# What force does it take?

Uses Newton’s second law F = m × a to find the net force from the mass and the acceleration, or the mass or the acceleration from the other two, in newtons, pounds-force, kilograms, pounds, m/s², ft/s² and g.

- Page: https://www.acalculator.org/physics/force-calculator
- JSON spec: https://www.acalculator.org/physics/force-calculator.json
- Version: a35d8c212817

## Default answer

Example with the default inputs (Find Force, Mass 1,000 kg, Acceleration 3, Acceleration unit m/s²): The answer is F = 3000 N (674.427 lbf).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| find | Find | Which of force, mass and acceleration to work out from the other two. |
| m | Mass | The mass of the object. |
| a | Acceleration | The acceleration of the object, in the unit chosen below. |
| au | Acceleration unit | The unit of the acceleration: metres or feet per second squared, or g (standard gravity). |
| F | Force | The net force on the object. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| result | Answer | The value worked out, to 6 significant figures, in its main units. |
| newtons | Force (N) | The net force in newtons: mass in kg × acceleration in m/s². |
| poundsForce | Force (lbf) | The net force in pounds-force (1 lbf = 4.4482216152605 N). |
| kilograms | Mass (kg) | The mass in kilograms. |
| pounds | Mass (lb) | The mass in pounds (1 lb = 0.45359237 kg). |
| mps2 | Acceleration (m/s²) | The acceleration in metres per second squared. |
| fps2 | Acceleration (ft/s²) | The acceleration in feet per second squared. |
| gs | Acceleration (g) | The acceleration as a multiple of standard gravity, 9.80665 m/s². |

## Method

F = m × a; m = F ÷ a; a = F ÷ m. Forces in N = kg·m/s².

## Assumptions

- F is the net force: the sum of all forces on the object. To find a single push, add the other forces (such as friction) to the net force.
- Speeds are far below the speed of light, so the mass does not change.
- g here is standard gravity, exactly 9.80665 m/s²; real gravity varies slightly with place and height.

## Worked examples

1. find = force, m = 0.4, a = 3, au = mps2 gives newtons = 1.2, result = F = 1.2 N (0.269771 lbf). Source: OpenStax, University Physics Volume 1, §5.3 Newton’s Second Law (F_net = m a), https://openstax.org/books/university-physics-volume-1/pages/5-3-newtons-second-law (Example 5.5: (0.400 kg)(3.00 m/s²) = 1.20 N along x); NIST Special Publication 811, Appendix B (1 lbf = 4.4482216152605 N; standard gravity 9.80665 m/s²), https://www.nist.gov/pml/special-publication-811.
2. find = force, m = 2,100, a = 49, au = mps2 gives newtons = 102,900, gs = 4.996609. Source: OpenStax, University Physics Volume 1, §5.3 Newton’s Second Law (F_net = m a), https://openstax.org/books/university-physics-volume-1/pages/5-3-newtons-second-law (Example 5.4: m a = 2100 kg × 49 m/s²).
3. find = force, m = 1, a = 1, au = g gives newtons = 9.80665, poundsForce = 2.204623. Source: OpenStax, University Physics Volume 1, §5.4 Mass and Weight (w = m g), https://openstax.org/books/university-physics-volume-1/pages/5-4-mass-and-weight; NIST Special Publication 811, Appendix B (1 lbf = 4.4482216152605 N; standard gravity 9.80665 m/s²), https://www.nist.gov/pml/special-publication-811.
4. find = mass, F = 500, a = 2, au = mps2 gives kilograms = 250, pounds = 551.155655, result = m = 250 kg (551.156 lb). Source: OpenStax, University Physics Volume 1, §5.3 Newton’s Second Law (F_net = m a), https://openstax.org/books/university-physics-volume-1/pages/5-3-newtons-second-law.
5. find = accel, F = 4.448222, m = 0.453592, au = fps2 gives gs = 1, mps2 = 9.80665, fps2 = 32.174049, result = a = 32.174 ft/s². Source: NIST Special Publication 811, Appendix B (1 lbf = 4.4482216152605 N; standard gravity 9.80665 m/s²), https://www.nist.gov/pml/special-publication-811.

## FAQ

### How do I calculate force?

Multiply the mass in kilograms by the acceleration in metres per second squared: F = m × a, in newtons. A 1,000 kg car speeding up at 3 m/s² needs a net force of 3,000 N.

### What is a newton?

The force that gives 1 kg an acceleration of 1 m/s². One newton is about 0.2248 pounds-force, roughly the weight of a small apple.

### How do I find mass from force and acceleration?

Divide the force by the acceleration: m = F ÷ a. A net force of 500 N that gives 2 m/s² acts on 250 kg (551.156 lb).

### How do I find acceleration from force and mass?

Divide the force by the mass: a = F ÷ m. One pound-force on a one-pound mass gives exactly 1 g, which is 9.80665 m/s² or 32.174 ft/s².

### Is this the net force or one force?

The net force: the sum of every force on the object. If friction of 650 N holds back a sled, the push must be the net force plus 650 N.

### How is weight related to this?

Weight is the force of gravity on a mass: w = m × g. Choose g as the acceleration unit and type 1 to get the weight. 1 kg weighs 9.80665 N at standard gravity.

## Sources

- OpenStax, University Physics Volume 1, §5.3 Newton’s Second Law: F_net = m a; Example 5.4 (rocket sled, 2,100 kg at 49 m/s²) and Example 5.5 (0.400 kg ball at 3.00 m/s² along x). https://openstax.org/books/university-physics-volume-1/pages/5-3-newtons-second-law (retrieved 2026-10-02)
- OpenStax, University Physics Volume 1, §5.4 Mass and Weight: w = m g. https://openstax.org/books/university-physics-volume-1/pages/5-4-mass-and-weight (retrieved 2026-10-02)
- NIST Special Publication 811, Appendix B: 1 lbf = 4.4482216152605 N, 1 lb = 0.45359237 kg, 1 ft = 0.3048 m, standard gravity g = 9.80665 m/s² (all exact). https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-02)