Centripetal Force Calculator
Inward force for circular motion from mass, speed, and radius.
What it does
Every curve demands an inward pull. A car holding a bend, a stone on a string, and a satellite overhead all obey one rule: mass times speed squared divided by radius. Miss that force and the motion flies straight instead.
The tool above takes mass, speed, and radius in metric or imperial and returns the force, the acceleration, and the g loading. The default car (1000 kg, 20 m/s, 50 m) needs 8,000.0 N inward at 0.82 g, with the imperial twin (2204.6 lb, 44.74 mph, 164 ft) agreeing.
OpenStax teaches this from two doors: College Physics frames force as mass times centripetal acceleration, and University Physics derives the same v squared over r from the direction change of velocity. Both texts stress that centripetal names a role, not a new force; friction or tension plays it.
Speed dominates every what if. Because velocity enters squared, rushing a curve 50 % faster more than doubles the grip bill, while widening the radius trims it proportionally. Road designers bank curves and post advisory speeds on exactly this trade.
How to use
- Pick metric or imperial units.
- Type the moving mass.
- Type the steady speed along the curve.
- Type the curve radius, not the diameter.
- Read force first, then acceleration and g loading.
- Rerun at higher speed to feel the squared penalty.
Formula
- F
- Centripetal force in N (metric) or lbf (imperial).
- m
- Mass of the moving object.
- v
- Tangential speed along the path.
- r
- Radius of the circular path.
- a
- Centripetal acceleration toward the center.
Angular forms say the same thing: with v = w x r, force becomes m x w^2 x r. Subsonic speeds only here; near light speed relativity rewrites the inertia. The direction never changes: perpendicular to velocity, pointing centerward, doing no work on a steady circle.
Worked example
Example: 1000 kg car, 20 m/s, 50 m curve
Metric defaults already filled in the form.
- Square speed: 20^2 = 400 m2/s2.
- Multiply mass: 1000 x 400 = 400,000.
- Divide by radius: 400,000 / 50 = 8,000.0 N.
- Acceleration: 400 / 50 = 8 m/s2.
- G loading: 8 / 9.80665 = 0.82 g.
- Imperial check: 2204.6 lb, 44.74 mph, 164 ft return 1,799.0 lbf at 0.82 g.
Reference table
| Speed | Force | G loading |
|---|---|---|
| 10 m/s | 2,000.0 N | 0.2 g |
| 20 m/s | 8,000.0 N | 0.82 g |
| 30 m/s | 18,000.0 N | 1.84 g |
| 20 m/s, 100 m radius | 4,000.0 N | 0.41 g |
Limits
- Uniform circular motion only; spirals and braking need richer models.
- Point mass assumed; long vehicles add yaw and load transfer.
- Subsonic, non relativistic speeds; tires also cap usable grip.
- Says what force the path needs, not whether surfaces can supply it.
Common mistakes
- Using diameter instead of radius, doubling the answer wrongly.
- Forgetting to square speed, the costliest slip on this page.
- Calling centrifugal (outward, frame dependent) the required force.
- Mixing mph with meters without the unit toggle.
- Quoting force without checking available friction.
Try it yourself
Quick checks. Answers sit tucked under each question.
1500 kg car, 25 m/s, 100 m radius. Force?
1500 x 625 / 100 = 9,375.0 N at 6.25 m/s2 (0.64 g).
Same curve at 50 m/s instead of 25. Force?
Speed doubled, so force quadruples: 37,500 N.
Same speed and mass, radius doubled to 200 m?
Force halves to 4,687.5 N. Wide curves forgive.
Questions
What is centripetal force?
The net inward force keeping circular motion: m v^2 / r toward the center.
Is centrifugal force real?
It appears outward only in rotating frames; inertial frames need inward centripetal.
Why does speed matter so much?
It enters squared: 10 % faster needs 21 % more force.
What supplies it in a car?
Tire friction, helped by banking that tilts the normal force inward.
Can I use rpm instead?
Convert first: v = 2 x pi x r x rpm / 60, then use this page.
What breaks first in a fast curve?
Grip. Demand past mu x weight slides outward regardless of power.