the weight.
- Grams in a physics problem. 500 g is 0.5 kg; the unit selector does the conversion if you leave the value in grams.
Frequently asked questions
What does Newton's second law say?
The net force on a body equals its mass times its acceleration, F = m × a. One newton is the force that gives 1 kg an acceleration of 1 m/s². The same force gives half the acceleration to twice the mass.
Why "net" force?
The law uses the sum of all forces acting on the body. If you push a box with 50 N and friction holds it back with 30 N, the net force is 20 N, and that is the number to enter here.
What is an acceleration of 1 g?
It is the standard acceleration of gravity, 9.80665 m/s². The result in g tells you how many times the pull of gravity the acceleration is; a car that gains 3 m/s² accelerates at about 0.31 g.
Can I use pounds?
Yes. Pick lb for mass and lbf for force. One pound-force is the weight of one pound at standard gravity, 4.44822 N, so 100 lbf gives 100 lb an acceleration of exactly 1 g.