Newton's second law of motion relates force, mass, and acceleration — one of the foundational equations in classical mechanics. This calculator finds force in newtons from a given mass and acceleration.
The formula
Where F is force in newtons (N), m is mass in kilograms (kg), and a is acceleration in meters per second squared (m/s²). For a 10 kg object accelerating at 9.8 m/s² (approximately Earth's gravity): F = 10 × 9.8 = 98 N.
Worked examples
| Mass | Acceleration | Force |
|---|---|---|
| 2 kg | 5 m/s² | 10 N |
| 1,200 kg (car) | 3 m/s² | 3,600 N |
| 0.5 kg | 20 m/s² | 10 N |
What a newton represents
One newton is the force required to accelerate a 1 kg mass at 1 m/s². It's a relatively small unit — a medium-sized apple resting on your hand exerts roughly 1 newton of force due to gravity.
Common mistakes
- Using weight instead of mass. Mass (kg) and weight (a force, in newtons) are different quantities — weight is actually mass times gravitational acceleration, so be careful not to double-apply gravity.
- Mixing units. Mass must be in kilograms and acceleration in m/s² for the result to come out directly in newtons.
Frequently asked questions
What is Newton's second law?
Newton's second law states that force equals mass times acceleration (F = m × a), describing how an object's motion changes in response to an applied force.
What unit is force measured in?
Newtons (N) in the SI system. One newton is the force needed to accelerate a 1 kilogram mass at 1 meter per second squared.
What's the difference between mass and weight?
Mass is the amount of matter in an object, measured in kilograms, and doesn't change with location. Weight is the force of gravity on that mass, measured in newtons, and varies depending on the local gravitational acceleration.