Newton's second law: the net force on an object equals its mass times its acceleration, in the same direction — F = m·a. This free calculator solves for the force, the mass or the acceleration, in any unit, shows the weight of the mass on Earth, and gives every step of the working.
Newton's second law is the quantitative heart of mechanics: the net force on an object equals its mass times its acceleration, in the same direction — F = m·a. For the full background, see our guide to Newton's second law. The law is fully vector: components add independently, so you must sum every contribution — applied forces, gravity, the normal force and the friction force opposing motion — to find the net force F before using it here. Rearranged as a = F/m, the same law gives the acceleration a given net force produces; rearranged as m = F/a it gives the mass.
There are three steps. First, decide what you want — the force F, the mass m or the acceleration a — and pick it in the calculator's Solve for menu. Second, enter the two values you know: force in newtons, kilonewtons or pounds-force; mass in kilograms, grams or tonnes; and acceleration in m/s² or as a multiple of g. Third, read the answer with the worked steps, which show the formula, your numbers substituted in, and the result with units. The weight of the mass on Earth, W = m·g, is shown alongside.
Two relationships are worth feeling directly. For a fixed mass, acceleration is proportional to net force — double the force and the acceleration doubles. For a fixed force, acceleration is inversely proportional to mass — a heavier object accelerates less under the same push. This is why a sports car with a powerful engine but light body out-accelerates a loaded truck: more force, less mass.
Weight is Newton's second law applied to gravity. Set the acceleration to g, the acceleration due to gravity (about 9.81 m/s² on Earth), and F = m·a becomes W = m·g. To explore the energy a moving mass carries, see the kinetic energy calculator; to follow the momentum a force changes over time, see the momentum calculator, or look up a term in the physics glossary.
A 10 kg crate is pushed so that it accelerates at 3 m/s². The net force is F = m·a = 10 × 3 = 30 N. Double the acceleration to 6 m/s² and the force needed doubles to 60 N; double the mass to 20 kg at the original 3 m/s² and again 60 N is required — a direct illustration of the proportional relationships in F = m·a. That same 10 kg mass weighs W = m·g = 10 × 9.81 = 98.1 N on Earth.
Newton's second law underlies structural and mechanical engineering, rocketry and spaceflight, automotive and aircraft design, robotics, and essentially every dynamics problem in mechanics. Anywhere a force has to be turned into motion — or a required motion has to be turned back into the force that produces it — F = m·a is the starting point.
Newton's second law states that the net force on an object equals its mass times its acceleration, F = m·a, with the force and acceleration pointing in the same direction. Equivalently, the acceleration a body undergoes is the net force divided by its mass, a = F/m. It is the quantitative heart of classical mechanics: it links the cause of motion (force) to its effect (acceleration).
F in F = m·a is the net (resultant) force — the vector sum of every force acting on the object, including gravity, the normal force, applied pushes and the friction force opposing motion. A single force on its own does not determine the acceleration; only the net force does. Because force is a vector, components add independently, so you sum each direction (x, y, z) separately to find the resultant.
Weight is simply Newton’s second law applied to gravity: the acceleration is g, the acceleration due to gravity, so W = m·g. On Earth g ≈ 9.81 m/s², so a 10 kg mass weighs about 98.1 N. Weight is a force measured in newtons and changes with location (it is smaller on the Moon), whereas mass in kilograms is the same everywhere.
Force is in newtons (N), with kilonewtons and pounds-force available; mass is in kilograms (kg), with grams and tonnes; and acceleration is in m/s², with the option to enter it as a multiple of g (9.81 m/s²). One newton is the force that gives a 1 kg mass an acceleration of 1 m/s². The calculator converts every unit to SI internally and returns the result with the weight on Earth alongside.
F = m·a is an excellent approximation for everyday speeds, but it breaks down as objects approach the speed of light, where special relativity takes over and the simple m·a form no longer holds. For ordinary engineering, vehicles, projectiles and machinery it is exact for all practical purposes; only at relativistic speeds, or for very small particles governed by quantum mechanics, do other laws apply.