Centrifugal Force Calculator
Last Updated: October 29, 2025
Calculate centrifugal force from mass, velocity, radius, angular velocity, frequency, and period using circular motion equations. Essential tool for physics rotating systems, circular motion, and mechanical engineering analysis.
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Table of Contents
What is Centrifugal Force Calculator?
Understanding Rotating Systems and Circular Motion
The Centrifugal Force Calculator is a specialized physics tool that calculates centrifugal force (F) from various parameters including mass, velocity, radius, angular velocity, frequency, and period. Centrifugal force is the apparent outward force experienced in rotating reference frames and is fundamental to understanding circular motion, rotating systems, and mechanical engineering applications.
This calculator is essential for analyzing rotating systems in physics, engineering, and mechanical applications. It provides accurate calculations for centrifugal force using multiple methods, including mass-velocity-radius relationships, angular velocity conversions, and frequency-period conversions.
Key Concepts
Centrifugal Force (F): Apparent outward force in rotating frames, measured in Newtons (N). This is a "fictitious" or "pseudo" force that appears in non-inertial (rotating) reference frames, equal in magnitude but opposite in direction to centripetal force.
Mass (m): Mass of the rotating object, measured in kilograms (kg). Heavier objects experience greater centrifugal force at the same rotation rate and radius.
Linear Velocity (v): Tangential speed in circular motion, measured in meters per second (m/s). The speed along the circular path determines the centrifugal force magnitude.
Angular Velocity (ω): Rate of rotation about an axis, measured in radians per second (rad/s). Faster rotation produces greater centrifugal force, and the relationship is quadratic (doubling angular velocity quadruples force).
Radius (r): Distance from axis of rotation, measured in meters (m). Objects farther from the axis experience greater centrifugal force for the same rotation rate.
Physical Interpretation
Centrifugal force is not a real force in inertial reference frames - it's a fictitious force that appears when analyzing motion from a rotating frame of reference. In an inertial frame, objects moving in circles require centripetal force (inward). But from the rotating frame's perspective, objects appear to be pushed outward, which we call centrifugal force. This apparent force results from the frame's acceleration, not from any physical interaction between objects.
The magnitude of centrifugal force equals the magnitude of centripetal force (F = mv²/r = mω²r) but points in the opposite direction (outward instead of inward). This explains why you feel pushed outward on a rotating platform, why water stays in a spinning bucket, and why clothes stick to the drum in a washing machine. These effects are real experiences in rotating frames, even though centrifugal force isn't a fundamental force.
Relationship to Centripetal Force
Centrifugal force is equal in magnitude but opposite in direction to centripetal force. In inertial frames, only centripetal force exists (the real force causing circular motion). In rotating frames, centrifugal force appears to balance the centripetal force, creating an apparent equilibrium. This is why objects appear stationary relative to a rotating platform - from that frame's view, centrifugal and centripetal forces appear to cancel.
Practical Applications
Despite being a fictitious force, centrifugal force calculations are essential in engineering rotating systems. Centrifuges use it to separate materials by density. Rotating platforms use it to create artificial gravity. Washing machines use it to extract water from clothes. Understanding centrifugal force helps design safe rotating machinery, calculate stresses in rotating components, and predict material behavior in rotating systems.
Historical Development
Centrifugal force was recognized as part of analyzing rotating reference frames, developed alongside understanding of circular motion and inertia in the 17th and 18th centuries. The concept became important with the development of non-inertial reference frames and the principle of equivalence. It explains why objects appear pushed outward when rotating, from simple examples like water in a spinning bucket to complex machinery like centrifuges and turbines. The mathematical treatment of fictitious forces was formalized in classical mechanics and remains essential in engineering applications.
Units and Frame Dependence
SI Unit: N (Newton) - same units as real forces
Magnitude: F = mv²/r = mω²r = m(2πf)²r = m(2π/T)²r (same formulas as centripetal force)
Direction: Always outward from the axis of rotation (opposite to centripetal force)
Frame Dependence: Only appears in rotating/non-inertial reference frames; doesn't exist in inertial frames
Formulas and Equations
Centrifugal Force Calculation Methods
1. From Mass, Velocity, and Radius
F = mv²/r
Where:
- • F = Centrifugal force (N)
- • m = Mass (kg)
- • v = Linear (tangential) velocity (m/s)
- • r = Radius (m)
Use case: Calculate centrifugal force when you know mass, linear velocity, and radius. This is the most direct method using linear motion parameters. Essential for analyzing objects moving in circles where tangential speed is measured, such as vehicles on curved roads, objects on strings, or particles in circular paths. The squared velocity means doubling speed quadruples centrifugal force.
2. From Mass, Angular Velocity, and Radius
F = mω²r
Where:
- • F = Centrifugal force (N)
- • m = Mass (kg)
- • ω = Angular velocity (rad/s)
- • r = Radius (m)
Use case: Calculate centrifugal force using angular velocity, which is often more convenient for rotating systems where rotation rate is known. Derived from F = mv²/r using v = rω. Particularly useful for rotating machinery, centrifuges, flywheels, and any system where angular speed is measured or specified. Common in mechanical engineering applications involving rotating components.
3. From Mass, Frequency, and Radius
F = m(2πf)²r
Where:
- • F = Centrifugal force (N)
- • m = Mass (kg)
- • f = Frequency (Hz)
- • r = Radius (m)
- • π ≈ 3.14159
Use case: Calculate centrifugal force from frequency, common for rotating machinery, motors, and systems where rotation frequency is measured directly. Converts frequency to angular velocity using ω = 2πf, then applies the angular velocity formula. Useful for equipment with known operating frequencies, such as motors, pumps, and rotating tools. Frequency is often directly measured or specified in equipment datasheets.
4. From Mass, Period, and Radius
F = m(2π/T)²r
Where:
- • F = Centrifugal force (N)
- • m = Mass (kg)
- • T = Period (s)
- • r = Radius (m)
- • π ≈ 3.14159
Use case: Calculate centrifugal force from period, useful when you know the time for one complete rotation rather than rotation rate. Converts period to angular velocity using ω = 2π/T, then applies the angular velocity formula. Particularly useful in experimental physics where period measurements are common, or for analyzing slow-rotating systems like pendulums, rotating platforms, or periodic circular motion where time measurements are easier than speed measurements.
Applications of Centrifugal Force
Real-World Uses Across Industries
| Industry | Applications | Importance |
|---|---|---|
| Mechanical Engineering | Centrifuges, rotating machinery, pumps, separators, turbines, flywheels | Critical for design and stress analysis |
| Medical & Laboratory | Blood separation, sample processing, DNA extraction, cell culture | Essential for diagnostic procedures |
| Automotive | Tire balancing, engine balancing, washing machines, water pumps | Vital for vehicle performance and safety |
| Aerospace | Satellite stabilization, rotating space stations, gyroscopes, reaction wheels | Key for attitude control and artificial gravity |
| Industrial Processing | Material separation, wastewater treatment, oil processing, chemical separation | Fundamental for industrial processes |
Examples of Centrifugal Force Calculation
Real-World Applications and Use Cases
Example 1: Car Wheel at Highway Speed
Given:
- • Mass: m = 15 kg
- • Velocity: v = 100 km/h
- • Radius: r = 0.35 m
Step-by-step calculation:
Step 1: Convert velocity to m/s
v = 100 km/h = 100 × (1000/3600) = 27.78 m/s
Step 2: Apply centrifugal force formula
F = mv²/r
F = 15 × (27.78)² / 0.35
F = 15 × 771.6 / 0.35
F = 33,068 N
Final Answer
33,068 N (33.07 kN)
This represents the centrifugal force on the car wheel at highway speed
Example 2: Centrifuge Rotor
Given:
- • Mass: m = 0.1 kg
- • Angular Velocity: ω = 3000 rpm
- • Radius: r = 0.1 m
Step-by-step calculation:
Step 1: Convert angular velocity to rad/s
ω = 3000 rpm = 3000 × 2π / 60 = 314.16 rad/s
Step 2: Apply centrifugal force formula
F = mω²r
F = 0.1 × (314.16)² × 0.1
F = 0.1 × 98,660 × 0.1
F = 986.6 N
Final Answer
986.6 N
This represents the centrifugal force on the centrifuge sample, equivalent to about 1006 times its weight
Example 3: Washing Machine Spin Cycle (Frequency Method)
Given:
- • Mass of water: m = 2 kg
- • Spin frequency: f = 15 Hz (900 rpm)
- • Drum radius: r = 0.25 m
Step-by-step calculation:
Step 1: Apply centrifugal force formula with frequency
F = m(2πf)²r
F = (2 kg) × (2π × 15 Hz)² × (0.25 m)
F = 2 × (30π)² × 0.25
F = 2 × 8,876 × 0.25
F = 4,438 N
Step 2: Compare to weight
Weight = mg = 2 × 9.81 = 19.6 N
Centrifugal force / Weight = 4,438 / 19.6 = 226 times
Final Answer
4,438 N
This centrifugal force is 226 times the water's weight, explaining why water is effectively "thrown" out of clothes during the spin cycle, leaving them much drier than gravity alone could achieve.