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Walk-through

How to Use This Calculator

3 steps

1

Choose a mode

Pick Force (enter mass, velocity, radius), From RPM (enter mass, rotational speed in RPM, radius), or G-Force (see the result expressed as a multiple of standard gravity). Switching tabs keeps your other values in sync.

2

Enter mass, speed, and radius

Enter the object's mass in kilograms, its speed (tangential velocity in m/s, or rotational speed in RPM), and the radius of the circular path in meters. The calculator updates the centrifugal force instantly as you type.

3

Read the force and g-force

The result card shows the apparent centrifugal force in newtons and the equivalent g-force (a multiple of Earth's gravity). Use the g-force reading to compare against centrifuge specs, ride limits, or physiological tolerance thresholds.

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Reference

Formula & Methodology

3 formulas

Centrifugal force from speed

F = mv² / r

F is the apparent centrifugal force in newtons (N), m is mass in kilograms (kg), v is tangential velocity in meters per second (m/s), and r is the radius of the circular path in meters (m). This is the same magnitude as the real centripetal force — see the FAQ for why.

Centrifugal force from angular velocity

F = mω²r

ω (omega) is angular velocity in radians per second (rad/s). When rotational speed is given in RPM (revolutions per minute), convert first: ω = RPM × 2π / 60.

G-force

g-force = F / (m × 9.80665)

G-force expresses the force as a multiple of standard gravity (9.80665 m/s²), the conventional reference used for centrifuges, amusement rides, and aerospace/motorsport g-loading.

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Glossary

Key Terms Explained

6 terms

Centrifugal force The apparent outward force felt by an object moving in a circle, as observed from within the rotating reference frame. It has the same magnitude as the centripetal force but points outward instead of inward.

Centripetal force The real, inward-directed net force required to keep an object moving along a circular path, as observed from a non-rotating (inertial) frame. F = mv²/r, same formula and magnitude as centrifugal force.

Apparent force A force that appears to act on an object only because the observer is in a non-inertial (accelerating or rotating) reference frame. Centrifugal force, along with the Coriolis force, is the classic example — it does no work and has no physical source in the inertial frame.

Rotating frame A reference frame that spins along with the circular motion — for example, standing inside a spinning centrifuge drum. Newton's laws need the addition of apparent forces (centrifugal, Coriolis) to hold true in this frame.

Angular velocity The rate of rotation, denoted ω (omega), measured in radians per second (rad/s). Related to tangential velocity by v = ωr, and to RPM by ω = RPM × 2π / 60.

G-force A force expressed as a multiple of standard Earth gravity (1 g = 9.80665 m/s²). A g-force of 2g means the apparent force is twice the object's normal weight.

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Scenarios

Real-World Examples

3 worked examples

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Physics student

Ball on a string

Mass 1 kg Velocity 10 m/s Radius 5 m

F = mv²/r = 1 × 10² / 5 = 20 N. A 1 kg ball swung on a 5 m string at 10 m/s experiences (and exerts, from its own frame) 20 N of outward centrifugal force — matching the 20 N of inward centripetal force keeping it on its circular path.

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Mechanical engineer

Rotor from RPM

Mass 1 kg Rotational speed 19.1 RPM Radius 5 m

19.1 RPM converts to ω ≈ 2.0 rad/s (ω = RPM × 2π/60). F = mω²r = 1 × 2² × 5 = 20 N — the same force as the speed-based example above, since v = ωr = 2 × 5 = 10 m/s. Switching to the From RPM tab is useful whenever a spec sheet gives rotational speed instead of linear speed.

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Lab technician

Centrifuge g-force

Mass 0.02 kg (sample tube) Rotational speed 3,000 RPM Radius 0.1 m

3,000 RPM at a 0.1 m rotor radius gives ω ≈ 314.2 rad/s, so F = mω²r ≈ 0.02 × 314.2² × 0.1 ≈ 197.4 N. G-force = F / (m × 9.80665) ≈ 1,006 g — a realistic relative centrifugal force (RCF) for a benchtop microcentrifuge, which is why lab protocols specify spin speed in g rather than RPM.

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Deep Dive

Understanding Centrifugal Force

3 chapters · 4 min read

Centrifugal force is one of the most commonly misunderstood concepts in physics — it's not a "real" force in the sense of gravity or friction, but it's very real to whatever is experiencing it. This calculator computes the apparent outward force on an object moving in a circle, from mass, speed (or rotational speed), and radius, plus the equivalent g-force.

How the calculator works

The calculator uses F = mv²/r (or the angular-velocity equivalent F = mω²r) to compute the magnitude of the apparent centrifugal force. This is exactly the same formula and the same numeric value as the real centripetal force — the only difference is direction and reference frame: centripetal force points inward and is measured from a stationary observer, while centrifugal force points outward and is felt by an observer riding along in the rotating frame.

In the From RPM tab, rotational speed is converted to angular velocity via ω = RPM × 2π / 60 before applying F = mω²r. The G-Force tab expresses the same force as a multiple of standard gravity (9.80665 m/s²), which is the conventional unit for centrifuges, roller coasters, and motorsport or aerospace g-loading.

Inputs and what they mean

Mass (kg) — the mass of the rotating object. Velocity (m/s) — the tangential (linear) speed along the circular path, used in Force mode. Radius (m) — the radius of the circular path; must be greater than zero, since a zero radius makes the force undefined (division by zero). Rotational speed (RPM) — used in From RPM mode instead of velocity, common for motors, centrifuges, and rotors where spec sheets quote revolutions per minute rather than linear speed.

Limits and edge cases

This calculator assumes uniform circular motion (constant speed and radius) — it does not model changing radius, non-circular paths, or angular acceleration. A radius of zero or a negative radius is not physical and the calculator will show a partial result rather than an undefined (infinite) force. For lab centrifuge work, always confirm the rotor radius used matches the manufacturer's spec (some quote the radius to the tube bottom, others to the rotor center), since even a small radius error compounds through the squared angular velocity term.

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Questions

Frequently Asked Questions

6 questions

What is the formula for centrifugal force?+

F = mv²/r, where F is force in newtons, m is mass in kilograms, v is tangential velocity in meters per second, and r is the radius in meters. Equivalently, F = mω²r using angular velocity ω in radians per second.

Is centrifugal force a real force?+

Not in the same sense as gravity or a push/pull force. Centrifugal force is an "apparent" or "fictitious" force — it only appears when you analyze motion from within a rotating (non-inertial) reference frame. From outside the rotation, the only real force acting is the inward centripetal force. That said, anyone riding in the rotating frame — a passenger in a turning car, a sample in a centrifuge — genuinely feels the outward push, which is why the concept is still useful in practice.

How is centrifugal force different from centripetal force?+

They have the same magnitude (F = mv²/r) but opposite direction and come from different reference frames. Centripetal force is the real, inward force (from a stationary observer's frame) that keeps an object moving in a circle. Centrifugal force is the apparent, outward force felt by an observer riding along in the rotating frame.

How do I find the g-force in a centrifuge?+

Divide the centrifugal force by the object's weight: g-force = F / (m × 9.80665). Equivalently, g-force = ω²r / 9.80665, since F/m = ω²r. Lab centrifuges typically report this as relative centrifugal force (RCF), which is exactly this g-force value.

How do I calculate centrifugal force from RPM instead of speed?+

First convert RPM to angular velocity: ω = RPM × 2π / 60 (radians per second). Then apply F = mω²r. The From RPM tab on this calculator does this conversion automatically — just enter mass, RPM, and radius.

What units does the centrifugal force calculator use?+

Mass in kilograms (kg), velocity in meters per second (m/s), rotational speed in revolutions per minute (RPM), radius in meters (m), and the resulting force in newtons (N). G-force is unitless — it's a ratio relative to standard gravity (9.80665 m/s²).

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Centrifugal Force Calculator

Circular Motion Inputs

Result

How to Use This Calculator

Choose a mode

Enter mass, speed, and radius

Read the force and g-force

Formula & Methodology

Key Terms Explained

Real-World Examples

Physics student

Mechanical engineer

Lab technician

Understanding Centrifugal Force

How the calculator works

Inputs and what they mean

Limits and edge cases

Frequently Asked Questions

Get a branded PDF of your results

Centrifugal Force Calculator

Circular Motion Inputs

Result

How to Use This Calculator

Choose a mode

Enter mass, speed, and radius

Read the force and g-force

Formula & Methodology

Key Terms Explained

Real-World Examples

Understanding Centrifugal Force

How the calculator works

Inputs and what they mean

Limits and edge cases

Frequently Asked Questions

Get a branded PDF of your results

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