This calculator solves Newton's Second Law of Motion, F = ma, for whichever of the three variables you do not already know: force, mass, or acceleration. Physics and engineering problems rarely hand you all three values at once, so rather than rearranging the formula by hand you pick what you want to solve for from the dropdown, then enter the two values you do know. To find force, enter mass in kilograms and acceleration in metres per second squared. To find mass, enter force in newtons and acceleration. To find acceleration, enter force and mass. The calculator returns your answer in the main result tile, plus the same force value converted to kilonewtons and pound-force, and a calculation breakdown showing the formula used and each input alongside the solved value. A separate unit conversion table also expresses the force in newtons, kilonewtons, pound-force, dyne, and kilogram-force, and a worked example spells out the exact sum performed. It is useful for checking homework, sizing motors, brakes, or structural loads, or working out the weight of an object under a known gravitational acceleration. Because it applies Newton's Second Law directly, the figure it gives is the net force only; real mechanical systems also involve friction, drag, and other resistances that must be added separately, so treat the result as an indicative physics calculation rather than a full engineering design figure.
Newton's Second Law of Motion is one of the most fundamental relationships in classical physics. It states that the net force acting on an object is directly proportional to its mass and its acceleration. In equation form: F = m × a, where F is force in newtons (N), m is mass in kilograms (kg), and a is acceleration in metres per second squared (m/s²).
The law can be rearranged to solve for any of the three variables:
One newton (N) is the SI unit of force. It is defined as the force required to accelerate a mass of one kilogram at one metre per second squared. This means: 1 N = 1 kg × 1 m/s². Named after Sir Isaac Newton, who published his laws of motion in 1687 in his work Principia Mathematica, this unit is the standard throughout science and engineering.
| Context | Acceleration (m/s²) | Notes |
|---|---|---|
| Earth's surface gravity (g) | 9.81 | Standard gravity; used to calculate weight |
| Moon's surface gravity | 1.62 | About 1/6 of Earth's |
| Mars surface gravity | 3.72 | About 38% of Earth's |
| Free fall (Earth) | 9.81 | Ignoring air resistance |
| Typical car braking | 7 to 9 | Emergency braking on dry road |
| Sports car 0-100 km/h | 5 to 8 | Depends on vehicle |
A car of mass 1,500 kg accelerates at 3 m/s². What is the net force required?
F = m × a = 1,500 kg × 3 m/s² = 4,500 N (or 4.5 kN)
This is the net force, meaning the total forward thrust minus any friction or drag. In practice, the engine must produce more than 4,500 N of force to overcome resistance and still achieve this acceleration.
Weight is a common application of F = ma. Your weight in newtons is your mass in kilograms multiplied by the acceleration due to gravity (9.81 m/s² on Earth). For example, a person of mass 70 kg weighs 70 × 9.81 = 686.7 N. When you stand on bathroom scales, they measure this gravitational force and display it as kilograms for convenience. In physics, however, weight is always a force in newtons, while mass is always in kilograms.
Method: Formula applied: F = m × a (Newton's Second Law of Motion). Unit conversions: 1 kN = 1,000 N; 1 lbf = 4.44822 N; 1 dyne = 0.00001 N; 1 kgf = 9.80665 N. Reference: Newton, I. (1687). Philosophiae Naturalis Principia Mathematica. NIST SI Units (physics.nist.gov).
This calculator applies Newton's Second Law and assumes all values are in SI units (kg, m/s², N). It calculates net force only. Real-world forces include friction, drag, and other resistances which must be accounted for separately in engineering applications.