Force Calculator
Solve F = ma for force, mass or acceleration — in newtons, kilonewtons or pound-force — with the rearranged formula shown for whichever direction you pick.
F = m·a
Force
Formula used for this direction
F = m·a
Your values
m = 1,200 kg, a = 2.7 m/s²
Force, Mass and Acceleration
Newton's second law is the hinge of classical mechanics: F = ma. Push an object and it accelerates; push twice as hard and it accelerates twice as much; make it twice as heavy and the same push produces half the acceleration.
Because it is one equation in three quantities, any two give the third. Rearranged, m = F ÷ a tells you the mass implied by a known push and its result, and a = F ÷ m tells you how quickly a known force will speed something up. This calculator solves all three directions rather than only for F.
Worked example — accelerating a car
A 1,200 kg car accelerating at 2.7 m/s² needs a net force of:
F = 1200 × 2.7 = 3,240 N, which is 728.4 lbf.
Braking at the same rate needs the same magnitude in the opposite direction: -3,240 N. Tyres have to supply that either way, which is why hard braking and hard acceleration both find the limits of grip.
A second example, working backwards. If you measure a 3,240 N net force producing 2.7 m/s², the mass must be m = 3240 ÷ 2.7 = 1,200 kg — the same car, deduced from its behaviour.
And at human scale. Pushing a 150 kg crate with 500 N of force gives a = 500 ÷ 150 = 3.333 m/s², assuming a frictionless floor. Real friction subtracts from the net force, which is why a real crate moves more slowly than this.
Common mistake
Using weight where mass belongs. In F = ma, m is mass in kilograms, not weight in newtons or pounds. A 70 kg person weighs 686.5 N on Earth — if you substituted that weight figure into F = ma you would overstate the answer by a factor of about 9.81. For reference, a 100 g apple weighs 0.9807 N.
What a 70 kg Person Weighs Elsewhere
Mass is constant; weight is not. Each row is W = m·g computed at that body's gravity.
| Body | Gravity | Weight of 70 kg | In pound-force |
|---|---|---|---|
| Mercury | 3.7 m/s² | 259 N | 58.23 lbf |
| Venus | 8.9 m/s² | 623 N | 140.1 lbf |
| Earth | 9.8 m/s² | 686 N | 154.2 lbf |
| Moon | 1.6 m/s² | 112 N | 25.18 lbf |
| Mars | 3.7 m/s² | 259 N | 58.23 lbf |
| Jupiter | 23.1 m/s² | 1,617 N | 363.5 lbf |
| Saturn | 9 m/s² | 630 N | 141.6 lbf |
| Uranus | 8.7 m/s² | 609 N | 136.9 lbf |
| Neptune | 11 m/s² | 770 N | 173.1 lbf |
| Pluto | 0.7 m/s² | 49 N | 11.02 lbf |
Gravity figures from the NASA NSSDC Planetary Fact Sheet, fetched 2026-09-19.
Keep going
- Rearranging F = ma for acceleration tells you how fast a given force will speed something up; the acceleration calculator solves that direction. Acceleration Calculator
- A force applied over a distance does work; the work calculator turns the force you just found into energy transferred. Work Calculator
Frequently Asked Questions
What is Newton's second law?
F = ma: the net force on an object equals its mass times its acceleration. The word 'net' matters — it is the sum of all forces acting, so an object pushed forward by 100 N against 40 N of friction accelerates as though a single 60 N force acted on it.
What is a newton, physically?
One newton is the force needed to accelerate one kilogram at one metre per second squared. It is a small unit in everyday terms: holding a 100 gram apple against gravity takes roughly 0.98 N, which is where the apple story gets its convenient arithmetic.
What is the difference between mass and weight?
Mass is how much matter an object contains and never changes. Weight is the force gravity exerts on that mass, W = m·g, so it changes with location. A 70 kg person has 70 kg of mass everywhere, but weighs about 686 N on Earth and only about 112 N on the Moon.
Why can't this solve for mass when acceleration is zero?
Because m = F ÷ a divides by the acceleration. Physically, an object moving at constant velocity has zero net force and zero acceleration — and from those two facts alone you cannot deduce anything about its mass. A feather and a freight train both satisfy 'no net force, no acceleration'.
What is pound-force and how does it relate to newtons?
Pound-force is the weight of one avoirdupois pound under standard gravity, so 1 lbf = 0.45359237 kg × 9.80665 m/s² = about 4.448 N. It is a force unit, distinct from the pound as a mass unit, and conflating the two is a classic source of engineering error.
Related Calculators
- Momentum Calculator — Forces & Rotation
- Torque Calculator — Forces & Rotation
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