Force Calculator (F = ma)
Calculate force, mass, or acceleration using Newton's Second Law of Motion.
Why & What
Newton's Second Law of Motion is one of the most important principles in physics. It explains the relationship between force, mass, and acceleration—the foundation for understanding how objects move and interact.
Force (F) is a push or pull that can change an object's motion. Mass (m) is the amount of matter in an object—its resistance to acceleration. Acceleration (a) is the rate of change of velocity. The law states that force equals mass times acceleration.
Newton's Second Law
- Force: Newton (N) = kg⋅m/s²
- Mass: kilogram (kg)
- Acceleration: meters per second squared (m/s²)
Calculator
How to Read Results
Force in Newtons: 1 Newton is the force needed to accelerate 1 kg by 1 m/s². For reference, Earth's gravity exerts about 9.81 N on every kilogram of mass.
Everyday examples: Lifting an apple (about 1 N), pushing a shopping cart (50-100 N), a car engine's force (several thousand N).
Weight vs. Mass: Weight is a force (measured in Newtons) = mass × gravitational acceleration. On Earth, a 70 kg person weighs about 686 N.
Examples
A 5 kg object accelerates at 3 m/s². What force is applied?
F = 5 kg × 3 m/s² = 15 N
What is the weight of a 70 kg person on Earth? (g = 9.81 m/s²)
F = 70 kg × 9.81 m/s² = 686.7 N
A 1000 kg car is pushed with 5000 N of force. What is its acceleration?
a = 5000 N ÷ 1000 kg = 5 m/s²
Limitations & Disclaimer
- This calculator uses the classical (Newtonian) model, which breaks down at very high speeds (relativistic effects).
- Assumes a single net force—real situations often involve multiple forces.
- Does not account for friction, air resistance, or other opposing forces.
- Mass must be constant (not applicable to rockets losing fuel).
- For educational purposes only.