Speed in Circular Motion (v = 2πr/T)

v = \frac{2\pi r}{T}

v =

r =

T =

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

Constant used — built into this formula, no need to enter

\pi = 3.141592653589793

Pi · exact

Learning zone

An object in uniform circular motion covers exactly one circumference, 2πr, every period T — and that ratio fixes its speed. The International Space Station, orbiting at roughly r = 6,780 km from Earth's centre once every 93 minutes, moves at v = 2πr/T ≈ 7.6 km/s. The constant π = 3.14159265… is built into the calculation.

Speed in Circular Motion (v = 2πr/T)

v = \frac{2\pi r}{T}

Where

$v$ = Speed
$r$ = Radius
$T$ = Period

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

Speed — Speed, Distance & Time, Kinetic Energy
Radius — Centripetal Acceleration (a = v²/r), Centripetal Force (F = mv²/r)
Period — Angular Velocity from Period, Simple Pendulum Period

Part of this formula set

Circular and centripetal motion

7 formulasCentripetal acceleration and force in both linear and angular form, plus the curve-speed results that follow when friction or a bank supplies them.