Force equals mass times acceleration (F = ma). Choose which of the three to find, enter the other two in the units you like, and the answer is given in the unit you pick: 10 kg at 2 m/s² needs 20 N.
The formula
Force
F = m × aMass
m = F ÷ aAcceleration
a = F ÷ mUnits
1 N = 1 kg·m/s² · 1 lbf = 4.448222 N · 1 g₀ = 9.80665 m/s² · 1 ft/s² = 0.3048 m/s²Everything is converted to newtons, kilograms and metres per second squared, solved there, and converted back to your unit. The pound-force and standard gravity are defined by the values in the NIST Guide to the SI, Appendix B.9.
Worked example
Backwards, 50 N on an object accelerating at 5 m/s² gives a mass of 50 ÷ 5 = 10 kg. And 100 N on 20 kg gives an acceleration of 100 ÷ 20 = 5 m/s², which is 0.509858 g₀.
When to use it, and the mistakes to avoid
Use it for physics homework, for working out the force a motor, brake or engine must supply, or to turn a mass and an acceleration into a load in newtons or pounds-force.
- Mixing units. Kilograms and pounds are not interchangeable, and grams must be converted first. The calculator does it if you pick the right unit.
- Using weight for mass. Weight is a force in newtons. Mass is in kilograms.
- Forgetting that it is the net force. Friction and other forces reduce the net force, so use the total left over.
- Ignoring direction. A negative force or acceleration means the opposite direction, or slowing down.
- Expecting it to hold near light speed. F = ma applies at everyday speeds, not close to the speed of light.
FAQ
What does F = ma mean?
It is Newton's second law: the net force on an object equals its mass times its acceleration. A force of 20 newtons on a 10 kilogram object gives it an acceleration of 2 metres per second squared. For a given force, a heavier object accelerates less.
What is a newton?
The newton is the SI unit of force: the force that gives a 1 kilogram mass an acceleration of 1 metre per second squared, so 1 N = 1 kg·m/s². A 100 gram apple weighs about 1 N on Earth, because gravity pulls it down at about 9.81 m/s².
What is the difference between mass and weight?
Mass is how much matter an object has, in kilograms, and is the same everywhere. Weight is the force of gravity on that mass, in newtons: weight = mass × g. A 10 kg object weighs about 98.1 N on Earth and about 16 N on the Moon, yet its mass is 10 kg in both places.
How do pounds-force and standard gravity work here?
A pound-force is the force of gravity on one pound of mass at standard gravity, 9.80665 m/s², which makes 1 lbf equal to 4.448222 N. Standard gravity, written g₀, is also offered as an acceleration unit: 2 g₀ is 19.6133 m/s². So 150 lb accelerating at 1 g₀ needs exactly 150 lbf.
Why can the calculator not find a mass in some cases?
Because mass must be positive. With zero acceleration, any mass gives the same force, so there is nothing to solve for. And if the force and the acceleration point in opposite directions (one positive, one negative), the mass would have to be negative. Give them the same sign and a non-zero acceleration.