Calculate the total force exerted on an object. Enter the mass of that object and the acceleration, and this calculator will evaluate the total force.

Force Formula

The following formula is used to calculate a total force:

F = m * a

  • F is the force (N)
  • m is the mass (kg)
  • a is the acceleration (m/s^2)

The SI unit for force is Newtons (N) where mass is measured in kilograms (kg) and acceleration is measure in meters per second squared (m/s^2). The calculator above is again unit-less like most of our other calculators in science and engineering so that it allows you to determine the proper units yourself, or use whichever units your questions are using.

Force in Physics Definition

In physics, force is any influence that causes an object to undergo a change in speed, a change in direction, or both. A force may cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e. to accelerate.

Force can also be described by intuitive concepts such as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F. Force can be understood as a push or pull, often caused by gravity when applied to everyday objects on Earth; for example, the force exerted on an object is the reason why it does not fall straight down.

Force is also responsible for many other effects we see every day (and use every day), such as friction, which are caused by interactions between two objects that push or pull on each other.

Force Example Problem

How to calculate force from mass and acceleration?

Let’s take a look at an example of how to use the force equation above. Let’s assume you are given an object with a mass of 10kg and an initial velocity of 2m/s and a final velocity of 4m/s over a period of 2s. To calculate the acceleration of that object over time, you need to use the acceleration formula as follows:

(4m/s=2m/s)/2s = 1 m/s^2

Now that you have acceleration, you can plug it into the formula from above.

F = 1 m/s^2 * 10kg = 10N

The answer is, the force required to accelerate an object 1 m/s^2 that has a mass of 10kg is 10 Newtons.

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Basic Forces

There are four fundamental forces in nature: strong nuclear force, weak nuclear force, the electromagnetic force and gravitational force.

  1. The strong nuclear force is one of the four fundamental forces in physics. It is responsible for binding protons and neutrons into atomic nuclei, as well as keeping together quarks inside of protons and neutrons. It is also one of the most powerful forces in nature and acts over distances that are measured in subatomic length scales. The strong force is more than a hundred times stronger than electromagnetism and 10^39 (10 with 39 zeros after it) times stronger than gravity.
  2. The weak nuclear force is the second force from the left on the periodic table, and it is responsible for radioactive decay. It is weaker than the strong nuclear force, and it does not operate at long distances.
  3. Electromagnetic force is one of the four fundamental forces that affect matter. It is responsible for interactions between electrically charged particles, such as electrons and protons, and its strength is determined by the charges and current densities of the interacting particles. The electromagnetic force has an infinite range and acts at a distance, independent of the distance between objects.
  4. The force of gravity is a force that pulls all objects towards each other. It is the weakest of the four fundamental forces, but it overcomes electrostatic repulsion between positive charges and the strong interaction which binds protons and neutrons together in an atomic nucleus. Gravity has an infinite range.

Newton’s Three Laws of Motion

There are three laws of motion that form the basis of Newtonian Mechanics. They were developed by, you guessed it, Sir Isaac Newton and they are as follows:

First Law:  An object at rest will remain at rest unless acted upon by an unbalanced force. An object in motion will remain in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Second Law: The acceleration of an object is directly proportional to the net force acting on that object and inversely proportional to its mass. Acceleration and net force are vectors so both must be specified.

Third Law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.