Force Calculator
Calculate force using Newton's second law F = m × a. Solve for force, mass or acceleration instantly in newtons, with the rearranged formula and steps shown.
Updated 2026-06-14 · Free · No sign-up · Runs privately in your browser
Show the formula & steps
How the Force Calculator Works
This calculator applies Newton’s second law of motion to relate force, mass and acceleration. Pick which quantity you want to solve for — force, mass or acceleration — then enter the other two values. The result appears instantly in newtons (N), kilograms (kg) or m/s² as appropriate.
Newton’s second law states that the net force on an object equals its mass times its acceleration. A bigger force produces a bigger acceleration, while a heavier object needs more force to accelerate at the same rate.
The Formula
The core equation and its rearranged forms are:
F = m × a m = F ÷ a a = F ÷ m
Where:
- F = force (newtons, N)
- m = mass (kilograms, kg)
- a = acceleration (metres per second squared, m/s²)
Worked Example
Suppose a 20 kg cart is pushed so it accelerates at 5 m/s². To find the force:
- F = m × a
- F = 20 × 5 = 100 N
As an equivalent weight, 100 ÷ 9.80665 ≈ 10.2 kgf — roughly the gravitational pull on a 10 kg mass.
Now solve the reverse: if the same 100 N acts on the cart, the acceleration is a = F ÷ m = 100 ÷ 20 = 5 m/s², confirming the relationship.
Force, Mass and Acceleration at a Glance
The table shows how the three quantities trade off. Doubling the mass halves the acceleration for the same force; doubling the force doubles the acceleration for the same mass.
| Force (N) | Mass (kg) | Acceleration (m/s²) |
|---|---|---|
| 100 | 10 | 10 |
| 100 | 20 | 5 |
| 200 | 20 | 10 |
| 50 | 25 | 2 |
| 980.7 | 100 | 9.81 (Earth gravity) |
Common Mistakes to Avoid
- Mixing up mass and weight. Weight is a force (in newtons); mass is in kilograms. To get weight from mass, multiply by g ≈ 9.81 m/s².
- Using grams instead of kilograms. The formula requires mass in kilograms for the answer to come out in newtons. Convert grams to kg by dividing by 1000.
- Forgetting net force. F = m × a uses the net (resultant) force. If several forces act at once, add them first — see a net force calculator for that step.
Frequently asked questions
What is the formula for force?+
Force is found with Newton's second law: F = m × a, where m is mass in kilograms and a is acceleration in metres per second squared. The result is in newtons (N). One newton is the force that accelerates a 1 kg mass at 1 m/s².
How do you calculate force from mass and acceleration?+
Multiply the mass by the acceleration. For example, a 20 kg object accelerating at 5 m/s² experiences a force of F = 20 × 5 = 100 N. Keep mass in kilograms and acceleration in m/s² so the answer comes out in newtons.
How do you find mass or acceleration from force?+
Rearrange F = m × a. To find mass, divide force by acceleration: m = F ÷ a. To find acceleration, divide force by mass: a = F ÷ m. This calculator does all three by choosing which quantity to solve for.
What is a newton?+
A newton (N) is the SI unit of force. One newton equals one kilogram-metre per second squared (1 N = 1 kg·m/s²): the force needed to accelerate a 1 kg mass at 1 m/s². For reference, holding a small apple feels like about 1 N.
What is the difference between mass and weight?+
Mass is the amount of matter in an object, measured in kilograms, and stays the same everywhere. Weight is the gravitational force on that mass: W = m × g, where g ≈ 9.81 m/s² on Earth. So a 10 kg mass weighs about 98.1 N on Earth.