Newton's second law is the engine of mechanics: the net force on an object equals its mass times its acceleration, F = ma. Push something and it speeds up; push the same amount on something heavier and it speeds up less. The law ties together the three quantities so tightly that knowing any two gives the third — and it also defines weight, which is just the force of gravity on a mass, W = mg. That distinction between mass (how much stuff) and weight (the pull on it) trips up many, and this calculator keeps them straight.
Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: Newton's second law of motion.
The force equations
With mass in kilograms and acceleration in metres per second squared, force comes out in newtons — one newton accelerates 1 kg by 1 m/s². Because acceleration is force divided by mass, doubling the mass halves the acceleration for the same push, and doubling the force doubles the acceleration. Weight is a special case where the acceleration is gravity, which is why a mass "weighs" different amounts on different worlds.
Worked example — accelerating a car
Scenario: A 1,500 kg car accelerates at 3 m/s². What driving force is needed, and what does the car weigh?
The engine must deliver 4,500 N at the wheels to give 3 m/s². That same 4,500 N on a lighter 900 kg car would produce a brisker 5 m/s², since a = F/m. The car's weight — the gravity force holding it on the road — is a much larger 14,715 N, the force you would feel supporting its 1,500 kg mass. Force expressed as ~459 kgf simply means "as heavy as a 459 kg mass."
Frequently Asked Questions
F = m × a. A 1500 kg car at 3 m/s² needs 4500 N. Mass in kg, acceleration in m/s² → force in newtons.
Net force = mass × acceleration (F = ma). Heavier objects accelerate less under the same force.
m = F/a, a = F/m. 4500 N on 1500 kg = 3 m/s²; on 900 kg = 5 m/s².
Mass (kg) is fixed; weight is gravity's force W = mg (N). 10 kg weighs ~98 N on Earth, ~16 N on the Moon.
kgf = N ÷ 9.81 (4500 N ≈ 459 kgf); lbf = N × 0.224809 (4500 N ≈ 1012 lbf).