Force Calculator
Find the force, mass or acceleration from the other two with Newton's second law, F = m × a. Mix units freely. Advanced adds weight on other planets, friction, forces on a slope, acceleration from a change in speed and the net force from several pushes and pulls.
F = m × a
The answer appears in the highlighted box; change its unit to see it another way. Mix units freely, for example pounds with m/s². A negative acceleration or force means slowing down (pointing the other way).
Weight and gravity
Weight is the force of gravity on the mass above: W = m × g. Earth uses standard gravity, 9.80665 m/s² (exact by definition); the others are approximate surface averages.
Friction on flat ground
Friction = μ × N. On flat ground the normal force N is the weight above. Is your force enough to slide the mass, and how fast does it speed up?
Forces on a slope
The mass above on a slope, with the friction coefficient and gravity from the sections above.
Acceleration from a change in speed
a = (final speed − starting speed) ÷ time, then F = m × a with the mass above.
Net force from several forces
Forces along one straight line. Pick the way each one pushes; the net force is the sum, and a = net force ÷ the mass above.
How your force is worked out
Your numbers: mass into kg, acceleration into m/s², then multiply them.
- 1
Mass in kg
10 kgalready kg
- 2
Acceleration in m/s²
2 m/s²already m/s²
- 3
Mass × acceleration
10 × 2= 20 N
- 4
Into your unit
20 Nalready newtons
Read more: the formula, worked examples, weight, friction and slopes
A force is a push or a pull. Newton's second law says the harder you push, the faster something speeds up, and the heavier it is, the slower it speeds up. Put as a formula, force = mass × acceleration.
The formula
force F = mass m × acceleration a
mass m = F ÷ a
acceleration a = F ÷ m
weight W = m × g, g = 9.80665 m/s² on Earth
friction = μ × normal force N
on a slope: down it = m × g × sin θ, into it = m × g × cos θ
net force on a slope = m × g × sin θ − μ × m × g × cos θ
acceleration from speeds a = (final speed − starting speed) ÷ time
net force = sum of the forces one way − sum of the forces the other way
m in kg, a in m/s², F in newtons (N)
Worked example
Force (the default): a 10 kg mass speeding up at 2 m/s². F = 10 × 2 = 20 N = 0.02 kN = 4.4962 lbf (20 ÷ 4.4482216152605) = 2.0394 kgf (20 ÷ 9.80665) = 2,000,000 dyn. The acceleration is 2 ÷ 9.80665 = 0.20394 g.
Mass: 20 N giving 2 m/s². m = 20 ÷ 2 = 10 kg.
Acceleration: 20 N on 10 kg. a = 20 ÷ 10 = 2 m/s².
US units: 1 lbf on a 1 lb mass. 1 lbf = 4.4482216152605 N and 1 lb = 0.45359237 kg, so a = 4.4482216152605 ÷ 0.45359237 = 9.80665 m/s², exactly 1 g.
Weight: 10 kg on Earth weighs 10 × 9.80665 = 98.0665 N (10 kgf). On the Moon (≈ 1.62 m/s²) it weighs about 10 × 1.62 = 16.2 N, on Mars (≈ 3.71) about 37.1 N and on Jupiter (≈ 24.79) about 247.9 N.
Friction on flat ground: greased steel, μ ≈ 0.1. Friction = 0.1 × 98.0665 = 9.80665 N. Pushing with the 20 N from above leaves 20 − 9.80665 = 10.19335 N, so the box speeds up at 10.19335 ÷ 10 = 1.019335 m/s², about half of what it would be with no friction.
Slope: the same 10 kg on a 30° slope, μ ≈ 0.1. Down the slope: 98.0665 × sin 30° = 98.0665 × 0.5 = 49.03325 N. Into the slope: 98.0665 × cos 30° = 98.0665 × 0.8660254 = 84.92808 N. Friction: 0.1 × 84.92808 = 8.49281 N. Net force: 49.03325 − 8.49281 = 40.54044 N, so it slides down at 40.54044 ÷ 10 = 4.05404 m/s². To push it up at a steady speed takes 49.03325 + 8.49281 = 57.52606 N. With μ = 0.1 it would stay put on slopes up to tan⁻¹(0.1) = 5.71°.
Change in speed: 0 to 100 km/h in 10 s. 100 km/h = 100 ÷ 3.6 = 27.7778 m/s, so a = (27.7778 − 0) ÷ 10 = 2.77778 m/s² (0.28325 g). For 10 kg that takes 10 × 2.77778 = 27.7778 N.
Net force: 50 N to the right, 15 N and 5 N to the left. Net = 50 − (15 + 5) = 30 N to the right, so 10 kg speeds up at 30 ÷ 10 = 3 m/s².
Force units
| Unit | In newtons | What it is |
|---|---|---|
| newton (N) | 1 | 1 kg × 1 m/s² |
| kilonewton (kN) | 1,000 | 1,000 N |
| pound-force (lbf) | 4.4482216152605 | weight of 1 lb under standard gravity |
| kilogram-force (kgf) | 9.80665 | weight of 1 kg under standard gravity |
| dyne (dyn) | 0.00001 | 1 g × 1 cm/s² |
Gravity on other worlds
| Where | g (m/s²) | Weight of 10 kg |
|---|---|---|
| Earth (standard) | 9.80665 | 98.0665 N |
| Moon | ≈ 1.62 | ≈ 16.2 N |
| Mars | ≈ 3.71 | ≈ 37.1 N |
| Jupiter | ≈ 24.79 | ≈ 247.9 N |
Rough friction coefficients
Typical sliding values only. Real friction changes a lot with the surface finish, dirt, wetness, temperature and speed, and the force to start something moving (static friction) is usually a bit higher than to keep it sliding.
| Surfaces | μ (rough) | Friction on 10 kg, flat |
|---|---|---|
| Rubber on dry concrete | 0.7 | 68.65 N |
| Rubber on wet concrete | 0.5 | 49.03 N |
| Wood on wood | 0.3 | 29.42 N |
| Steel on steel, greased | 0.1 | 9.807 N |
| Waxed ski on snow | 0.05 | 4.903 N |
| Steel on ice | 0.03 | 2.942 N |
Notes
- Standard gravity g = 9.80665 m/s² is a defined value; real gravity on Earth is about 9.78 m/s² at the equator and 9.83 m/s² at the poles. Moon, Mars and Jupiter values are rounded surface averages.
- The friction and slope sections use one μ for both starting and sliding, ignore air resistance and treat the mass as a block that slides rather than rolls. Use them as a rough guide, not for safety-critical design.
- The net force section adds forces along one straight line. Forces at an angle need splitting into parts first (like the slope section does).
- Unit factors are exact by definition: 1 lb = 0.45359237 kg, 1 ft = 0.3048 m, 1 kgf = 9.80665 N, 1 lbf = 4.4482216152605 N, 1 dyn = 0.00001 N.
Common questions
What is the formula for force?
Newton's second law: force = mass × acceleration, F = m × a. Mass in kilograms times acceleration in metres per second squared gives the force in newtons. Pushing a 10 kg box so it speeds up by 2 m/s every second takes 10 × 2 = 20 N.
What is a newton?
One newton (1 N) is the force that makes a 1 kg mass speed up by 1 m/s every second. It is about the weight of a small apple (102 g) on Earth. 1 kN = 1,000 N.
How do I find mass or acceleration from force?
Turn the formula around: m = F ÷ a and a = F ÷ m. 20 N giving 2 m/s² means a mass of 20 ÷ 2 = 10 kg; 20 N on 10 kg gives 20 ÷ 10 = 2 m/s².
What is the difference between mass and weight?
Mass is how much stuff there is (kg) and is the same everywhere. Weight is the force gravity puts on it: W = m × g. On Earth g = 9.80665 m/s², so 10 kg weighs 98.07 N. On the Moon (about 1.62 m/s²) the same 10 kg weighs only about 16.2 N.
What are lbf and kgf?
Pound-force (lbf) and kilogram-force (kgf) are the weights of 1 lb and 1 kg under standard gravity. 1 kgf = 9.80665 N exactly and 1 lbf = 0.45359237 × 9.80665 = 4.4482216152605 N exactly. So 1 lbf pushing on 1 lb gives an acceleration of exactly 1 g.
How do I work out friction force?
Friction = μ × N, where μ is the friction coefficient between the two surfaces and N is the normal force pressing them together. On flat ground N is the weight. A 10 kg box on greased steel (μ ≈ 0.1) has 0.1 × 98.07 = 9.81 N of friction to overcome.
How do I find the force on a slope?
Gravity splits into two parts: m × g × sin θ pulls the object down the slope and m × g × cos θ presses it into the slope. Friction is μ × m × g × cos θ. If the pull down the slope is bigger than the friction, the object slides with acceleration (pull − friction) ÷ m.
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