Linear Speed from Rotation (v = ωr)

v = \omega r

v =

ω =

r =

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

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Every point on a spinning object shares the same angular velocity, but the farther a point sits from the axis, the faster it actually moves — linearly in the radius. That is why the outer edge of a merry-go-round feels so much wilder than the center, and why a 30 cm circular saw blade at 3600 rpm has a rim speed of 0.15 × 377 ≈ 57 m/s, over 200 km/h.

Linear Speed from Rotation (v = ωr)

v = \omega r

Where

$v$ = Linear speed
$\omega$ = Angular velocity
$r$ = Radius

Missing one of these? Work it out first, then come back

Linear speed — Speed, Distance & Time, Kinetic Energy
Angular velocity — Angular Velocity (ω = θ/t), Angular Velocity from Period
Radius — Centripetal Acceleration (a = v²/r), Centripetal Force (F = mv²/r)

Part of this formula set

The rotational equations of motion

13 formulasThe angular twins of the linear equations — θ, ω and α in place of d, v and a, and torque, moment of inertia and Iω in place of F, m and p.