Force Calculator (Newton's Law)
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
Newton's second law gives force with F = m × a, where m is mass in kg and a is acceleration in m/s². For a 10 kg mass under gravitational acceleration (9.81 m/s²), the force is 98.1 N.
Explanation
Newton's second law (the fundamental principle of dynamics) relates the net force applied to an object, its mass, and the acceleration it undergoes: F = m × a. This relationship means that for the same mass, an object accelerates faster the greater the force applied to it, and that for the same force, a more massive object accelerates more slowly than a lighter one. The resulting force is expressed in newtons (N), the SI unit of force, defined precisely as the force needed to give a 1 kg mass an acceleration of 1 m/s². A very common special case of this law is calculating an object's weight, where the acceleration is that of Earth's gravity (about 9.81 m/s²): our weight calculator applies this exact case directly. This calculator stays deliberately more general, with a free acceleration input, for any scenario where the acceleration isn't Earth's gravity (braking, a vehicle accelerating, centripetal force, physics applied to another celestial body). For the energy associated with a moving object rather than the force that accelerates it, see our kinetic energy calculator.
Example: a 10 kg mass under Earth's gravity
Inputs
Mass: 10 kg. Acceleration: 9.81 m/s².
Calculation
Force = 10 × 9.81 = 98.1 N.
Result
The force exerted on this mass is 98.1 N — that's also its weight on Earth.
Frequently asked questions
What's the difference between force and weight?
Weight is a special case of force: it's the force exerted by gravity on an object, calculated with this same formula F = m × a, but with the acceleration set to that of gravity (about 9.81 m/s² on Earth, different on the Moon or another planet). This calculator leaves acceleration free, for any scenario where a force accelerates a mass, not just under gravity.
What happens if the acceleration is negative?
A negative acceleration corresponds to slowing down (deceleration) relative to the direction chosen as positive. The formula still works as written: the result then gives a negative force, pointing opposite to the direction of motion — exactly what happens when braking.
Does this formula apply at speeds close to the speed of light?
No, F = m × a is a law of classical (Newtonian) mechanics, valid at speeds far below the speed of light — which covers nearly all everyday and engineering situations. At relativistic speeds, the relationship between force, mass, and acceleration becomes more complex and falls under Einstein's relativistic mechanics.