Newton's Second Law Calculator

Created by Miłosz Panfil, PhD and Dominik Czernia, PhD
Reviewed by Bogna Szyk and Adena Benn
Last updated: Sep 19, 2023

The Newton's second law calculator is a perfect tool that helps you understand the second law of motion due to Isaac Newton. Have you ever wondered what Newton's second law of motion is or how to calculate a force acting on an object? The following short article has all the answers.

Isaac Newton was an English mathematician, physicist, and astronomer who is mostly known for his law of universal gravitation. Legend says that Newton sat under an apple tree when suddenly an apple fell on his head, making him realize that the fall of bodies to Earth and the movement of celestial bodies are caused by the same force — gravity.

Newton also laid the foundation for classical mechanics with his three laws of motion, which describe the resulting movement of the object under the forces acting upon it:

  • The first law of motion — an object will remain at rest or in uniform motion in a straight line unless acted upon by a non-zero net force;

  • The second law of motion — which our Newton's second law calculator is about — explains how to calculate force by knowing the body's acceleration; and

  • The third law of motion — when one body exerts a force on a second body, the second body exerts a force that is equal in magnitude and opposite in direction on the first body (to every action, there is always an opposite and equal reaction).

What is Newton's second law of motion?

The Newton's second law of motion states that acceleration of an object is proportional to the net force F acting on it and inversely proportional to its mass m. It is expressed with the following equation:

a = F / m


  • a [m/s²] is the acceleration of an object;
  • F [N] is the force acting on an object; and
  • m [kg] is the mass of an object.

The above law says that objects accelerate due to force acting on them. The effect of the force, the acceleration, depends on the object's inertia: the unwillingness to change the velocity. The larger the mass, the larger the inertia.

How to calculate the force?

Now that you know what Newton's second law of motion is, we can easily find a force acting on a body. Turning around this law, we find an expression for the force. In practice, it is difficult to determine the acceleration directly. Instead, we can refer to its definition. Acceleration is the ratio of change of the velocity to the time it took to accelerate. Using this piece of information, we can rewrite the formula for the force as:

F=m×(vfvi)/dtF = m × (v_f - v_i) / dt

The new symbols are:

  • vf [m/s]v_f\rm\ [m/s] — the final velocity;
  • vi [m/s]v_i\rm \ [m/s] — the initial velocity; and
  • dt [s]dt\rm \ [s] — the time it took to change the velocity.

With this formula, you can compute the force you were looking for. You can also turn the equation around and ask what is the change of the velocity if you subject an object of mass m to the force F for dt seconds.

There is a related concept to the force, which is the impulse. Check the impulse and momentum calculator to learn more about it!

Newton's second law calculator

Computing the force is very easy with our Newton's second law calculator. Let us calculate the force it takes to stop a moving car.

The car weighs 3500 lb (1586 kg) and moves at the speed of 60 mph (97 km/h). To stop it in 20 s, you need a force of -2129 N (check the force converter for different measures of force). The minus sign signals that the force is acting opposite to the motion of the car: it's stopping the vehicle.

Speaking of Newton, you might wanna take a look at our newton meter (nm) to joules converter. It is worth checking out.

You could also check out the acceleration using force and mass calculator if you're looking to apply Newton's second law to find acceleration.


What are Newton's 1st, 2nd and 3rd laws of motion?

Newton's first law is that an object will remain at rest or in constant motion unless a net force acts upon it to accelerate it.

Newton's second law states that the acceleration (a) of an object is proportional to the net force (F) acting upon it and inversely proportional to its mass (m). This gives rise to the equation:

F = ma

Finally, Newton's third law says that for every action, there is an equal and opposite reaction.

When was Newton's 2nd law?

Newton's 2nd law was first published in 1687 in his book Philosophiæ Naturalis Principia Mathematica. It was the first time this law of motion appeared in print; however, Newton didn't discover it himself. Many scientists and philosophers were working on the problem of relating forces and the movement of objects.

Why is Newton's second law called the acceleration law?

Newton's second law is often called the acceleration law as it tells us how quickly an object will accelerate due to a force acting upon it, given we know the object's mass. To calculate the acceleration (m/s²), we divide the force (Newtons) by the mass (kg).

What's the driving force of a car that accelerates at 5 m/s²?

We can calculate the driving force of the car by:

  1. Assume the car has a mass of 2,000 kg.
  2. Multiply the mass by the acceleration: 2000 × 5.
  3. In this example, the answer is 10,000 newtons.
Miłosz Panfil, PhD and Dominik Czernia, PhD
Initial velocity
Final velocity
Time difference
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