What force does it take?
Pick what to find, then type the other two values in any unit. The force calculator uses Newton’s second law, F = m × a, and shows the answer in newtons and pounds-force, kilograms and pounds, and m/s², ft/s² and g.
- Answer
- F = 3000 N (674.427 lbf)
The answer is F = 3000 N (674.427 lbf).
- Force (N)
- 3,000
- Force (lbf)
- 674.427
- Mass (kg)
- 1,000
- Mass (lb)
- 2,204.62
- Acceleration (m/s²)
- 3
- Acceleration (ft/s²)
- 9.84252
- Acceleration (g)
- 0.305915
Answer: F = 3000 N (674.427 lbf). The answer is F = 3000 N (674.427 lbf).
How to calculate
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.
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).
Method: F = m × a; m = F ÷ a; a = F ÷ m. Forces in N = kg·m/s².
- 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
Each example is checked against the calculator on every build.
- Find Force, Mass 0.4 kg, Acceleration 3, Acceleration unit m/s² gives Force (N) 1.2, Answer 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
- Find Force, Mass 2,100 kg, Acceleration 49, Acceleration unit m/s² gives Force (N) 102,900, Acceleration (g) 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)
- Find Force, Mass 1 kg, Acceleration 1, Acceleration unit g gives Force (N) 9.80665, Force (lbf) 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
- Find Mass, Force 500 N, Acceleration 2, Acceleration unit m/s² gives Mass (kg) 250, Mass (lb) 551.155655, Answer 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
- Find Acceleration, Force 4.448 N, Mass 0.4536 kg, Acceleration unit ft/s² gives Acceleration (g) 1, Acceleration (m/s²) 9.80665, Acceleration (ft/s²) 32.174049, Answer 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
How it works
Newton’s second law: the net force on an object equals its mass times its acceleration.
- Find force: F = m × a.
- Find mass: m = F ÷ a.
- Find acceleration: a = F ÷ m.
Everything is worked in SI units first: mass in kg, acceleration in m/s², force in N (1 N = 1 kg·m/s²). The units:
| Unit | In SI |
|---|---|
| g (gram), lb, oz, t | 0.001 kg, 0.45359237 kg, 0.028349523125 kg, 1,000 kg |
| ft/s², g | 0.3048 m/s², 9.80665 m/s² |
| kN, lbf, dyn, kgf | 1,000 N, 4.4482216152605 N, 0.00001 N, 9.80665 N |
Every result is then given in N and lbf, kg and lb, and m/s², ft/s² and g.
Rules. Mass from 0.000001 kg (1 mg) to 1,000,000,000 kg; force from 0.000001 N to 10¹² N; the typed acceleration from 0.000001 to 1,000,000,000 in its unit.
Exact arithmetic. A typed value is read as the exact decimal you typed in its unit, and each unit size above is an exact decimal, so every result is an exact fraction rounded once for display.
Output format. The answer line and every value show 6 significant figures; the answer line uses no thousands separators and drops trailing zeros.
Assumptions
- F is the net (total) force on the object.
- Speeds are far below the speed of light, so mass is constant.
- g is standard gravity, 9.80665 m/s².
Worked examples by hand
A 0.400 kg ball at 3.00 m/s² (OpenStax Example 5.5, x part). F = 0.4 × 3 = 1.2 N = 1.2 ÷ 4.4482216152605 = 0.269771 lbf.
A 2,100 kg rocket sled at 49 m/s² (OpenStax Example 5.4). F = 2,100 × 49 = 102,900 N net. 49 ÷ 9.80665 = 4.99661 g.
1 kg at 1 g. F = 1 × 9.80665 = 9.80665 N = 2.20462 lbf (one kilogram-force).
Mass from 500 N and 2 m/s². m = 500 ÷ 2 = 250 kg = 250 ÷ 0.45359237 = 551.156 lb.
Acceleration from 1 lbf on 1 lb. a = 4.4482216152605 N ÷ 0.45359237 kg = 9.80665 m/s² = 1 g = 9.80665 ÷ 0.3048 = 32.174 ft/s².
Other questions people ask
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.