Circular Motion Calculator — Velocity, Frequency & Centripetal Force
Enter the radius of the circular path and the period (time per revolution) to find linear velocity, angular velocity, frequency, centripetal acceleration and — optionally — centripetal force for a given mass.
m
s
kg
v = 2πr / T — speed along the circular path
- 1
Angular velocity
ω = 2π ÷ T = 2π ÷ 3 = 2.0944ω is the angle swept per second (radians per second). - 2
Linear velocity
v = ω × r = 2.0944 × 2 = 4.1888
How does this calculator work?
For uniform circular motion with radius r and period T: v = 2πr/T (linear speed), ω = 2π/T (angular speed), a_c = v²/r (centripetal acceleration), F_c = ma_c (centripetal force). Enter radius, period and optional mass to get all quantities.
Formula
How this is calculated
In uniform circular motion an object travels at constant speed along a circular path of radius r with period T (the time for one full revolution). The angular velocity ω = 2π/T (radians per second) describes how fast the angle sweeps. The linear velocity v = ωr = 2πr/T is the tangential speed — the rate at which the object moves along the arc.
Although the speed is constant, the direction continuously changes, meaning there is a net acceleration. This centripetal (centre-seeking) acceleration always points toward the centre: a_c = v²/r = ω²r. By Newton's second law, a net force must cause this acceleration: F_c = m × a_c = mv²/r. This force is supplied by whatever keeps the object on its path — tension in a string, gravity for an orbiting satellite, friction for a car rounding a bend.
This calculator assumes uniform circular motion (constant speed). If the speed varies, the tangential and centripetal acceleration components must be treated separately. Relativistic effects are ignored; the formulas hold for v ≪ c.
Frequently asked questions
It depends on the scenario. For a ball on a string: string tension. For a car on a curved road: static friction between tyres and road. For a planet orbiting the Sun: gravitational attraction. The centripetal force is not a new force — it is always an existing force (or component of one) directed toward the centre.
Angular velocity ω (rad/s) measures how fast the angle changes — the same ω for any point on a rigid rotating body. Linear velocity v = ωr measures actual speed along the arc — points farther from the centre move faster, even at the same ω.
Frequency f = 1/T (Hz, revolutions per second). RPM = f × 60. For example, T = 0.5 s gives f = 2 Hz and 120 rpm. The calculator shows all three automatically.
Also known as
TG we-Calculate Editorial Team. (2026). Circular Motion Calculator — Velocity, Frequency & Centripetal Force [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/circular-motion-calculator
TG we-Calculate Editorial Team. "Circular Motion Calculator — Velocity, Frequency & Centripetal Force." TG we-Calculate. 2026. https://we-calculate.com/calculator/circular-motion-calculator.
TG we-Calculate Editorial Team, "Circular Motion Calculator — Velocity, Frequency & Centripetal Force," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/circular-motion-calculator
@misc{wecalculate_circular_motion_calculator, title = {Circular Motion Calculator — Velocity, Frequency & Centripetal Force}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/circular-motion-calculator}}, year = {2026}, note = {TG we-Calculate} }
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