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Unit Conversions · Engineering & science · Rotation, oscillations & waves

Angular and Linear Velocity Calculator

Convert between angular speed, tangential speed, radius, period, frequency, and RPM for ideal circular motion.

Unit Conversions · Engineering & science · Rotation, oscillations & waves

Angular and Linear Velocity Calculator

Private in-browser calculation · explicit units, solve direction, assumptions, reconciliation, and companion outputs

Every label states the corresponding SI and customary input unit. Outputs include both systems where useful.

Leave the field selected as the unknown blank; enter the other required values.

Calculation result

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Enter valid values to see the result.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

Quick guide

How to use this calculator

  1. Choose the physical relationship and solve direction that match the known measurements rather than forcing unlike quantities into one formula.
  2. Enter every unit, sign, reference direction, geometry, material property, fluid property, temperature basis, coefficient, and idealization explicitly. The calculator normalizes compatible quantities internally and exposes intermediate values.
  3. Use reconciliation and companion outputs to catch entry mistakes, then retain the stated model boundary. A theoretical result is not a design approval, material certificate, equipment rating, or safety determination.

Calculation method

How the angular and linear velocity calculator works

Join compatible angular and linear motion quantities without confusing angular frequency, rotational frequency, and tangential speed.

v=ωr; f=ω/(2π); period=2π/ω; RPM=60f.

Worked example

Angular and Linear Velocity example

At 4 rad/s and 3 m radius, tangential speed is 12 m/s, frequency about 0.637 Hz, and speed about 38.2 RPM.

v=ωr; f=ω/(2π); period=2π/ω; RPM=60f.

Supported inputs

Precision and limits

Engineering-model boundary

The model assumes rigid rotation at one angular speed and a stated radius. Slip, belt pitch, gear tooth counts, deformation, and variable rotation require separate models.

Units and precision

Calculations normalize compatible inputs to SI, retain working precision, and round only for display. Very small and large nonzero values use scientific notation; displayed digits cannot create accuracy beyond the entered measurements and properties.

Decision boundary

This page solves the declared idealized relationship only. Verify applicable material data, operating conditions, geometry, loads, coefficients, standards, codes, manufacturer requirements, uncertainty, and professional approval before consequential use.

Category ownership

Generic mechanics, materials, fluid, aerodynamic, wave, and thermodynamic relationships live here. Trade-specific pipe, HVAC, motor, electrical, construction, automotive, radiation, statistical, chemical, and astronomical workflows remain with their established categories.

Privacy

Entered values and results stay in this browser and are not sent to analytics or third parties.

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