Centripetal Acceleration Calculator

Technical article

Understand Centripetal Acceleration Calculator

This calculator finds the missing quantity among centripetal acceleration a, tangential speed v and circle radius r from the other two. Using a washing machine's spin cycle as an example, it shows how extreme centripetal acceleration can become at small radius and high rotational speed.

What does this quantity describe?

The centripetal acceleration of a body on a circular path is a = v²/r. It always points toward the centre of the circle and describes the change in direction of velocity at constant magnitude.

A washing machine drum with a 45 cm diameter (r = 0.225 m), spinning at 1,200 revolutions per minute, reaches a centripetal acceleration of about 3,550 m/s² — roughly 360 times gravitational acceleration. This enormous acceleration forces water outward through the drum's holes while the fabric is held back by the hole size.

Formula and variables

a = v² / r

a = v² / r
v = √(a·r)
r = v²/a

Symbol / input	Meaning
Centripetal acceleration a	The radially inward acceleration that continuously changes the direction of motion toward the centre – even at constant path speed v the body is accelerating because its direction changes.
Tangential speed v	The path speed on the circular path. Source: a measurement, or computed from v = π·d·n/60.
Circle radius r	The radius of the circular path, measured from the centre of rotation to the body.

Choose the inputs correctly

Enter two of the three quantities. Centripetal acceleration requires speed and radius, speed requires acceleration and radius (via a square root), radius requires acceleration and speed.

How to use the calculator

Select the target quantity and enter the two known values with units. If you know rotational speed instead of tangential speed, first compute v = π·d·n/60 before entering the result here.

Worked example

Given v = 10 m/s and r = 10 m, substitution gives a = 10² m²/s² / 10 m = 10 m/s².

Understand the result and units

A centripetal acceleration of 10 m/s² is roughly equal to gravitational acceleration (1 g). At very small radii and high tangential speeds, as in a washing machine drum or laboratory centrifuge, accelerations of several hundred g can instead be reached.

The SI unit is m/s². At very high accelerations, the multiple of gravitational acceleration g (9.80665 m/s²) is often additionally stated, e.g. '360 g'.

Typical applications

Centripetal acceleration is used to design centrifuges, washing machine drums and carousels, assess loading on rotating components, and classify g-forces in training and medical diagnostics.

Assumptions, limits and common mistakes

The formula assumes uniform circular motion at constant tangential speed. If speed changes during the motion (e.g. a centrifuge spinning up), an additional tangential acceleration occurs that is not captured here.

Common mistake: Do not confuse centripetal acceleration with angular acceleration: a = v²/r describes radial acceleration at constant angular velocity, not a change in rotational speed itself. Also, when converting rotational speed to tangential speed, use the radius (not the diameter) correctly in v = ω·r or v = π·d·n/60.

Frequently asked questions

Why does spinning a washing machine push water out?

Because at high rotational speed the drum generates very high centripetal acceleration, forcing water outward through the drum's holes while fabric is held back by the hole size.

How many g does a typical washing machine reach while spinning?

At about 1,200 rpm with a drum diameter of about 45 cm, that works out to about 3,550 m/s², roughly 360 times gravitational acceleration.

How do I convert rotational speed to tangential speed for this formula?

Via v = π·d·n/60 (d in m, n in rpm), or v = ω·r with ω in rad/s, before substituting v into a = v²/r.