Force Calculator
Solve Newton's second law for force, mass or acceleration; find weight from mass and gravity; work out friction from a coefficient and the normal force; or add several forces at different angles to get the net force and the acceleration it causes. Each answer comes with its working, and the net-force mode draws a free-body diagram. Runs in your browser; free, no sign-up.
Newton's second law: the net force on an object equals its mass times its acceleration. Enter the net force, not just one of the forces acting.
Calculated
Results
3000 N
Net force F
The working
- Start from F = m × a.
- F = 1200 × 2.5 = 3000 N
How to Use the Force Calculator
- 1. Choose the calculation. F = ma for the net force on an object, W = mg for weight, f = μN for friction, or Net force to combine several forces.
- 2. Pick the unknown and fill in the rest. The box you are solving for becomes the answer. Every box has its own unit menu — newtons, kilonewtons, pounds-force, kilograms or pounds, m/s² or g.
- 3. For several forces, give sizes and angles. Measure each angle counter-clockwise from the positive x axis: 0° is right, 90° up, 180° left, 270° down. Add a mass if you want the acceleration.
- 4. Read the working. The equation, the rearrangement and the substituted numbers are shown, and the net-force mode adds a table of components and a free-body diagram.
The Equations
| Quantity | Equation | Notes |
|---|---|---|
| Newton's second law | F = m × a | F is the net force on the object, in newtons (1 N = 1 kg·m/s²) |
| Weight | W = m × g | g = 9.80665 m/s² at standard gravity, so 1 kg weighs 9.80665 N |
| Friction | f = μ × N | N is the normal force; μs gives the maximum static friction, μk the sliding friction |
| Friction on level ground | f = μ × m × g | The normal force on a flat surface equals the weight when nothing else pushes vertically |
| Net force | ΣFx = ΣF cos θ, ΣFy = ΣF sin θ | Add components, then |F| = √(ΣFx² + ΣFy²) |
Reference: OpenStax University Physics, Volume 1, sections 5.3 and 6.2. Standard gravity is exact by definition (CGPM, 1901).
Worked Examples
F = ma. A 1,200 kg car accelerating at 2.5 m/s² needs a net force of 1200 × 2.5 = 3000 N (the default). Note that this is the net force: engine thrust minus drag and rolling resistance.
Weight. A 70 kg person weighs 70 × 9.80665 = 686.5 N on Earth, but 70 × 1.62 = 113.4 N on the Moon. Their mass is 70 kg in both places.
Friction. A block pressing on a surface with a normal force of 200 N and μ = 0.4 feels 0.4 × 200 = 80 N of friction. For a 10 kg block on level ground with μ = 0.4, f = 0.4 × 10 × 9.80665 = 39.23 N.
Net force. Pull with 10 N to the right, 6 N upward and 4 N to the left. The x components sum to 10 − 4 = 6 N and the y components to 6 N, so the net force is √(6² + 6²) = 8.485 N at 45°. If the object has a mass of 2 kg, its acceleration is 8.485 ÷ 2 = 4.243 m/s² in that same direction.
Friction Coefficients
| Surfaces | Static μs | Kinetic μk |
|---|---|---|
| Rubber on dry concrete | 1.0 | 0.7 |
| Wood on wood | 0.5 | 0.3 |
| Steel on steel (dry) | 0.6 | 0.3 |
| Shoes on ice | 0.1 | 0.05 |
| Teflon on steel | 0.04 | 0.04 |
Approximate values from OpenStax University Physics, Volume 1, Table 6.1. Real coefficients vary with surface condition.
Common Mistakes
- Using one force instead of the net force. In F = ma, F is the vector sum of all forces. A 50 N push against 50 N of friction gives zero acceleration.
- Mixing up mass and weight. Mass is in kilograms and does not change; weight is a force in newtons and depends on g. A scale in kilograms really measures weight and divides by g.
- Using weight as the normal force on a slope or when pulled at an angle. The normal force then differs from mg; use the Inclined Plane Calculator for ramps.
- Treating μ as a property of one object. It belongs to a pair of surfaces.
Frequently Asked Questions
- How do you calculate force?
- Multiply mass by acceleration: F = ma. A 5 kg object accelerating at 3 m/s² requires a net force of 15 N. If several forces act, add them as vectors first, and use the resulting net force.
- What is a newton?
- One newton is the force that gives a 1 kg mass an acceleration of 1 m/s², so 1 N = 1 kg·m/s². Near Earth's surface it is roughly the weight of a small apple, about 100 g.
- What is the difference between mass and weight?
- Mass measures how much matter an object has and is the same everywhere. Weight is the gravitational force on that mass, W = mg, so it changes with location. The same 70 kg person weighs about 686.5 N on Earth and 113.4 N on the Moon.
- How do you find the net force from several forces?
- Resolve each force into x and y components (F cos θ and F sin θ), add all the x components and all the y components, then combine the two sums with the Pythagorean theorem. The direction is atan2 of ΣFy over ΣFx.
- What does zero net force mean?
- The object is in equilibrium: it stays at rest or moves at constant velocity. Zero net force does not mean no forces act, only that they cancel. The calculator reports this case explicitly.
- How do I convert pounds-force to newtons?
- Multiply by 4.448222: 1 lbf is the weight of a one-pound mass at standard gravity, 0.45359237 kg × 9.80665 m/s². A kilogram-force is exactly 9.80665 N. The unit menus do these conversions for you.