Force Calculator (F = ma)
Calculate force using Newton's second law F = ma. Enter mass (kg) and acceleration (m/s²) to get force in Newtons, plus the object's weight on Earth.
How to use this tool
- Enter mass and acceleration in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your force and the full breakdown beneath it.
Newton's second law: F = ma. Force (N) equals mass (kg) times acceleration (m/s²). Weight is the force of gravity: W = mg where g = 9.81 m/s² on Earth's surface.
Formula
F = m × a
Weight on Earth: W = m × 9.81
Where m = mass (kg), a = acceleration (m/s²). Force and weight are in Newtons (N).
How it works
This calculator applies Newton's second law of motion: the net force on an object equals its mass multiplied by its acceleration. It also computes the object's weight — the gravitational force Earth exerts on it — using the fixed standard gravity of 9.81 m/s². The weight result assumes the object is stationary at sea level; weight varies slightly by latitude and altitude.
Worked example
- Given: mass m = 5 kg, acceleration a = 2 m/s².
- Calculate force: F = m × a = 5 × 2 = 10 N.
- Calculate weight on Earth: W = m × 9.81 = 5 × 9.81 = 49.05 N.
Force = 10 N; Weight on Earth = 49.05 N
Common mistakes to avoid
- Confusing net force with applied force -- if friction or air resistance is present, the net acceleration is lower than the applied force implies.
- Entering weight (in Newtons) instead of mass (in kg) for m, inflating the calculated force by 9.81x.
- Forgetting that F = ma gives the resultant force on the object, not the force the object exerts on another surface (Newton's third law is separate).
Key terms
- Newton's second law
- The principle that the net force acting on an object equals the product of its mass and acceleration (F = ma).
- Newton (N)
- The SI unit of force. 1 N is the force needed to accelerate a 1 kg mass at 1 m/s².
- Weight
- The gravitational force acting on a mass. On Earth, W = m × 9.81 N. Weight changes with local gravity; mass does not.
- Acceleration
- The rate of change of velocity, measured in m/s². A net force causes acceleration; zero net force means constant velocity.
Frequently asked questions
- What is the difference between mass and weight?
- Mass (kg) is a measure of the amount of matter — it doesn't change with location. Weight (N) is the gravitational force on that mass, which varies by planet.
- Can acceleration be negative?
- Yes — a negative value means deceleration (the force opposes motion).