Force Calculator

What the force calculator does

Force, mass, and acceleration are bound together by one of the most important relationships in physics. Give this calculator any two of them and it returns the third, whether you want the force needed to accelerate a mass, the acceleration a force produces, or the mass that a known force and acceleration imply.

It is built on Newton's second law, the rule that ties a push to the motion it creates. Below is what that law says, the equation behind every answer, and a worked example.

How to use it

1. Choose what to find: force, mass, or acceleration.
2. Enter the other two, each with its own unit. Mass runs from micrograms up to the mass of the Earth, and acceleration can be entered in g, multiples of Earth's gravity.
3. Press Calculate for the answer, shown in every unit at once, or Reset to clear it.

Force, mass, and Newton's second law

A force is simply a push or a pull. What Newton saw is that a force does not set the speed of an object, it sets the rate at which the speed changes, the acceleration. Push harder and a thing speeds up faster. Push the same on something heavier and it speeds up more slowly. That is the whole of the second law: the force equals the mass times the acceleration.

Because acceleration has a direction, so does force, which makes force a vector. A familiar example is weight: gravity pulls on every mass with a force equal to the mass times the acceleration of gravity, which is why a kilogram at the Earth's surface weighs about 9.81 newtons. The same law connects the thrust of an engine, the pull of a tow rope, and the shove of your hand on a door.

The equation it solves

Newton's second law, with F for force, m for mass, and a for acceleration, is:

F = m a

Rearranged, that gives the other two quantities the calculator can find: the acceleration a force produces on a mass, a = F ÷ m, and the mass implied by a force and an acceleration, m = F ÷ a. All three are the same statement read three ways.

Units and precision

The SI unit of force is the newton, defined so that one newton accelerates one kilogram at one metre per second squared, which is why the law works cleanly in SI. The calculator converts your entries to kilograms and metres per second squared, computes, then shows the result in every unit of that quantity, from newtons and kilonewtons up to meganewtons, alongside pounds-force, kips, and dynes. Acceleration can be given in g, where 1 g is 9.80665 m/s². Results are carried to many figures, far more than any real measurement needs, so the rounding lives only in the display.

A worked example

How much force does it take to accelerate a 1,000 kg car at 3 m/s²?

Straight from the law, F = 1,000 × 3 = 3,000 N, or 3 kN. Turn the question around and the same tool tells you that this 3,000 N acting on the car gives 3 m/s², or that a 3,000 N force producing 3 m/s² implies a 1,000 kg mass.

Questions people ask

What is the formula for force?

Force equals mass times acceleration, F = ma. Knowing any two of force, mass, and acceleration fixes the third.

What is a newton?

It is the SI unit of force, the force that gives a one-kilogram mass an acceleration of one metre per second squared. So one newton is one kilogram-metre per second squared.

Is weight a force?

Yes. Weight is the force of gravity on a mass, equal to the mass times the acceleration of gravity. A 10 kg mass weighs about 98 newtons at the Earth's surface.

What is the difference between mass and force?

Mass is how much matter an object contains and does not change with location. Force is a push or pull, and the same mass needs more or less force depending on the acceleration you want.

References

A quick note on where the physics comes from. Newton's second law, F = ma, is the foundation of classical mechanics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The newton and the other SI units follow the US National Institute of Standards and Technology.

1. OpenStax, University Physics Volume 1, Section 5.3, Newton's Second Law of Motion. https://openstax.org/books/university-physics-volume-1/pages/5-3-newtons-second-law-of-motion
2. HyperPhysics, Georgia State University, Newton's Laws. http://hyperphysics.phy-astr.gsu.edu/hbase/newt.html
3. National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811