Force Mass Acceleration Calculator

Want to calculate the force, mass, or acceleration of an object? Cool, try this calculator.









About This Calculator

This force, mass, and acceleration calculator is based on one of the most fundamental formulas in physics, namely:

F = m a

where

F = Force
m = Mass
a = Acceleration

This formula allows you to calculate the force acting upon an object if you know the mass of the object and its rate of acceleration. Want to calculate the mass of an object, given the acceleration of the object and the force acting upon it? No problem, use this variation of the formula:

m = F / a

Or, if you want to know the acceleration of an object given its mass and the force acting upon it, use this variation of the formula:

a = F / m


Force, Mass, and Acceleration Units

There are countless unit types that can be used to measure force, mass, and acceleration, but the most common ones (and those used by this calculator) are shown below:

Metric

force → N (Newtons)
mass → kg (kilograms)
acceleration → m/s2 (meters per second squared)

Imperial

force → lbf (pounds force)
mass → lbm (pounds mass)
acceleration → ft/s2 (feet per second squared)


Understanding Force, Mass, and Acceleration

Physics is generally much easier to understand if you can visualize what's going on, so I'll try my best here to explain (in a way that helps you to picture it) the general concepts behind the force, mass, and acceleration formula.

Force:

You can imagine a "force" as any kind of push or pull acting on an object. It's typically measured in Newtons (metric system) or pounds force (imperial system). There are unlimited examples of forces acting on objects that I could provide, but here are just a few:

  • When you push something. Imagine pushing a cup across a tabletop with your hand. When you do that your hand is exerting a force on the cup (and the cup is actually also exerting the exact opposite force on your hand).

  • When a rocket blasts off. The rocket is pushing exhaust gases out of the engine nozzle, and those exhaust gases are pushing back on the rocket as they leave the nozzle, exerting a force that pushes the rocket up into the sky.

  • When you are standing on the ground. Gravity is pulling you down toward the ground. Your weight is the force created by gravity that pulls you toward the earth. You can feel your weight in your feet when you are standing because the ground is pushing back on your feet with the same amount of force (i.e. your weight) that is pulling you down.

Mass:

Mass is the amount of matter in an object. It's typically measured in kilograms (metric system) or pounds mass (imperial system). Mass is not the same thing as weight (which is a force). To illustrate, you might weigh a certain amount on earth, but if you went to the moon you would weigh less because the moon exerts a different gravitational pull than earth does. However, your mass on the moon would be the same as it is on earth because the amount of matter that you are made up of has not changed.

Acceleration:

Acceleration is just a change in speed. It's typically measured in "meters per second squared" (metric system) or "feet per second squared" (imperial system). "Feet per second squared" seems like a tough unit of measurement to wrap your head around, but it's actually not that bad. Another way of saying it would be "feet per second, per second." Let's say that you are moving at a speed of 10 feet per second, that's your speed. It means that you travel 10 feet every second. Now, suppose that we accelerate you (meaning we speed you up) at a rate of 10 "feet per second squared" (or, in other words, 10 "feet per second, per second"). This means that we are increasing your speed by 10 feet per second, each second. So, you were already travelling at a constant 10 feet per second (your speed). Now, when we accelerate you at 10 feet per second squared we are increasing your speed by 10 feet per second for every second that goes by. That means that one second after we start accelerating you, you will be travelling at a speed of 20 feet per second. Two seconds after we start accelerating you, you will be travelling at a speed of 30 feet per second. Three seconds after, you will be travelling at a speed of 40 feet per second. And so on.


Understanding the Force, Mass, and Acceleration Formula

To visualize the force, mass, and acceleration formula in action you just need to imagine yourself pushing something. Imagine you have to push a car that has broken down. You already intuitively understand the factors that are at play when assessing how hard you'll have to push to get the car up to a certain speed, but you may not realize that those factors are actually just the real life manifestation of the "F = m a" formula. The size of the car is the car's mass. How hard you have to push is the force. The time it takes you to get to a certain speed (let's say jogging speed) is your acceleration. If the car is big (i.e. its mass is large), then you will have to push harder (i.e. exert a large force) to get to jogging speed quickly (i.e. achieve high acceleration). If the car is small (i.e. its mass is low) then you won't have to push as hard (i.e. you can exert a smaller force) to get up to jogging speed quickly (i.e. achieve high acceleration).


A Note About "Slugs" When Using the Imperial System for Force, Mass, and Acceleration

When you're using the force, mass, and acceleration formula in the imperial system (i.e. when you're using units of pounds force, pounds mass, and feet per second squared) there's a unit of mass that you need to be aware of, called the "slug." A slug is the amount of mass that will accelerate at 1 ft/s2 when one pound force (lbf) is exerted on it. A slug has a mass of 32.174049 pounds mass (or 14.593903 kilograms).

The slug essentially exists to help us move back and forth between pounds mass and pounds force, which are not the same things. Pounds force (lbf) measures an actual force (remember, a force is a push or pull), like your weight or the thrust of a rocket. In metric the equivalent unit of measurement for pounds force (lbf) is the Newton (N). Pounds mass (lbm) measures the amount of matter in an object. In metric the equivalent unit of measurement for pounds mass (lbm) is the kilogram (kg).

To illustrate, let's first walk through an example in the metric system, where we're calculating the force required to accelerate an 8 kg object at 10 m/s2. According to the "F = m a" formula, that force is:

F = m a

F = (8 kg) (10 m/s2)

F = 80 kg m/s2

F = 80 N

In the metric system example above, you can see that 80 kg m/s2 becomes 80 Newtons (N). The reason for that is because the metric system is all nice and tidy, with the actual definition of a Newton being "the amount of force required to accelerate 1 kg at 1 m/s2." Therefore, 1 kg m/s2 = 1 N, and so, from our example, 80 kg m/s2 = 80 N.

Now, let's walk through an example in the imperial system, where we're calculating the force required to accelerate an 8 lbm object at 10 ft/s2. According to the "F = m a" formula, that force is:

F = m a

F = (8 lbm) (10 ft/s2)

F = 80 lbm ft/s2

But here's where we reach a problem. In the metric system we could say that 80 kg m/s2 is 80 N, because 1 kg m/s2 is equal to 1 N. However, in the imperial system we can't make such an easy transition and say that 80 lbm ft/s2 is equal to 80 lbf, because 1 lbm ft/s2 is not equal to 1 lbf (because the imperial system is not all nice and tidy like the metric system). This is where we have to go back to the definition of a slug. Remember, as described a few paragraphs above, a slug is the amount of mass that will accelerate at 1 ft/s2 when one pound force (lbf) is exerted on it. Another way of saying it is that the definition of a pound force is "the amount of force required to accelerate 1 slug at 1 ft/s2." Therefore, 1 slug ft/s2 = 1 lbf, and so, we can continue our equation as follows:

F = m a

F = (8 lbm) (10 ft/s2)

F = 80 lbm ft/s2

(now, remembering that 1 slug is equal to 32.2 lbm, we can replace pounds mass with slugs in our equation)

F = 80 lbm ft/s2 x 1 slug / 32.2 lbm

F = 80 / 32.2 slugs ft/s2

(and now, remembering that 1 slug ft/s2 is equal to 1 lbf, we can replace slugs ft/s2 with lbf in our equation)

F = 2.48 lbf