Centrifugal Force Calculator
Calculate the centrifugal (outward) force and centripetal acceleration for an object moving in a circular path using linear or angular velocity.
Enter the object's mass, the radius of its circular path, and its velocity (linear or angular) to compute the centrifugal force and centripetal acceleration.
Centrifugal Force Calculator
Calculate the centrifugal (outward) force and centripetal acceleration for an object moving in a circular path using linear or angular velocity.
About the Centrifugal Force Calculator
Centrifugal force is described as an apparent or fictitious force that seems to push an object outward when it is constrained to travel in a circular path. It arises from inertia — the natural tendency of any object to continue moving in a straight line. When a force (the centripetal force) is applied to divert the object from its straight-line path into a curved one, the object's inertia resists the change, creating the sensation of an outward push. This calculator quantifies that apparent force and the centripetal acceleration required to maintain circular motion.
The two fundamental formulas for centrifugal force depend on how velocity is specified. For linear (tangential) velocity, the formula is F = m × v² / r, where F is the centrifugal force in Newtons, m is the mass in kilograms, v is the tangential speed in metres per second, and r is the radius of the circular path in metres. For angular velocity, the formula is F = m × ω² × r, where ω (omega) is the angular velocity in radians per second. If you know the rotation speed in RPM, convert using ω = RPM × 2π / 60 before applying this formula.
Centripetal acceleration, a = v²/r (or a = ω²×r), is the inward acceleration that must be supplied to keep the object in its circular path. The centrifugal force is exactly equal in magnitude to the centripetal force (m × a) but is directed outward rather than inward. In an inertial (non-rotating) reference frame, only the centripetal force is real; centrifugal force is the reaction as experienced in the rotating reference frame of the object itself.
It is essential to distinguish centrifugal force from centripetal force. Centripetal force is the real, centre-directed force that must be supplied to maintain circular motion — for example, tension in a string, gravitational attraction, normal force from a banked road, or magnetic force on a charged particle. Centrifugal force is the pseudo-force experienced by an observer in the rotating frame, always equal in magnitude to the centripetal force and directed radially outward.
Centrifugal force has widespread applications in engineering and science. Centrifuges in laboratories spin biological samples at high RPM to separate components by density, with the centrifugal effect pushing denser particles outward and leaving lighter material closer to the centre. Washing machines exploit centrifugal force in the spin cycle to expel water from clothing. Cream separators in dairy processing spin milk at high speed to separate cream (lower density) from skim milk (higher density). Banked road curves are engineered so that the normal force from the road provides a centripetal component that reduces the required friction for safe cornering at design speed.
This calculator supports both linear and angular velocity inputs, as well as multiple unit options for mass (kg, g, lb), radius (m, cm, ft, in), linear speed (m/s, km/h), and angular speed (RPM, rad/s), making it versatile for automotive, aerospace, laboratory, and physics applications.
Centrifugal Force Examples
Real-world scenarios demonstrating centrifugal force calculations.
| Inputs | Centrifugal Force | Application |
|---|---|---|
| m = 1500 kg, r = 50 m, v = 60 km/h (16.67 m/s) | F ≈ 8,333 N | Car navigating a 50 m radius curve at 60 km/h. The friction force required to maintain the curve is 8.3 kN, about 0.57 g of lateral acceleration. |
| m = 0.1 kg, r = 0.2 m, ω = 3000 RPM (314 rad/s) | F ≈ 1,974 N | Centrifuge tube sample at 3000 RPM, 200 mm radius. The sample experiences nearly 2000 × g, allowing rapid separation of cellular components. |
| m = 40 kg, r = 2.5 m, v = 3 m/s | F = 144 N | Child on a merry-go-round. The 144 N outward force equals 0.37 g, which is noticeable but safely within the grip strength of a child holding the bar. |
| m = 1000 kg, r = 6,771,000 m, ω = 0.0000727 rad/s (once per day) | F ≈ 35.8 N | Object at 6771 km radius rotating at Earth's sidereal day rate. The very low angular velocity (7.27×10⁻⁵ rad/s) produces only ~35.8 N despite the enormous radius. |
How to Use the Centrifugal Force Calculator
- Enter the mass of the object and select the appropriate unit (kg, g, or lb). For a car, this is the vehicle mass; for a lab sample, the sample mass.
- Enter the radius of the circular path and select the unit (m, cm, ft, or in). This is the distance from the object to the centre of rotation.
- Choose the velocity type: Linear Velocity if you know the object's tangential speed, or Angular Velocity if you know its rotation rate.
- Enter the velocity value and select its unit — m/s or km/h for linear, RPM or rad/s for angular. Then click Calculate.
- Read the results: Centrifugal Force in Newtons (the outward apparent force) and Centripetal Acceleration in m/s² (the inward acceleration required to maintain the circular path).
Centrifugal Force FAQ
Is centrifugal force a real force?
Centrifugal force is a pseudo-force or fictitious force — it does not arise from a physical interaction but from the mathematics of describing motion in a rotating reference frame. In an inertial (non-rotating) frame, only the centripetal force is real. In the rotating frame of the object, centrifugal force appears as a real outward force that exactly cancels the centripetal force, resulting in apparent equilibrium. For engineering calculations of forces on rotating objects, treating centrifugal force as real gives correct numerical results.
What is the difference between centrifugal and centripetal force?
Centripetal force is the real, centre-seeking force that causes circular motion — it can be gravity, tension, friction, a normal force component, or magnetic force. It always acts toward the centre of the circular path. Centrifugal force is the equal and opposite apparent force experienced by the object in the rotating reference frame, directed outward from the centre. They are equal in magnitude but opposite in direction; the centripetal force is the cause of circular motion, while centrifugal force is its perceived effect from within the rotating system.
How do I convert RPM to rad/s?
Multiply RPM by 2π and divide by 60: ω (rad/s) = RPM × 2π / 60. For example, 3000 RPM equals 3000 × 2π / 60 ≈ 314.16 rad/s. This conversion is handled automatically by the calculator when you select the RPM unit for angular velocity, so you can enter RPM directly without manual conversion.
Why does centrifugal force increase with the square of velocity?
Because the centripetal acceleration required to maintain circular motion is a = v²/r. Doubling the speed requires four times the centripetal acceleration, and therefore four times the centrifugal force. This quadratic relationship means that small increases in speed cause large increases in force at constant radius, which is why centrifuges are so effective at high RPM and why speeding vehicles require much greater cornering forces on curves.
How is centrifugal force used in centrifuges?
Laboratory centrifuges spin samples at thousands or tens of thousands of RPM to create centrifugal forces many times greater than gravity (expressed as multiples of g, called RCF or relative centrifugal force). The outward force pushes denser particles toward the bottom of the tube faster than gravity alone would allow, enabling rapid separation of blood cells from plasma, organelles from cells, proteins from solutions, and many other biological and chemical separations. The RCF is calculated as ω²r/g, where g = 9.81 m/s².
What is centripetal acceleration?
Centripetal acceleration is the inward acceleration that an object experiences when moving in a circular path. It is directed toward the centre of the circle and has magnitude a = v²/r for linear velocity, or a = ω²r for angular velocity. It is not slowing the object down — the object's speed stays constant — but continuously changes its direction toward the centre. The net force producing this acceleration (F = ma) is the centripetal force, supplied by whatever physical constraint keeps the object on its circular path.