# Centrifugal Force Calculator

Rotational motion is present in many real-life situations, such as the movement of centrifugal pumps, car engines, orbital period formula, or the tagada of amusement parks; for that reason, we created this centrifugal force calculator.

In the following section, we talk about:

- The definition of centrifugal force.
- The acceleration and centrifugal force formulas.
- The equation for centrifugal force calculation, with velocity in rpm instead of rad/s.

🔎 If you're dealing with tangential forces, our angular displacement calculator can be helpful. Then, you can use that displacement and the tangential force to find the work using .

## Centrifugal force definition

Centrifugal force is the fictitious or inertial force that a rotating object feels. We consider it fictitious because it only appears in non-inertial frames of reference, while the observers in an inertial reference frame don't perceive it.

## Centrifugal acceleration formula

Understanding the centrifugal acceleration is necessary to know where the centrifugal force formula comes from.

The centrifugal acceleration formula is:

where:

- $a$ — centrifugal acceleration (
**m/s**);^{2} - $\omega$ — angular speed (
**m/s**); and - $r$ — radial distance to the axis of rotation (
**m**).

We can also express the centrifugal acceleration formula in terms of the tangential velocity $v$:

## Centrifugal force formula

The equation for centrifugal force comes from the definition of force, which says it equals mass times acceleration. Multiplying mass by angular acceleration, we have:

where:

- $F$ — Centrifugal force, usually expressed in newtons (check the for more information about force units);
- $m$ — Mass of the object;
- $\omega$ — Angular velocity
- $r$ — Radial distance to the axis of rotation.

As with centrifugal acceleration, we can express the centrifugal force equation in terms of tangential speed:

Since the centrifugal force is strictly related to the rotational motion, you may want to express the coordinates with a **more convenient system**. Check our cartesian to polar coordinates calculator to see the latter method's advantages.

## Centrifugal force formula in rpm

Sometimes we need to calculate the centrifugal force, but we possess the angular velocity in rpm instead of rad/s. Instead of converting from rad/s to rpm, we can develop a centrifugal force formula for rpm inputs:

First, let's remember the relationship between rad/s to rpm.

Considering the previous relationship, we can calculate the centrifugal force (using rev/min) with the following formula:

In the previous formula, $RPM$ is the angular velocity in revolutions per minute.