Force Calculator

Force is any kind of push or pull that changes the motion of an object. To represent a force numerically, the method derived from Newton's second law of mechanics is most practical.

When you multiply the mass of an object by its acceleration, you get the resulting force acting on that object. This calculation tool takes into account all directions and allows to determine the third magnitude when two out of three magnitudes (force, mass, acceleration) are entered. Also, acceleration can be calculated from change in velocity.

Formula for calculating force:

The force is equal to mass times acceleration.

where F is the resulting force, m is mass and a is acceleration. In SI units, mass is measured in kilograms and acceleration in meters per second squared, giving the unit for the calculated force as the newton.

The newton is a derived unit. One newton is the force required to accelerate one kilogram of mass at the rate of one meter per second squared; i.e., 1 N = 1 kg⋅m/s2.

For example.

How much force is required to move a body of mass 20 kilograms with an acceleration of 3 meters per second squared?

You multiply the mass by the acceleration. Since 20 x 3 = 60, the object requires a resulting force of 60 newtons. If a lighter object has the same acceleration but only weighs 5 kilograms, then it would require a force of only 5 x 3 = 15 newtons, because the force is proportional to the mass.

Here's how to use this calculator.

This calculator allows you to fill in two out of three fields and get the third value instantly. If you leave the field for force blank, it will calculate the force from mass and acceleration. If either the mass or acceleration field is left blank, it will solve for that value given a known force.

There is a separate option for each input field to change the unit. Mass is entered in pounds and acceleration in feet per second squared, and the result of force can be shown as either Newtons or pound weight. All conversions are done by a calculator tool.

Calculating mass or acceleration from force.

Since these three quantities are related by only one equation, knowing any two of them allows the third to be calculated. By rearranging the formula F = ma in various ways, we can obtain two other useful formulas for calculating force.

If force and acceleration are known and mass is to be calculated, use the first formula. For example, to determine an object's mass from its state of motion under a known force. If force and mass are known and acceleration is to be calculated, use the second formula. For example, to determine the acceleration of a rocket engine given its thrust. The calculator automatically selects the correct formula if the field for the desired quantity is left blank.

Calculating force from change in velocity.

Even though the actual value of acceleration is not known, it is often known how much an object speeds up or slows down. Acceleration is defined as the change in velocity divided by the time taken for that change to occur.

If you open the "Velocity change" section and enter initial velocity, final velocity and time, the calculator will calculate acceleration. If mass is also entered, it will show force required for this velocity change as well.

A 1200 kg car accelerates from rest to 20 meters per second in 10 seconds. The acceleration is (20 - 0) / 10 = 2 meters per second squared, so the force required is 1200 x 2 = 2400 Newtons. This is about equivalent to the weight of a 245-kilogram object on Earth.

The same principle can also be used to explain impact forces. The shorter the time it takes for something to come to a stop, the greater the deceleration and therefore the force. If a car collides with something or a fist hits a target in a very short amount of time, even relatively low speeds can result in enormous forces.

Newton's three laws of motion are:

The formula for force is equivalent to Newton's second law of motion and these three laws work together.

The first law states that an object at rest or moving with a constant speed will remain at rest or keep moving in the same direction and at the same speed unless acted upon by an outside force. This is inertia.

The second law F=ma shows that the resultant force changes an object's state of motion. For a given acceleration, a heavier object needs more force.

The third law states that for every action there is an equal and opposite reaction. If you push against a wall, the wall pushes back with an equal amount of force.

Types of forces

Force is a broad concept that takes many forms. The most common forces encountered in everyday life include gravity, normal force, frictional force, tension force, applied push or pull, resistive forces and the restoring force of springs.

Resultant Force and Direction

Force is a vector; it has both magnitude and direction. When multiple forces act at the same time, it is the resultant force, which is the vector sum of all forces, that accelerates an object.

When the forces are balanced in all directions then the resultant force is zero and the body does not accelerate. This state is called equilibrium. This tool only deals with resultant forces in a straight line. If forces need to be combined at angles to resolve into components, please use a separate resultant calculator or vector tool.

Mass is not the same as weight.

Although often confused with weight, mass is not the same thing. Mass is measured in kilograms and refers to the amount of matter in an object; it does not change with location.

Weight is the force acting on a mass due to gravity and is calculated using the formula W = m * g where the unit is Newtons. The acceleration due to gravity on Earth is approximately 9.81 meters per second squared so an object with a mass of one kilogram has a weight of about 9.81 Newtons. To use this calculator, enter in the mass and set the acceleration to g or 9.81 meters per second squared to calculate weight.

Units of force

The result of the calculation will be shown in the unit you select. While newtons are the SI unit, other units are often used in engineering and older documents.

Where are force formulas used?

Engineers use this formula frequently. It is used in many applications from calculating the thrust required for rockets and airplanes to determining the stresses on mechanical parts and structures to the braking and impact forces that a vehicle must withstand.

This formula also has wide application in everyday life and sports. The force a sprinter exerts on the starting blocks, the force with which a boxer lands a punch, or the pulling force required to tow a trailer - all of these can ultimately be explained by multiplying mass and acceleration.

Common mistakes:

The most common mistake is confusing mass and weight. The unit of mass is kilograms while the unit for weight is newtons. Enter your mass, not your weight, into the field provided.

Be sure to pay attention to the units and make sure they are consistent or let the calculator do the conversion for you. Also remember that both force and acceleration have a direction. This tool only deals with resultant forces in a straight line, so other forces acting in opposite directions (such as friction) must be added separately.

This tool is for general educational purposes and solving common problems. For technical applications, safety issues or other risky activities you should verify the calculated values against standards and data required by your particular project.