Force Calculator
Newton’s second law in one place: solve F = ma in any units, combine forces pulling in different directions, and weigh anything on any planet.
By Manzoor Ahmad, pharmacist · Updated How do you calculate force?
Force = mass × acceleration (F = ma). With mass in kilograms and acceleration in m/s², the answer is in newtons. A 1,500 kg car accelerating at 3 m/s² needs a net force of 1,500 × 3 = 4,500 N. Rearranged, m = F ÷ a and a = F ÷ m.
Forces (N) and directions (0° = right, 90° = up)
Everyday forces in newtons
| Situation | Approximate force | How it is estimated |
|---|---|---|
| Holding an apple | 1 N | 0.1 kg × 9.81 m/s² |
| Weight of a 70 kg adult | 686 N | 70 × 9.81 |
| Car accelerating briskly | 4,500 N | 1,500 kg × 3 m/s² |
| Emergency stop in a car | ≈ 12,000 N | 1,500 kg × 8 m/s² |
| Boeing 737 takeoff thrust | ≈ 240 kN | two engines × ~120 kN |
| Saturn V liftoff thrust | ≈ 35 MN | five F-1 engines × 6.8 MN |
Newton’s three laws in one line each
- First law: with zero net force, an object keeps its velocity (at rest or moving straight at constant speed).
- Second law: net force equals mass times acceleration, F = ma. See also the acceleration calculator.
- Third law: every force has an equal and opposite partner acting on the other object.
Force FAQs
Newton's second law: F = m × a. Force in newtons equals mass in kilograms times acceleration in m/s². One newton accelerates 1 kg at 1 m/s².
Multiply them. A 1,500 kg car accelerating at 3 m/s² needs a net force of 1,500 × 3 = 4,500 N (4.5 kN).
Rearrange to m = F ÷ a. A 500 N net force producing 2 m/s² means the object's mass is 250 kg.
Use a = F ÷ m. A 20 N push on a 4 kg cart gives 5 m/s², ignoring friction.
Net force is the vector sum of all forces on an object. Forces in opposite directions subtract; forces at angles combine by components: Fx = ΣF cos θ, Fy = ΣF sin θ, and |F| = √(Fx² + Fy²).
√(3² + 4²) = 5 N, pointing 53.1° from the 3 N force toward the 4 N force.
Mass (kg) is the amount of matter and does not change. Weight is the gravitational force on that mass, W = mg, measured in newtons. A 70 kg person weighs 686 N on Earth and 113 N on the Moon.
On Earth, a 1 kg mass weighs 9.80665 N under standard gravity, which equals 1 kilogram-force (kgf). Kilograms measure mass, newtons measure force.
Divide by 4.448222. 1,000 N ≈ 224.8 lbf, and 1 lbf = 4.448 N.
The object stays at rest or keeps moving at constant velocity (Newton's first law). Balanced forces mean zero acceleration, not necessarily zero motion.
Yes. Force has both magnitude and direction, which is why two 10 N forces can add to anything from 0 N (opposite) to 20 N (same direction).
The SI unit is the newton (N = kg·m/s²). Others include the kilonewton (kN), pound-force (lbf), kilogram-force (kgf) and dyne (1 dyn = 10⁻⁵ N).
Sources
F = ma gives the net force. Real situations also involve friction, drag and other forces that you must include in the sum. Standard gravity is 9.80665 m/s².