How do I convert rad/s to rpm?
rpm = ω × 60/(2π) ≈ ω × 9.549. So 5 rad/s ≈ 47.7 rpm.
Angular Velocity Calculator
ω = v/r
Calculate angular velocity from tangential speed and radius. ω = v/r. Also ω = 2π/T = 2πf.
Calculate
Enter values above to calculate
How it calculates
1
ω = v / r
2
v in m/s, r in metres
3
Result in rad/s (multiply by 60/2π for rpm)
Formula
ω = v/r
Variable Table
| Symbol | Quantity | SI Unit |
|---|---|---|
| ω | Angular velocity | rad/s |
| v | Tangential speed | m/s |
| r | Radius | m |
| T | Period = 2π/ω | s |
| f | Frequency = ω/2π | Hz |
How to Use This Calculator
This angular velocity calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.
Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.
Assumptions and Limits
The formula ω = v/r is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.
Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.
Worked Example
A point 2 m from the axis moves at 10 m/s. Find angular velocity.
Step 1: ω = v / r
Step 2: ω = 10 / 2
Answer: ω = 5 rad/s (≈ 47.7 rpm)
Common Mistakes
- ω is in rad/s, not rpm — convert: rpm = ω × 60/2π
- All points on a rigid rotating body share the same ω but different v
- ω = 2πf = 2π/T relates to frequency and period
Related
Frequently Asked Questions
Do all points on a wheel have the same angular velocity?
Yes — ω is the same everywhere on a rigid body, but linear speed v = ωr increases with distance from the axis.