Centrifugal Force Calculator – Calculate F = mv²/r & mω²r Online

  • Adam
  • November 27, 2025

Calculate centrifugal force instantly from velocity, angular velocity, or RPM. Free calculator with step-by-step solutions, multiple calculation modes, and comprehensive formulas for rotating systems in Newtons.

Centrifugal Force Calculator - Calculate F = mv²/r & mω²r

A centrifugal force calculator determines the apparent outward force experienced by objects in rotating reference frames. While centrifugal force is a fictitious or pseudo force from an inertial perspective, it has real effects in rotating systems including centrifuges, vehicles navigating curves, and spinning objects, making accurate calculations essential for engineering and physics applications.

Calculate Centrifugal Force

Result:

What is Centrifugal Force?

Centrifugal force is an apparent outward force that acts on objects moving in a circular path when observed from a rotating reference frame. In physics, it is classified as a fictitious or inertial force because it does not result from physical interaction but rather from the frame of reference itself. Despite being "fictitious" from an inertial viewpoint, centrifugal force produces real, measurable effects in rotating systems and must be accounted for in engineering calculations involving rotation.

Key Characteristics of Centrifugal Force:

  • Fictitious force: Appears only in non-inertial (rotating) reference frames, not in inertial frames
  • Outward direction: Always points radially outward from the center of rotation
  • Equal magnitude: Has the same magnitude as centripetal force but opposite direction
  • Real effects: Produces tangible consequences like tension in rotating systems and forces on occupants in turning vehicles
  • Units: Measured in Newtons (N) in SI units
  • Proportional to radius: Increases with distance from the rotation axis for constant angular velocity

Centrifugal Force Formula

Centrifugal force can be calculated using different formulas depending on which parameters are known. The fundamental equations relate force to mass, velocity, radius, and angular velocity.

Centrifugal Force from Linear Velocity

Fc = mv² / r

Where:

  • Fc = centrifugal force (Newtons, N)
  • m = mass of the object (kg)
  • v = tangential/linear velocity (m/s)
  • r = radius of circular path (m)

Centrifugal Force from Angular Velocity

Fc = mω²r

Where:

  • Fc = centrifugal force (N)
  • m = mass (kg)
  • ω = angular velocity (rad/s)
  • r = radius (m)

Relationship Between Formulas

The two formulas are equivalent because linear velocity and angular velocity are related by v = ωr:

Substituting v = ωr into F = mv²/r:

F = m(ωr)²/r = mω²r²/r = mω²r

This confirms both formulas describe the same physical quantity

Centrifugal Acceleration

The centrifugal acceleration (acceleration experienced in the rotating frame) is:

ac = v²/r = ω²r

Force from acceleration:

Fc = mac

Centrifugal Force vs Centripetal Force

Understanding the distinction between centrifugal and centripetal forces is crucial for correctly analyzing circular motion:

Characteristic Centripetal Force Centrifugal Force
Definition Real force causing circular motion Apparent force in rotating frame
Direction Inward toward center Outward away from center
Nature Real force (physical interaction) Fictitious/inertial force
Reference Frame Exists in inertial frames Exists only in rotating frames
Magnitude F = mv²/r F = mv²/r (same magnitude)
Examples Tension, gravity, friction Sensation in turning vehicle

Key Distinction:

From an inertial (stationary) observer's perspective, only centripetal force exists—it's the real force pulling the object toward the center to maintain circular motion. From the rotating object's perspective, the object appears stationary while experiencing an outward centrifugal force. Both perspectives are valid for their respective reference frames, but only centripetal force is a "real" force arising from physical interaction.

How to Calculate Centrifugal Force

Calculating centrifugal force requires identifying the known parameters and selecting the appropriate formula. Follow these systematic steps:

  1. Identify known parameters: Determine what information you have—mass, linear velocity, angular velocity, RPM, or radius.
  2. Select the appropriate formula: Use F = mv²/r for linear velocity or F = mω²r for angular velocity.
  3. Convert units if necessary: Ensure mass is in kg, velocity in m/s, radius in meters, and angular velocity in rad/s.
  4. Convert RPM to rad/s if needed: Use ω = 2πn/60 where n is RPM.
  5. Substitute values: Plug all known values into the selected formula.
  6. Calculate the result: Perform the mathematical operations to find force in Newtons.
  7. Verify reasonableness: Check that the result makes physical sense for the system being analyzed.

Calculation Example 1: From Linear Velocity

Problem: A 1000 kg car travels at 20 m/s around a curve with radius 50 meters. Calculate the centrifugal force experienced by the car (from the car's reference frame).

Solution:

Given: m = 1000 kg, v = 20 m/s, r = 50 m

Using formula: Fc = mv²/r

Fc = 1000 × (20)² / 50

Fc = 1000 × 400 / 50

Fc = 400,000 / 50

Fc = 8,000 N = 8 kN

Interpretation: From the car's rotating reference frame, occupants experience an apparent outward force of 8,000 N pushing them toward the outside of the curve.

Calculation Example 2: From Angular Velocity

Problem: A 0.5 kg object in a centrifuge rotates at 10 rad/s at a radius of 0.2 m. Find the centrifugal force.

Solution:

Given: m = 0.5 kg, ω = 10 rad/s, r = 0.2 m

Using formula: Fc = mω²r

Fc = 0.5 × (10)² × 0.2

Fc = 0.5 × 100 × 0.2

Fc = 10 N

Additional calculation:

Linear velocity: v = ωr = 10 × 0.2 = 2 m/s

Verification: F = mv²/r = 0.5 × (2)²/0.2 = 10 N ✓

Calculation Example 3: From RPM

Problem: A 2 kg mass rotates at 300 RPM at a radius of 0.5 m. Calculate the centrifugal force.

Solution:

Step 1: Convert RPM to rad/s

ω = 2πn/60 = 2π × 300/60 = 10π rad/s = 31.42 rad/s

Step 2: Calculate centrifugal force

Fc = mω²r = 2 × (31.42)² × 0.5

Fc = 2 × 987.24 × 0.5

Fc = 987.24 N

Note: This significant force (about 100 kg-force) demonstrates why proper structural design is critical for rotating machinery.

Applications of Centrifugal Force

Centrifugal force concepts and calculations are essential across numerous practical applications:

  • Centrifuges: Separating substances by density in laboratory, medical, and industrial centrifuges using controlled centrifugal acceleration
  • Vehicle Dynamics: Analyzing forces on passengers and structural loads in vehicles navigating curves at various speeds
  • Washing Machines: Spin cycles use centrifugal force to extract water from clothes by forcing it radially outward
  • Amusement Rides: Designing safe roller coasters, centrifuges, and spinning rides that produce controlled centrifugal effects
  • Rotating Machinery: Calculating stresses in turbines, flywheels, and rotating components to prevent mechanical failure
  • Space Stations: Proposed artificial gravity in rotating space stations using centrifugal acceleration
  • Cream Separators: Dairy industry devices that separate cream from milk based on density differences
  • Centrifugal Pumps: Fluid movement devices that use rotation to create pressure through centrifugal acceleration
  • Planetary Motion: Understanding orbital mechanics from rotating reference frames

Centrifugal Force in Different Scenarios

Banking of Roads

Road curves are often banked (tilted) to help vehicles navigate safely at higher speeds by providing a component of the normal force toward the center:

Optimal banking angle:

tan θ = v² / (rg)

Where θ is banking angle, v is velocity, r is radius, and g is gravitational acceleration

Centrifugal Force in Rotating Reference Frames

In a rotating reference frame (like a merry-go-round), objects experience centrifugal force even when stationary relative to the frame:

Force on stationary object in rotating frame:

An object at rest in a rotating frame experiences centrifugal force F = mω²r directed outward. This explains why riders on a merry-go-round must hold on—the centrifugal force tries to throw them outward despite being "stationary" relative to the platform.

Frequently Asked Questions

What is the formula for centrifugal force?
The centrifugal force formula is Fc = mv²/r where m is mass (kg), v is tangential velocity (m/s), and r is radius (m). Alternatively, using angular velocity: Fc = mω²r where ω is angular velocity (rad/s). Both formulas are equivalent since v = ωr. The force is measured in Newtons (N) and represents the apparent outward force in a rotating reference frame. For example, a 10 kg object moving at 5 m/s in a 2 m radius circle experiences F = 10 × 25/2 = 125 N of centrifugal force.
What is the difference between centrifugal and centripetal force?
Centripetal force is a real force directed inward toward the center of rotation that causes circular motion (like tension or gravity). Centrifugal force is a fictitious force directed outward that appears only in rotating reference frames. They have equal magnitude (F = mv²/r) but opposite directions. From an inertial observer's view, only centripetal force exists. From a rotating object's view, centrifugal force appears to push outward. For example, in a turning car, friction provides real centripetal force, while passengers feel apparent centrifugal force pushing them outward.
How do you calculate centrifugal force from RPM?
To calculate from RPM: (1) Convert RPM to angular velocity using ω = 2πn/60 where n is RPM, (2) Use formula F = mω²r. Example: For 600 RPM, m = 5 kg, r = 0.3 m: ω = 2π(600)/60 = 20π = 62.83 rad/s, then F = 5 × (62.83)² × 0.3 = 5,921 N. Alternatively, convert RPM to linear velocity first using v = 2πrn/60, then use F = mv²/r. Both methods give identical results.
Is centrifugal force real or fictitious?
Centrifugal force is classified as a fictitious or pseudo force because it does not arise from physical interaction between objects. It appears only in non-inertial (rotating) reference frames due to the frame's acceleration, not from a physical push or pull. However, its effects are real—it produces measurable tension, deformation, and motion in rotating systems. The distinction matters for physics analysis: in inertial frames, use only real centripetal force; in rotating frames, include fictitious centrifugal force for calculations.
Why does centrifugal force increase with radius?
For constant angular velocity ω, centrifugal force F = mω²r increases linearly with radius r because objects farther from the axis must travel faster (v = ωr increases) to maintain the same rotation rate. Since force depends on v² or ωr, doubling the radius doubles the centrifugal force at constant angular velocity. This explains why outer parts of rotating machinery experience higher stresses and why riders on the outside edge of a merry-go-round feel stronger outward force than those near the center.
How do you calculate centrifugal acceleration?
Centrifugal acceleration is calculated using ac = v²/r or ac = ω²r, measured in m/s². It represents the acceleration experienced in the rotating frame. To find force, multiply by mass: F = mac. Example: For v = 10 m/s, r = 5 m: ac = 100/5 = 20 m/s². For a 50 kg person, F = 50 × 20 = 1,000 N. This acceleration is often expressed in g-forces: ac/g where g = 9.8 m/s². In this example: 20/9.8 = 2.04 g.
What factors affect centrifugal force?
Centrifugal force depends on three factors: (1) Mass—directly proportional; doubling mass doubles force, (2) Velocity—proportional to velocity squared (v²); doubling velocity quadruples force, (3) Radius—inversely proportional for linear velocity (F = mv²/r); halving radius doubles force at constant v. For angular velocity, radius has opposite effect (F = mω²r); larger radius increases force at constant ω. Temperature, altitude, and other environmental factors don't directly affect centrifugal force but may influence material properties in rotating systems.
How is centrifugal force used in centrifuges?
Centrifuges use high-speed rotation to create strong centrifugal force that separates substances by density. Denser materials experience greater centrifugal force and move outward faster than less dense materials. Laboratory centrifuges reach 3,000-15,000 RPM creating forces of hundreds to thousands of g's. The separation rate depends on F = mω²r—higher rotation speeds (ω) and larger radii (r) create stronger separation forces. Medical centrifuges separate blood components, while industrial centrifuges process chemicals, purify liquids, and extract materials.
Can centrifugal force cause objects to break?
Yes, excessive centrifugal force can cause structural failure in rotating objects. As rotation speed increases, centrifugal stress (force per unit area) increases proportionally to ω². When this stress exceeds the material's tensile strength, the object breaks. This is why flywheels, turbines, and rotating machinery have maximum rated speeds. For example, a disc rotating at 10,000 RPM experiences tremendous radial stress that could cause it to burst if material strength is insufficient. Engineers must calculate maximum centrifugal forces and design with appropriate safety factors.
What is the relationship between centrifugal force and speed?
Centrifugal force is proportional to the square of velocity: F = mv²/r. This quadratic relationship means force increases dramatically with speed—doubling speed quadruples the force, tripling speed increases force ninefold. For example, at 10 m/s, F might be 100 N, but at 20 m/s, F becomes 400 N. This explains why vehicle accidents on curves are much more severe at higher speeds and why precise speed control is critical in centrifuge operations. The v² dependence makes high-speed rotation particularly demanding on structural components.

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