Force (F = ma) Calculator

Newton's Second Law Calculator

F = ma

What would you like to calculate?

Mass:

Acceleration:

Common Acceleration Values:

Earth's Gravity

9.81 m/s²

Acceleration due to gravity at Earth's surface

Moon's Gravity

1.62 m/s²

Acceleration due to gravity on the Moon

Mars' Gravity

3.72 m/s²

Acceleration due to gravity on Mars

Car (0-100 km/h in 10s)

2.78 m/s²

Typical car acceleration from 0 to 100 km/h in 10 seconds

Sports Car (0-100 km/h in 3s)

9.26 m/s²

High-performance car acceleration from 0 to 100 km/h in 3 seconds

Space Shuttle Launch

29.4 m/s²

Initial acceleration of space shuttle at launch (3g)

Fighter Jet Catapult

49 m/s²

Aircraft carrier catapult launch acceleration (5g)

About Newton's Second Law

Newton's Second Law of Motion states that the force acting on an object is equal to the mass of that object multiplied by its acceleration. It is one of the most fundamental laws in classical mechanics.

F = ma

Where:

F is the net force acting on the object (in newtons, N)
m is the mass of the object (in kilograms, kg)
a is the acceleration produced (in meters per second squared, m/s²)

This law explains why heavier objects require more force to move at the same acceleration as lighter objects. It also explains why the same force causes a greater acceleration in a lighter object compared to a heavier one.

+ Learn More About Newton's Laws

Newton's Three Laws of Motion

Sir Isaac Newton published three laws of motion in his 1687 work "Philosophiæ Naturalis Principia Mathematica" (Mathematical Principles of Natural Philosophy):

First Law (Law of Inertia): An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Second Law (F = ma): The force acting on an object is equal to the mass of that object multiplied by its acceleration.

Third Law: For every action, there is an equal and opposite reaction.

Alternative Forms

Newton's Second Law can also be written as:

F = Δ(mv)/Δt

Where Δ(mv) is the change in momentum and Δt is the time interval. This form is more general and applies even when mass is not constant.

Units of Measurement

In the International System of Units (SI):

Force is measured in newtons (N)
Mass is measured in kilograms (kg)
Acceleration is measured in meters per second squared (m/s²)

One newton is defined as the force needed to accelerate one kilogram of mass at a rate of one meter per second squared.

Applications

Newton's Second Law is used in countless applications:

Engineering design of vehicles, machinery, and structures
Sports science for optimizing athletic performance
Aerospace engineering for designing aircraft and spacecraft
Safety engineering for designing protective equipment
Robotics and control systems

Limitations

Newton's Second Law breaks down in certain scenarios:

At speeds approaching the speed of light (relativistic effects become significant)
At quantum scales (quantum mechanics replaces classical mechanics)
In extremely strong gravitational fields (general relativity applies)

Force Calculator (F = ma)