Centripetal Force Calculator

Solve circular motion problems for force, mass, speed, radius, acceleration, angular velocity, period, or RPM. Includes g-force, unit conversion, presets, and calculation steps for classroom, ride, vehicle, aviation, and orbital examples. Calculations run locally in your browser.

Inputs

Object, rider, vehicle, or payload mass.
Linear speed along the circular path.
Path radius; smaller radii ↑ g-forces for the same speed.
Use if acceleration or g-load is already known.
The inward net force required to maintain the curve.
Equivalent spin rate around the circle.
Time for one complete revolution.
Spin rate in revolutions per minute.

Formula summary

  • F = mv²/rforce from mass, speed, and radius
  • a = v²/rcentripetal acceleration
  • F = mω²rforce from angular velocity
  • v = ωrtangential speed from angular velocity
  • T = 2π/ωperiod for one revolution
  • g-force = a/g₀where g₀ = 9.80665 m/s²

Tip: choose the missing value in "Solve for." The selected input is ignored and filled from the other values. The URL updates so you can bookmark or share your setup.

Results

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How to calculate centripetal force

  1. Convert mass, speed, and radius to consistent units. The calculator converts common metric, imperial, and physics units automatically.
  2. Square the tangential speed: v².
  3. Divide by radius to get centripetal acceleration: a = v²/r.
  4. Multiply by mass to get the inward net force: F = ma = mv²/r.
  5. Divide acceleration by g₀ = 9.80665 m/s² to express the load as g-force.

Formula rearrangements

FindUse
ForceF = mv²/r = mω²r = ma
Massm = F/a = Fr/v²
Speedv = √(ar) = √(Fr/m) = ωr
Radiusr = v²/a = mv²/F = v/ω
Angular velocityω = v/r = 2π/T
Period and RPMT = 2π/ω, RPM = 60/T

Supported units

QuantityUnits
Masskg, lb, slug
Radiusm, ft, km, mi
Speedm/s, km/h, mph, ft/s
Angular velocityrad/s, RPM
ForceN, kN, lbf, dyne
Accelerationm/s², ft/s², g

Common examples

Use the preset buttons for quick checks: a car cornering on a 50 m curve, a roller coaster loop, a small mass on a string, a washing machine drum, and a low Earth orbit case. Each preset fills realistic values and reports force, acceleration, g-force, angular speed, period, and RPM.

Pitfalls and checks

  • Direction: centripetal acceleration and force point toward the center. Tangential velocity points along the path.
  • Speed matters most: doubling speed quadruples acceleration and force.
  • Mass changes force, not acceleration: for the same speed and radius, a heavier object needs more inward force but has the same centripetal acceleration.
  • Vertical loops need extra context: the calculator gives the required radial net force. At the top or bottom of a loop, weight changes the normal force riders feel.
  • Centripetal is not a new force: it is the inward net result of gravity, friction, tension, a track force, or another real interaction.

Methodology and assumptions

  • Assumes uniform circular motion unless you enter a known acceleration or force directly.
  • Reports magnitudes; force and acceleration directions are inward toward the circle center.
  • Uses standard gravity g₀ = 9.80665 m/s², exact mile and foot conversions, and standard pound-force conversion.
  • Calculations run locally in your browser; entered values are not sent to a server by this calculator.
  • Editorial note: formulas reviewed against introductory mechanics relationships. Last reviewed: June 10, 2026.

Centripetal force FAQ

How do you calculate centripetal force?

Use F = mv²/r. Convert units first, square speed, divide by radius, then multiply by mass.

What is the difference between centripetal and centrifugal force?

Centripetal force is the real inward net force that curves the motion. Centrifugal force is the outward apparent force used in a rotating rider frame.

What causes centripetal force?

It can come from friction, tension, gravity, a track normal force, or any combination whose net force points inward.

What happens if speed, radius, or mass changes?

Force grows linearly with mass, grows with the square of speed, and decreases when radius increases.

How do you find velocity from centripetal force?

Rearrange F = mv²/r to v = √(Fr/m). Use consistent units before taking the square root.

How do you find radius from centripetal force?

Rearrange to r = mv²/F. A larger radius means a gentler turn for the same speed and mass.

Is centripetal force a separate force?

No. It describes the inward net force required for circular motion, supplied by ordinary forces such as gravity, friction, tension, or support from a track.

5 Fun Facts about Centripetal Force

ISS feels 0 g but pulls 0.9 g

The International Space Station circles Earth at 7.66 km/s with a radius of ~6,780 km, so it’s constantly accelerating inward at 8.7 m/s² (0.89 g)—astronauts feel weightless because they’re in steady free fall.

Orbit intuition

Fighter-jet turns are brutal

A jet pulling 9 g at 250 m/s needs a turn radius of just 710 m. A 75 kg pilot effectively “weighs” 675 kg, so their seat must push with about 6.6 kN.

Aviation loads

Coasters juggle g’s around a loop

Take a 20 m radius loop at 20 m/s: the bottom loads riders with 3.0 g while the top eases to 1.0 g. Tweaking radius or speed keeps restraints comfortable yet exciting.

Thrill math

Spin gravity sweet spot

A rotating habitat with a 100 m radius only needs 3 RPM to mimic 1 g. Double the radius to 200 m and you can drop to 2.1 RPM—slow enough to keep most people comfortable.

Space habitats

Washing machines hit 400 g

A 0.25 m drum spinning at 1,200 RPM sees 3,950 m/s² of inward pull (~403 g). No wonder rinse water gets ripped out so fast.

Household physics

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