Force Calculator
Force (N)98.1000
Mass (kg)10.0000
Acceleration (m/s²)9.8100
Newton's second law, F = ma, ties together the three quantities at the heart of classical mechanics: the net force on an object, its mass, and the acceleration that force produces. This calculator lets you pick which of the three you want to solve for and supplies the other two, rearranging the law accordingly. With mass in kilograms and acceleration in metres per second squared, the force comes out in newtons.
Formula
F = m × a (rearranged to m = F ÷ a and a = F ÷ m)
- F
- Net force in newtons (N)
- m
- Mass in kilograms (kg)
- a
- Acceleration in metres per second squared (m/s²)
How it works
- Choose which variable to solve for — force (F), mass (m), or acceleration (a) — using the solve-for selector.
- Enter the two known quantities. The calculator applies F = ma directly, or rearranges it to m = F ÷ a or a = F ÷ m as needed.
- It guards against dividing by zero, so solving for mass requires a non-zero acceleration and solving for acceleration requires a non-zero mass.
Worked example
Find the force needed to accelerate a 10 kg mass at 9.8 m/s² (roughly the weight of the mass under gravity).
- Select solve-for force, then enter mass = 10 and acceleration = 9.8.
- Apply F = m × a: 10 × 9.8.
F = 98 newtons.
Frequently asked questions
- What is the difference between force and weight?
- Weight is just the force gravity exerts on a mass, equal to mass times gravitational acceleration (about 9.8 m/s² on Earth). Force in general is any push or pull, F = ma, so weight is one specific case of this law.
- What units should I use?
- For an answer in newtons, use SI units: mass in kilograms and acceleration in metres per second squared. One newton is the force that accelerates 1 kg at 1 m/s².
- Why does solving for mass need a non-zero acceleration?
- Rearranging the law gives m = F ÷ a, and dividing by an acceleration of zero is undefined. Likewise, solving for acceleration uses a = F ÷ m and requires a non-zero mass, so the calculator rejects zero in the denominator.
- Is this net force or total force?
- F = ma uses the net (resultant) force — the vector sum of all forces acting on the object. If several forces act at once, add them up first and enter the net value to get the resulting acceleration.