Acceleration Using Force and Mass Calculator

Acceleration is the rate of change in velocity of an object. If the resultant force acting on an object and its mass are known then the acceleration can be calculated directly from Newton's second law.

Dividing the resulting force by the mass gives acceleration. This calculator supports two way calculations, you can enter a force and a mass to find the acceleration or leave one of the fields blank to calculate either the force or the mass. Acceleration can also be calculated from change in velocity.

Formula for calculating acceleration:

Acceleration is the result of dividing the resulting force by mass.

In this equation 'a' stands for acceleration, 'F' is the resulting force and 'm' is mass. In the SI system of units, force is measured in Newtons (N), mass in kilograms (kg) and so the unit of acceleration calculated will be metres per second squared (m/s2).

This is Newton's second law of motion. This law is usually expressed as F = ma but here it has been rearranged to solve for acceleration. The greater the force, the greater the acceleration. Objects with more mass are harder to change their state of motion so they accelerate less for a given amount of force.

Example calculation:

If a force of 50 newtons is applied to an object with a mass of 10 kilograms, what will the acceleration be?

Divide the force by the mass: 50/10 = 5. The acceleration of the object is thus 5 meters per second squared. If the same 50 Newtons of force were applied to an object with a greater mass, say 25 kilograms, the acceleration would be much less: 50/25 = 2 meters per second squared. This is because acceleration and mass are inversely proportional.

To use this calculator:

Enter force and mass, and the calculator will calculate acceleration. Since units can be changed separately for each entry, you can enter force in pounds of weight, mass in pounds, and display acceleration in meters per second squared, feet per second squared, or g's.

All three values can be calculated against each other. If you leave the acceleration blank, the tool will calculate it from the force and mass. Conversely, you can also leave a force or mass blank and work out the acceleration from the known values.

Calculate force or mass backwards.

Since force, mass and acceleration are related by the same equation, if any two of these quantities are known, the remaining quantity can be found. The equation a=F/m can be rearranged to give two other forms.

If mass and acceleration are known and force is to be found, the first equation is used. If force and acceleration are known and mass is to be found, the second equation is used. By entering the value for the desired quantity into its respective field, the calculator will automatically select the correct rearranged equation.

Calculate acceleration from change in speed.

Even if the force is unknown, there may be situations in which it is known whether an object is accelerating or decelerating. Acceleration is the value obtained by dividing the change in velocity by the time taken for that change to occur.

When the change in velocity field is opened and the initial velocity, final velocity, and time are entered, the calculator will calculate acceleration. If mass is also entered, the tool will show both the total force required to create this change in velocity as well as the distance traveled based on F=ma.

Suppose a car accelerates from rest to 20 meters per second in 4 seconds. The acceleration is (20 - 0) / 4 = 5 meters per second squared. If the car reaches 20 meters per second and takes 10 seconds to come to a stop by braking, then the acceleration is (0 - 20) / 10 = -2 meters per second squared. The negative sign indicates that the car is decelerating.

Acceleration as a multiple of Earth's gravity

It is common to specify acceleration in terms of "g", which is a multiple of the Earth's gravitational acceleration. The Earth's gravitational acceleration is approximately 9.81 meters per second squared. An acceleration of 1 g means that an object's velocity changes as quickly as it would under free fall on Earth.

This representation makes it easier to intuitively understand large accelerations. Acceleration when a car is rapidly accelerating is usually a fraction of g, while hard braking can be about 1g. Roller coasters have accelerations near the top that are close to 4-6g and airplane pilots can experience accelerations as high as 9g for short periods of time. The calculator also shows the acceleration in terms of multiples of Earth's gravity.

Newton's three laws of motion

The formula for acceleration is derived from the second law of Newton's three laws of motion. These three laws together describe how objects move.

The first law states that a body at rest or moving with uniform velocity will remain so unless acted upon by an external force. This is the law of inertia.

The second law F = ma shows that the resultant force changes the state of motion of a body and causes an acceleration a = F / m. The larger the mass of a body is, the greater must be the force to produce the same acceleration.

The third law says forces always appear in pairs: whatever force one object applies to another comes back equal in size and opposite in direction. A sprinter accelerates because the track pushes forward on the foot exactly as hard as the foot pushes back on the track.

The resulting force is decisive.

The force used in the equation a = F / m is the resultant force. This is the overall force obtained by vector addition of all forces (pushes and pulls) acting on an object. If multiple forces are acting at the same time, they must first be added together using the rules of vector addition.

If each individual force is balanced by another, the resultant force will be zero and the body will not experience acceleration. The body will remain at rest or continue its uniform motion. A common mistake is to only consider the driving force and ignore forces acting in the opposite direction (e.g. frictional forces or resistive forces). This results in a larger calculated acceleration than actually exists.

Mass and weight are different.

Although mass and weight are often confused, they are different quantities. Mass is measured in kilograms and refers to the amount of matter in an object; it does not change with location. When stating a quantity of mass, always state the mass itself, not the weight.

Weight is the force of gravity acting on an object and is calculated using the formula W = m * g, where the unit is Newtons. On Earth, g is approximately 9.81 meters per second squared. If you input the weight in Newtons as a force and specify the mass of the object, the tool calculates the value of g. This also explains why the acceleration due to gravity is about 9.81 meters per second squared and independent of the mass of the object.

Acceleration units:

Acceleration can be expressed in any units. The SI unit is meters per second squared but there are other common units as well.

Practical applications of the acceleration formula.

This formula has wide application, from engineering to everyday life. Car manufacturers calculate the acceleration of a vehicle based on the force generated by the engine and the mass of the vehicle. Rocket developers divide thrust by mass to determine acceleration at launch. As the mass of a rocket decreases due to fuel consumption, its acceleration gradually increases.

This formula also helps explain everyday motion phenomena. An empty shopping cart has a much greater acceleration than a loaded one when the same force is applied. A lighter bike accelerates faster than a heavier one if you pedal with the same amount of force.

Common mistakes:

The most common mistake is confusing mass and weight. The unit of mass is the kilogram, while weight is a type of force and has the unit Newtons. When doing calculations make sure you divide by the mass not the weight to get the force.

Be sure to pay attention to units and make sure they are consistent or convert the values using a calculator. Also keep in mind that acceleration and force have direction. This tool will treat the resulting force as being in a straight line. A negative result indicates that an object is slowing down or moving in the opposite direction of the chosen positive direction.

This tool is for general learning and solving everyday problems. If used in engineering, safety or other important tasks, verify the results against standards and data required by your project.