Force Calculator (F = ma)
Pick what you want to find, enter the other two quantities and choose your units. The calculator applies F = m × a and also shows the weight of the mass.
Updated
Report a problem
Formula
Newton's second law of motion:
F = m × a which rearranges to m = F ÷ a and a = F ÷ m
Weight is the force of gravity on a mass: W = m × g, with standard gravity g = 9.80665 m/s².
Constants used (all exact definitions): 1 lb = 0.45359237 kg, 1 ft = 0.3048 m, 1 lbf = 0.45359237 × 9.80665 = 4.4482216152605 N, 1 g = 9.80665 m/s².
Worked example
A 10 kg mass accelerating at 2.5 m/s²: F = 10 × 2.5 = 25 N.
Solving the other way round with the same force of 100 N: acceleration 100 ÷ 10 = 10 m/s²; mass at 2.5 m/s² is 100 ÷ 2.5 = 40 kg; the weight of the 10 kg mass is 10 × 9.80665 = 98.0665 N.
Frequently asked questions
What is the formula for force?
Newton's second law says force equals mass times acceleration, F = m × a. A 10 kg mass accelerating at 2.5 m/s² needs 10 × 2.5 = 25 N.
How do I find mass or acceleration from force?
Rearrange the formula: m = F ÷ a and a = F ÷ m. A 100 N force on a 10 kg mass gives an acceleration of 100 ÷ 10 = 10 m/s², and the same force producing 2.5 m/s² means a mass of 40 kg.
How is weight different from mass?
Mass is the amount of matter and is measured in kg. Weight is the gravitational force on that mass, W = m × g with g = 9.80665 m/s² at standard gravity. A 70 kg person weighs 70 × 9.80665 = 686.47 N.
How many newtons are in a pound-force?
One pound-force is the weight of one pound at standard gravity: 0.45359237 kg × 9.80665 m/s² = 4.448222 N. A 10 lb mass accelerating at 3 ft/s² (0.9144 m/s²) takes 4.148 N, which is 0.932 lbf.