Force calculator
Enter two of force, mass and acceleration, get the third.
How do I calculate force?
Newton's second law: force = mass × acceleration. A 10 kg object accelerating at 3 m/s² needs 10 × 3 = 30 newtons.
What is a newton?
The force that accelerates 1 kilogram by 1 meter per second squared. One pound-force is 4.448 newtons.
How much does 1 kg weigh in newtons?
Its weight is mass × g: 1 kg × 9.80665 m/s² = 9.807 N under standard gravity.
How do I find acceleration from force?
a = F ÷ m: 30 N on 10 kg gives 3 m/s². Pick "Acceleration" to solve for it.
What is a pound-force?
The weight of one pound under standard gravity: 0.45359237 kg × 9.80665 m/s² = 4.448 N.
How do I convert newtons to pounds-force?
Divide by 4.448222, since 1 lbf = 4.448222 N (NIST SP 811), or multiply by 0.2248. OpenStax University Physics, section 5.4, rounds this to 1 N = 0.225 lb and notes that a 225-lb person weighs about 1,000 N.
What is the net force, and which force do I enter?
F in F = ma is the vector sum of every force on the object, not just the push you are thinking about. A 1,000 kg car whose engine pushes with 3,000 N while friction and drag total 1,200 N has a net force of 1,800 N, so a = 1.8 m/s². Enter 1,800 N, not 3,000 N.
How do I find the force needed to stop a moving object?
Find the acceleration first, then multiply by the mass. A 1,500 kg car at 60 mph (26.82 m/s) that stops in 40 m with a steady braking force has a = v² ÷ 2s = 8.99 m/s², so F = 1,500 × 8.99 = 13,490 N (3,033 lbf).
The formula and what it assumes
Newton’s second law says the net external force on an object equals its mass times its acceleration, F = ma (OpenStax University Physics, Volume 1, section 5.3, Eq. 5.3–5.4). The acceleration points the way the net force points, and a larger mass gives a smaller acceleration for the same force. One newton is the force that gives 1 kg an acceleration of 1 m/s². The form F = ma assumes a constant mass; the general statement is F = dp/dt (Eq. 5.6).
Worked example: a 3,200 lb car in US units
A car of mass 3,200 lb speeds up at 6 ft/s². In SI that is 1,451.5 kg (3,200 × 0.45359237) and 1.8288 m/s² (6 × 0.3048). The net force is 1,451.5 × 1.8288 = 2,654 N, which is 596.8 lbf. A shortcut gives the same result: pounds times ft/s² divided by 32.174 ft/s² (standard gravity) is pound-force, and 3,200 × 6 ÷ 32.174 = 596.8 lbf.
Common mistakes
Mixing pounds as mass with pounds-force as force is the classic error. Here “lb” in the mass box is a mass of 0.45359237 kg, and “lbf” is the force that gravity exerts on that mass at standard gravity, 4.448222 N; the two only look equal because 1 lb weighs 1 lbf at 1 g. A person who weighs 160 lbf on a scale has a mass of 160 lb, or 72.6 kg, so enter 160 in the mass box. Do not confuse weight with mass either: the 5.0 kg object of OpenStax section 5.4 weighs 49 N on Earth and 8.4 N on the Moon but has the same mass in both places, and F = ma uses the mass.
Sources: OpenStax University Physics, Volume 1, section 5.3 (Newton’s second law, Eq. 5.3–5.6; Example 5.2: a net force of 51 N on a 24 kg lawn mower gives 2.1 m/s²) and section 5.4 (mass and weight); NIST SP 811, Appendix B.8, for the pound (0.45359237 kg), the pound-force (4.448222 N) and standard gravity (9.80665 m/s², exact). Related: acceleration calculator, kinematics calculator, friction calculator and weight on other planets calculator.