How to calculate force, mass and acceleration
Newton's second law of motion ties together three quantities with one simple equation: F = m × a. Here F is the net force acting on an object, measured in newtons (N); m is the object's mass in kilograms (kg); and a is its acceleration in metres per second squared (m/s²). Because the three are linked by a single relationship, knowing any two of them lets you rearrange the formula and find the third.
To solve for one quantity, rearrange the equation: F = m × a for force, m = F / a for mass, and a = F / m for acceleration. This calculator detects which field you leave blank and applies the matching form automatically, guarding against division by zero when a needed value is missing.
Units do not have to be SI. Force may be entered in newtons (N), kilonewtons (kN) or pound-force (lbf); mass in kilograms (kg), grams (g) or pounds (lb); and acceleration in m/s², multiples of standard gravity g, or ft/s². The calculator converts every input to newtons, kilograms and m/s², computes with F = m × a, then converts the answer back into the unit you selected. Switching on the weight preset fixes the acceleration at standard gravity, g = 9.80665 m/s², so you can read an object's weight force directly from its mass.
Common units and SI conversions
| Quantity | Unit | SI conversion |
|---|---|---|
| Force (F) | kN | 1 kN = 1,000 N |
| Force (F) | lbf | 1 lbf ≈ 4.4482216 N |
| Mass (m) | g | 1 g = 0.001 kg |
| Mass (m) | lb | 1 lb ≈ 0.45359237 kg |
| Acceleration (a) | g | 1 g = 9.80665 m/s² |
| Acceleration (a) | ft/s² | 1 ft/s² = 0.3048 m/s² |
Reference note: this is a neutral physics math tool. F = m × a applies to the net (total) force on an object of constant mass in an inertial frame. Standard gravity is defined as g = 9.80665 m/s²; local gravity varies slightly with latitude and altitude. The pound-force and pound-mass conversions use the international avoirdupois pound.
Frequently asked questions
- What is the force formula?
- The force formula is Newton's second law: F = m × a, where F is the net force in newtons, m is the mass in kilograms and a is the acceleration in m/s². Rearranged, mass is m = F / a and acceleration is a = F / m, so any two of the three quantities give the third.
- What is a newton?
- A newton (N) is the SI unit of force. One newton accelerates a one-kilogram mass at one metre per second squared, so 1 N = 1 kg·m/s². Holding a small 100-gram apple against gravity takes roughly one newton.
- How do I find mass from force?
- Rearrange F = m × a to m = F / a: divide the force by the acceleration. A 20 N force producing 4 m/s² acts on 20 / 4 = 5 kg. Enter the force and acceleration, leave the mass blank, and the calculator solves for it.
- What is the difference between mass and weight?
- Mass is the amount of matter in an object, in kilograms, and does not change with location. Weight is the force of gravity on that mass, in newtons, equal to W = m × g. On Earth g ≈ 9.80665 m/s², so a 1 kg mass weighs about 9.81 N.
- How do I convert lbf to N?
- One pound-force equals about 4.4482216 newtons. Multiply lbf by 4.4482216 to get newtons, or divide newtons by 4.4482216 to get lbf. For example, 10 lbf ≈ 44.48 N. This tool converts inputs to newtons internally before computing.
- What is F=ma?
- F = ma is Newton's second law of motion: the net force on an object equals its mass times its acceleration. A larger force gives a larger acceleration, while a larger mass resists acceleration, so for the same force a heavier object speeds up more slowly.