Force Calculator: F = m × a (Newton's 2nd Law)
Solve force, mass or acceleration from the other two with Newton's second law, F = m·a. Pick units such as N, lbf, m/s² and g, and see each step. Free and private.
Fill in all but one field: the empty field is the one you solve for.
About the Force Calculator
The Force Calculator applies Newton's second law, F = m × a, and solves for whichever of Force, Mass or Acceleration you leave empty. Type two values and the third appears as you type, together with the formula in standard notation and a one-line substitution such as 1,500 kg × 2 m/s² = 3,000 N.
Newton's second law says that the net force on an object equals its mass times its acceleration. Push a heavier object and it speeds up more slowly. Push a lighter one with the same force and it speeds up more. This single relationship underlies most introductory mechanics, from cars and rockets to lifts and playground swings.
How to use the force calculator
Steps
- Fill in two of the three fields and leave the one you want to find empty.
- Choose a unit for each. Force offers N, kN, lbf and dyn, mass offers kg, g and lb, and acceleration offers m/s², ft/s² and g.
- Read the result under the formula. Change the unit of the empty field to see the answer in another unit.
- Press Clear all to reset every field.
Mass must be greater than zero. Force and acceleration can be negative, because a negative value simply means the force or acceleration points the other way. If all three fields are filled, clear one so the calculator knows what to solve, and if fewer than two are filled, it shows a hint.
Formula
One newton is the force that gives a 1 kg mass an acceleration of 1 m/s², so 1 N = 1 kg·m/s². The force in the formula is the net force, the sum of every force acting on the object, not just one of them.
Worked examples
Example 1: find the force
A 1,500 kg car accelerates at 2 m/s². The net force is F = 1,500 × 2 = 3,000 N, or 3 kN.
Example 2: find the acceleration
A 12 kg trolley is pushed with a net force of 60 N. Its acceleration is a = 60 ÷ 12 = 5 m/s².
Example 3: find the mass
A net force of 500 N produces an acceleration of 2.5 m/s². The mass is m = 500 ÷ 2.5 = 200 kg.
Common mistakes
- Using one force instead of the net force. If you push a box with 50 N and friction pushes back with 20 N, the net force is 30 N, and that is the value to use.
- Mixing mass and weight. Mass is measured in kilograms. Weight is a force, in newtons. The Weight Calculator converts between them.
- Forgetting the unit. An acceleration entered as 2 g is about 19.6 m/s², not 2 m/s². Pick the unit that matches your number.
Privacy
Nothing is uploaded; every calculation runs in your browser and never leaves your device.
Related tools
The Force Converter changes newtons to pounds-force and back, the Acceleration Converter converts between m/s², ft/s² and g, and the Momentum Calculator covers the closely related p = m × v.
Frequently asked questions
What is Newton's second law?
It states that the net force on an object equals its mass times its acceleration, F = m × a. A bigger force gives a bigger acceleration, and a bigger mass gives a smaller one for the same force.
How do I calculate force from mass and acceleration?
Enter the mass and the acceleration and leave the force field empty. A 1,500 kg car accelerating at 2 m/s² needs a net force of 3,000 N. The calculator shows the formula and the substitution.
Can I find mass or acceleration instead?
Yes. Fill in force and acceleration to get mass, or force and mass to get acceleration. For example, 60 N on a 12 kg trolley gives 5 m/s², and 500 N at 2.5 m/s² means a mass of 200 kg.
Which units are supported?
Force offers N, kN, lbf and dyn. Mass offers kg, g and lb. Acceleration offers m/s², ft/s² and g, where 1 g is 9.80665 m/s². The answer uses the unit chosen on the empty field.
Is the force the same as weight?
No. The force in F = m × a is the net force that causes the acceleration. Weight is a specific force, mass times gravitational acceleration, and you can compute it with the Weight Calculator.
Can force or acceleration be negative?
Yes. A negative sign means the force or acceleration points in the opposite direction. Mass must be greater than zero, and the calculator shows a message beside the field if it is not.
Is anything uploaded when I calculate?
No. The mass, force and acceleration you type are processed locally in your browser, and nothing is uploaded, stored or shared with a server, so private design numbers stay on your device.