Rotational Speed and Rim Speed Calculator
Convert rpm, angular speed and tangential rim speed using a radius or diameter. Find frequency, period and centripetal acceleration with explicit units.
YOUR CALCULATION
Result
—
Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Convert the entered rotational speed to radians per second, or divide tangential speed by radius. One revolution is2πradians, and one minute is60 seconds. Usev=ωr andac=ω²r for a point on the rim.
ω=2πrpm/60; v=ωr; f=ω/(2π); period=1/f; ac=ω²r
Worked example
A10cm radius rotating at60rpm hasω=2πrad/s, rim speed≈0.628319m/s, frequency1Hz, period1s and centripetal acceleration≈3.947842m/s².
Assumptions and input details
Speeds are nonnegative magnitudes; rotation direction is not encoded. Entered radius/diameter is positive, between1e−12 and1e9m. Entered angular speed and linear speed are capped at1e12 in base units. Zero speed has no finite revolution period. Uniform circular kinematics are assumed. The schematic arrows show perpendicular directions, not scaled magnitudes. This calculates rim kinematics, not gearing, material strength or a machine speed rating.
References: OpenStax uniform circular motion
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
One revolution is 2π radians or 360 degrees. One minute is 60 seconds, so 1 rpm = 2π/60 rad/s. Rotational frequency in hertz counts revolutions per second.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Calculate one external gear pair’s ratio, output speed, torque and power. Enter tooth counts and your own efficiency to compare the two shafts.
Find a circle’s diameter, circumference and area from its radius. Choose regional length units and see a labeled circle and conversion table.
Find translational kinetic energy, mass or speed from the other two values. Choose explicit units, compare energy equivalents and see how energy changes with speed.
Reserved advertising space.