Physics
Force Calculator
Solve for force, mass, or acceleration using Newton's second law, F = m · a. Pick any unit, fill in two values, and the third updates live — with the full working shown.
Solve for
20
Solved from the other two
Force
20N
F = m · a
Force
20 N
Mass
10 kg
Accel
2 m/s²
Recomputes live as you type.
Try an example
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The basics
What is force?
A force is a push or a pull — an interaction that can change an object's motion. Newton's second law makes that precise: the net force on a body equals its mass times the acceleration it produces. Force, mass, and acceleration are locked together by one equation, so knowing any two always gives you the third.
F = m · a
The law of motion
Net force equals mass times acceleration. Bigger mass or faster acceleration means a bigger force. This is the form you reach for when you know m and a.
10 kg · 2 m/s² = 20 N
1 N = 1 kg·m/s²
What a newton is
The newton is built from the law itself: the force that accelerates one kilogram at one metre per second squared. It is the SI unit force is always reported in.
≈ the weight of a small apple
Method
How to calculate force by hand
Three steps, whichever quantity you are solving for.
- 1
Identify what you know and what you want
Note which two of F, m, and a you have, and which one is missing.
have m and a → want F - 2
Pick the right form of the law
Use F = m · a for force, m = F ÷ a for mass, or a = F ÷ m for acceleration.
F = m · a - 3
Substitute in SI units and compute
Put mass in kilograms and acceleration in m/s², multiply or divide, and read the answer in newtons.
F = 10 · 2 = 20 N
Worked examples
Solve for each quantity
The same law, rearranged three ways. Switch tabs to see force, mass, and acceleration each worked out from the other two.
Given m = 8 kg, a = 5 m/s²
Write the law: F = m · a
Substitute: F = 8 · 5
F = 40 N
Worth knowing
The everyday forces
The single number from F = m · a is the net force — the sum of all the individual pushes and pulls acting at once.
W = m · g
Gravity (weight)
The pull of a planet on a mass. On Earth it points down and sets how heavy something feels.
N ⟂ surface
Normal force
The push a surface gives back, perpendicular to it, that stops objects sinking through the floor.
f ≤ μN
Friction
Resists sliding between surfaces. It always opposes the direction of motion or attempted motion.
T along rope
Tension
The pull transmitted through a rope, cable, or chain, directed along its length.
Where it shows up
Why the law matters
One equation that designs cars, launches rockets, and keeps buildings standing.
F = m · a
Vehicle engineering
Engineers size engines and brakes from the force needed to accelerate — and stop — a known mass.
thrust > weight
Rocketry
A rocket lifts off only when engine thrust beats its weight, leaving a net upward force to accelerate it.
ΣF = 0
Structures
Bridges and buildings are designed so forces balance to zero — no net force, no unwanted acceleration.
Reference
How big is a newton?
A gut-feel scale for everyday forces, so the answers from the calculator mean something.
Resting an apple in your hand≈ 1 N
Weight of a 1 kg bag of sugar≈ 9.8 N
Pressing a doorbell button≈ 5 N
Weight of an adult human (70 kg)≈ 686 N
Force to open a heavy door≈ 50 N
Bite force of a human jaw≈ 700 N
Pull of a small car engine≈ 2,000 N
Thrust of a jet engine≈ 1,000,000 N
Quick chart
What would you weigh on each planet?
Your mass stays the same everywhere, but weight is a force — W = m · g — so it changes with each world's gravity. Enter a mass to see it across the solar system.
A mass of
weighs this on each body (W = m · g)kg
BodyGravity (m/s²)Weight
Sun
274
19180 N
27.94× Earth
Jupiter
24.79
1735.3 N
2.53× Earth
Neptune
11.15
780.5 N
1.14× Earth
Saturn
10.44
730.8 N
1.06× Earth
EarthYou are here
9.80665
686.4655 N
1.00× Earth
Venus
8.87
620.9 N
0.90× Earth
Uranus
8.69
608.3 N
0.89× Earth
Mars
3.721
260.47 N
0.38× Earth
Mercury
3.7
259 N
0.38× Earth
Moon
1.62
113.4 N
0.17× Earth
Pluto
0.62
43.4 N
0.06× Earth
Earth's standard gravity g = 9.80665 m/s². Your mass never changes — only the weight does.
Properties
Rules worth remembering
A handful of facts that keep F = m · a from tripping you up.
ΣF = m · a
It's the net force
Only the resultant of all forces drives acceleration. Balanced forces sum to zero and leave motion unchanged.
ΣF = 0 → a = 0
No net force, no acceleration
An object with zero net force keeps doing what it was doing — at rest or at constant velocity. That is Newton's first law.
m ≠ weight
Mass is not weight
Mass is constant; weight is the gravitational force on it and shifts with location. Confusing the two is the most common mistake.
F is a vector
Direction counts
Force has direction. Add forces as vectors before applying the law, and the acceleration points the same way as the net force.
1 N = 1 kg·m/s²
Keep units consistent
Newtons need kilograms and m/s². Mixing pounds with m/s² gives nonsense — convert first, as the calculator does for you.
F₁₂ = −F₂₁
Forces come in pairs
Every force has an equal and opposite reaction. The two act on different objects, so they do not cancel on either one.
Going further
Formulas built on force
Once you can find a force, these related quantities follow directly.
W = F · d
Work
Force applied over a distance does work, measured in joules — the energy transferred to the object.
p = m · v
Momentum
Net force is also the rate of change of momentum, the deeper form of Newton's second law.
P = F / A
Pressure
Spread a force over an area and you get pressure, in pascals — why sharp blades cut and wide skis float.
Lookup chart
Common forces at a glance
The force needed to accelerate an everyday mass, worked straight from F = m · a — the fast answer to “how much force to accelerate a 1,000 kg car”.
ScenarioMassAccel.Force
Apple in free fall0.1 kg9.81 m/s²0.98 N
Cart given a push20 kg1.5 m/s²30 N
Cyclist + bike easing off90 kg1 m/s²90 N
Person in an accelerating lift70 kg2 m/s²140 N
Sprinter off the blocks75 kg8 m/s²600 N
Compact car pulling away1,200 kg3 m/s²3,600 N
Loaded pickup2,500 kg2 m/s²5,000 N
Sedan hard acceleration1,500 kg4 m/s²6,000 N
And the weight of a common mass on Earth — a force too, from W = m · g with g ≈ 9.81 m/s².
1 kg9.81 N
5 kg49.05 N
10 kg98.1 N
20 kg196.2 N
50 kg490.5 N
70 kg686.7 N
100 kg981 N
1,000 kg9,810 N
FAQ
Common questions
Newton's second law states that the net force on an object equals its mass times its acceleration: F = m · a. The more massive the object or the harder it accelerates, the larger the force involved.
Multiply mass by acceleration: F = m · a. A 10 kg box pushed to accelerate at 2 m/s² needs 10 × 2 = 20 newtons of net force.
A newton (N) is the SI unit of force. One newton is the force that accelerates a 1 kg mass at 1 m/s², so 1 N = 1 kg·m/s². Holding a small apple takes roughly one newton.
Rearrange F = m · a to m = F ÷ a, then divide the force by the acceleration. A 120 N force producing 4 m/s² acts on a mass of 120 ÷ 4 = 30 kg.
Rearrange to a = F ÷ m and divide the force by the mass. A 600 N force on a 75 kg sprinter gives 600 ÷ 75 = 8 m/s².
Mass is the amount of matter in an object and never changes. Weight is the gravitational force on that mass, W = m · g, so weight depends on where you are. A 70 kg person weighs about 686 N on Earth but only about 113 N on the Moon.
Weight is a force, so use W = m · g where g is the local gravity. On Earth g = 9.80665 m/s², so a 50 kg mass weighs 50 × 9.80665 ≈ 490 N.
Yes. Force has both a magnitude and a direction, and forces add as vectors. When several forces act, it is the net (resultant) force that goes into F = m · a.
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Ugo CharlesBuilt and fact-checked against our editorial standards · Last updated June 2026
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