Centripetal Acceleration (a = v²/r)

a_c = \frac{v^2}{r}

ac =

v =

r =

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Circular motion at constant speed still involves acceleration — directed toward the centre, with magnitude v²/r. The square on v is why tight turns at speed feel violent: double your speed and the acceleration quadruples, while a wider radius softens it. Solving for v takes the principal positive square root, since speed is a magnitude.

Centripetal Acceleration (a = v²/r)

a_c = \frac{v^2}{r}

Where

$a_c$ = Centripetal acceleration
$v$ = Speed
$r$ = Radius

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

Centripetal acceleration — Centripetal Acceleration (a = ω²r), Newton's Second Law
Speed — Speed, Distance & Time, Kinetic Energy
Radius — Centripetal Force (F = mv²/r), Speed in Circular Motion (v = 2πr/T)

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.