Calculate centrifugal force from mass, radius, and angular velocity. Free physics calculator with step-by-step solutions for circular motion problems.
Calculate centrifugal force, mass, velocity, or radius for objects in circular motion
Formula:
F = m × v² / r
Where: F = Centrifugal Force, m = Mass, v = Velocity, r = Radius
Copy the code below to embed this calculator on your website
From amusement park rides to industrial centrifuges, centrifugal force affects our daily lives in countless ways. Whether you're an engineer designing rotating machinery, a physics student solving circular motion problems, or a safety professional analyzing g-forces on riders, understanding how mass, radius, and rotational speed create outward forces is essential. Our centrifugal force calculator makes these complex calculations simple, helping you quickly determine the forces at play in any rotating system. For related motion calculations, explore our Angular Velocity Calculator to analyze rotational speed.
Follow these steps to get instant results:
Centrifugal force is the apparent outward force experienced by an object moving in a circular path. While technically an inertial force (felt in a rotating reference frame), it's calculated using the object's mass, rotational speed, and radius of rotation. The formula depends on whether you're using angular or linear velocity.
Fc = m × ω² × r
or
Fc = m × v² / r
Where: Fc = centrifugal force (N), m = mass (kg), ω = angular velocity (rad/s), r = radius (m), v = linear velocity (m/s)
Calculate the centrifugal force on a 5 kg object rotating at 10 rad/s with a radius of 2 meters:
Centrifugal force calculations are essential across numerous industries and scenarios:
Centripetal force is the real inward force that keeps an object moving in a circle, directed toward the center of rotation. Centrifugal force is the apparent outward force experienced in a rotating reference frame—it's what you feel pushing you outward on a merry-go-round. They are equal in magnitude but opposite in direction, and both are calculated using the same formula.
To convert revolutions per minute (RPM) to radians per second (rad/s), use this formula: ω (rad/s) = RPM × 2π / 60. For example, 300 RPM = 300 × 6.2832 / 60 = 31.42 rad/s. Many calculators handle this conversion automatically when you select RPM as your input unit.
Centrifugal force increases with the square of angular velocity (Fc = m × ω² × r), so doubling the rotation speed quadruples the centrifugal force. For example, if a system produces 100 N at 10 rad/s, it will produce 400 N at 20 rad/s. This quadratic relationship makes rotational speed the most influential factor.
No, centrifugal force magnitude is always positive since it's calculated using squared values (ω² or v²). The direction is always radially outward from the center of rotation. However, the centripetal force (which keeps the object in circular motion) points inward and is often represented as negative in equations.
A car turning at 30 mph (13.4 m/s) with a 50-meter radius experiences about 0.36 times gravity (3.6 m/s² acceleration). Industrial centrifuges can reach 100,000 g or more. Amusement park rides typically limit forces to 3-6 g for safety and comfort. Earth's rotation creates only 0.03 m/s² centrifugal acceleration at the equator—barely noticeable.
Mastering centrifugal force calculations empowers you to analyze and design rotating systems safely and effectively. Our calculator provides instant, accurate results whether you're working with high-speed machinery or studying fundamental physics concepts.
Explore more Physics tools: Check out our Acceleration Calculator for linear motion analysis or discover the Force Calculator for general force calculations.
Get instant results with our optimized calculation engine
Precise calculations you can trust for any project
Works perfectly on all devices and screen sizes