Centripetal Acceleration Calculator

centripetal acceleration formulas and interpretation

Centripetal acceleration points toward the centre of a circular path and continually changes the velocity direction.

Use linear speed and radius or angular velocity and radius while keeping the calculator’s original unit conversions.

How to use the centripetal acceleration calculator

Choose a model: Select the physical relationship that matches the known values.
Choose the unknown: Select the quantity you need to calculate.
Enter values and units: Provide every requested measurement using consistent units.
Calculate: Check the formula, converted result, sign, and units.

Formula and variables

Centripetal acceleration can be calculated from tangential speed or angular velocity.

ac = v² / r = ω²r

ac — Centripetal acceleration: Inward acceleration (m/s²)
v — Tangential speed: Speed along the path (m/s)
r — Radius: Distance from rotation axis (m)
ω — Angular velocity: Rotation rate (rad/s)

Circular track example

An object moves at 10 m/s around a circle with radius 5 m.

Speed: 10 m/s
Radius: 5 m

ac = 10² / 5
ac = 20 m/s²

Result: Centripetal acceleration is 20 m/s².

The velocity vector changes inward at 20 m/s each second.

Understanding your results

Interpreting the result

At fixed radius, doubling speed produces four times the centripetal acceleration.

A sign indicates direction only when a consistent rotational sign convention is used.

Assumptions

Rotation is evaluated about a specified axis.
Inputs are converted through coherent SI units.
The selected formula adequately represents the physical system.

Limitations

The calculator does not simulate time-varying inputs.
Vector directions and multiple axes must be resolved separately.
Losses such as friction are not added unless represented in the entered net value.

Common mistakes

Mixing RPM with radians per second.
Using diameter instead of radius.
Entering a zero divisor.
Ignoring the direction represented by a negative value.

Practical use cases

Physics and education

Check rotational kinematics and dynamics exercises.

Machines and mechanisms

Estimate quantities for wheels, shafts, rotors, and rotating equipment.

Frequently asked questions

Why are radians used in rotational formulas?

Radians make angular and linear relationships dimensionally coherent without an extra conversion factor.

Can the result be negative?

Yes. A negative value means the quantity points opposite the direction chosen as positive.

Sources and review

SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
Special Publication 811 — NIST. Accessed 2026-07-11.

Reviewed 2026-07-11.

Centripetal Acceleration Calculator