Centripetal Acceleration CalculatorFree online other calculator — instant results, no sign-up
Calculate radial acceleration for uniform circular motion.
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About the Centripetal Acceleration Calculator
The Centripetal Acceleration Calculator finds the inward, radial acceleration of an object moving at constant speed along a circular path. It uses speed in meters per second and radius in meters to calculate acceleration in m/s². With the default speed of 10 m/s and radius of 5 m, the result is 20 m/s².
- Speed (m/s)
- The object's speed along the circular path, measured in meters per second (m/s), with a default of 10.
- Radius (m)
- The distance from the center of the circular path to the object, measured in meters (m), with a default of 5.
Formula and method
a_c = v² / r = (10 m/s)² / (5 m) = 20 m/s²
- a_cCentripetal acceleration magnitude, in meters per second squared (m/s²), directed toward the circle's center.
- vSpeed along the circular path, in meters per second (m/s).
- rRadius of the circular path, in meters (m).
Square the speed, then divide by the radius. For the default inputs, squaring 10 m/s gives 100 m²/s²; dividing by 5 m gives a centripetal acceleration of 20 m/s².
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Speed10 m/s
- Radius5 m
Results
- Result20 m/s²
How to use the Centripetal Acceleration Calculator
- 1Enter the object's speed in Speed (m/s); keep 10 for the default example.
- 2Enter the circular path's radius in Radius (m); keep 5 for the default example.
- 3Check that the speed is nonnegative and the radius is greater than zero, and convert any measurements to the required units.
- 4Run the calculation to evaluate a_c = v² / r.
- 5Read the result in m/s²; the default inputs produce 20 m/s² directed toward the center.
Reading your result
The Result row reports the magnitude of centripetal acceleration in m/s². A result of 20 m/s² means the object's velocity is changing because its direction changes, even though its speed remains constant. The acceleration points toward the center of the circle; this output is not a force or an increase in speed.
Limitations
The calculator assumes uniform circular motion with a constant radius and speed. Radius must be greater than zero, and speed must be nonnegative. For changing speed along a circular path, v²/r still gives the instantaneous radial component, but the calculator does not include tangential acceleration or report total acceleration. It does not calculate force, which also requires mass, and the accuracy of the result depends on the input measurements.
Common questions
Why is there acceleration if the object moves at constant speed?+
Velocity includes both speed and direction. In circular motion, the direction changes continuously, requiring an inward acceleration even when the speed stays constant.
How do speed and radius affect centripetal acceleration?+
Acceleration is proportional to speed squared and inversely proportional to radius. At fixed radius, doubling speed quadruples acceleration; at fixed speed, doubling radius halves it.
Should I enter the circle's radius or its diameter?+
Enter the radius: the distance from the circle's center to the object. If you know the diameter, divide it by two before entering it in meters.
Does the default result of 20 m/s² mean the object speeds up by 20 m/s each second?+
No. With a speed of 10 m/s and radius of 5 m, the 20 m/s² acceleration points inward and changes the direction of velocity. In uniform circular motion, the speed remains 10 m/s.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.