Circular motion & centripetal force calculator

How to use (3 steps)

Pick a mode: basic circular motion or banked curve angle.
Enter radius, speed (or period/frequency/ω), optional mass, and gravity g (Earth/Moon/Mars presets help). Keep radius and speed in matching units; this tool does not auto-convert.
Press Compute to see acceleration, force, period, frequency, or the banking angle. Copy URL shares your setup.

Default example: r = 10 m, v = 10 m/s, m = 1000 kg, g = 9.8 m/s². It auto-computes on load so you see the results immediately.

Inputs

Keep units consistent (no automatic unit conversion). If r is in meters, use m/s for v; if r is in km, use km/s. Basic mode can derive speed from period, frequency, or angular speed; banked mode only needs radius, speed, and g.

Basic circular motion (centripetal force) Banked curve angle

Radius r m

Speed v m/s

Gravity g

m/s²

Known quantity for speed

Mass m (optional) kg

Period T s

Rotation frequency f 1/s

Angular speed ω rad/s

Only the selected speed input is enabled; others are derived but kept for sharing and reuse.

Results

Centripetal acceleration is 10 m/s² (about 1.020408 × g). Period T = 6.283185 s and frequency f = 0.159155 1/s. With mass 1000 kg, F_c = 10000 N.

Centripetal acceleration a_c10 m/s²

Centripetal force F_c10000 N

Relative to g1.020408 g

How it's calculated

Use radius r = 10 m, speed v = 10 m/s, mass m = 1000 kg, and gravity g = 9.8 m/s².
Angular speed is ω = v / r = 1 rad/s.
Period and frequency are T = 2πr / v = 6.283185 s and f = 1/T = 0.159155 1/s.
Centripetal acceleration is a_c = v² / r = 10 m/s², which is 1.020408 g.
Centripetal force is F_c = m·a_c = 10000 N.

FAQ

How are centripetal force and centrifugal force different?

Centripetal force is the inward force that keeps an object on a circular path. Centrifugal force appears only in a rotating frame as an outward “fictitious” force. This tool reports the inward centripetal force.

Must gravity g always be 9.8?

No. Earth is about 9.8 m/s², but you can switch g to explore the Moon, Mars, or any custom value. Use the presets for quick comparisons.

What is the banked-curve mode for?

It shows the ideal banking angle of a frictionless curve so a vehicle can turn without sliding. Real roads add friction and safety factors; this mode focuses on the core physics relationship.

Which inputs are required in each mode?

Basic mode needs the radius plus one speed quantity such as speed, period, frequency, or angular speed. Banked-curve mode needs radius, speed, and gravity. Mass is optional unless you want centripetal force.

Why do my results differ from another tool?

Differences usually come from unit choices, gravity values, rounding rules, or different input assumptions. Match those conditions before comparing the numbers.

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