Wheel Linear Speed Calculator
Convert angular speed to linear speed for a rolling wheel: v = ω · r.
Inputs
Drag the handle (or focus it and press ↑/↓) to reorder. Scientific notation such as 1.2e3 is accepted. Pick any unit; conversion is automatic.
Results
Enter values and press Calculate. Your answer will appear here.
Linear speed vs. wheel speed
For your radius, speed grows in direct proportion to rpm. The dot is your input; if you entered slip, the dashed line is the speed without slip.
What is being calculated
Common examples
| Case | ω | r | v |
|---|
Illustrative inputs, not manufacturer data.
Typical wheel sizes (approximate)
| Wheel | Radius |
|---|---|
| Car tyre 225/45R17 | ≈ 0.317 m |
| Road bicycle 700×25c | ≈ 0.34 m |
| Mountain bike 26 in | ≈ 0.33 m |
| Skateboard 56 mm wheel | 28 mm |
The effective rolling radius changes with tyre pressure and load; use the figure from your tyre maker for precision.
Unit conversions
| Quantity | Conversion |
|---|---|
| Speed | 1 m/s = 3.6 km/h = 2.23694 mph = 3.28084 ft/s = 1.94384 kn |
| Angular speed | 1 rpm = 0.104720 rad/s · 1 rps = 1 Hz = 6.28319 rad/s · 1 deg/s = 0.0174533 rad/s |
| Length | 1 in = 0.0254 m · 1 ft = 0.3048 m |
Formula
- v: linear speed (m/s)
- ω: angular speed (rad/s)
- r: wheel radius (m)
Example: 800 rpm = 83.776 rad/s and r = 0.33 m give v = 83.776 × 0.33 ≈ 27.65 m/s ≈ 99.5 km/h.
Advanced mode also reports the circumference C = 2πr, the period T = 2π / ω and the rim acceleration ω²·r. With slip s, the forward speed is v = ω·r·(1 − s). Angular speed in rpm must be multiplied by 2π/60 to get rad/s; the calculator does this for you.
References
- OpenStax University Physics Vol. 1, Rotational Variables: v = ω·r
- Wikipedia, Angular velocity: units and relation to linear speed
- NIST SP 811, Guide for the Use of the SI: unit conversion factors
How to Use This Tool
- Pick a preset, or enter the angular speed ω and choose its unit.
- Enter the wheel radius r and its unit.
- In Advanced, enter the diameter instead, add wheel slip, or choose the output speed unit.
- Click Calculate.
- Read v in the highlighted result and check the speed chart.
What This Tool Offers
- Basic and Advanced modes on one calculation engine
- Angular speed, length and speed unit conversion
- Radius or diameter input, optional wheel slip (Advanced)
- Circumference, period and rim acceleration (Advanced)
- Speed-vs-rpm chart and labelled wheel diagram
- Ready-made presets and a mobile-friendly layout
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| v | Linear (surface) speed of the wheel | m/s |
| omega | Angular velocity of the wheel | rad/s |
| r | Radius of the wheel | m |
What it means
For a wheel rolling without slipping, the linear speed at its contact point is equal to the product of its angular speed (ω) and its radius (r). This relation is used in odometry to compute the robot’s speed from wheel encoder counts (which give angular displacement). It is also used to convert motor speeds to wheel velocities. Understanding this formula is fundamental for mobile robot kinematics and for calibrating encoders.
Worked example
Wheel Linear Speed from Angular Speed – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| ω (rad/s) | 10 |
| r (m) | 0.05 |
| Parameter | Value |
|---|---|
| ω | 5 |
| r | 0.1 |
Common mistakes
- Wheel linear speed: v = ω·r – where ω is angular speed (rad/s) and r is wheel radius.
- Units: ω in rad/s, r in m → v in m/s.
- Radius: Use the effective rolling radius (may differ from nominal due to deformation).
- Slip: If there is slip, this formula gives the theoretical speed – actual may be lower.
- Sign: v is positive for forward motion – ω positive for forward rotation (right‑hand rule).
Applications
Wheel linear speed from angular speed, v = ω·r, relates the rotational speed of a wheel to its linear velocity. This is fundamental for wheeled robots and vehicles. Engineers use it to convert encoder counts (angular position) to distance travelled, to compute speed commands for motors, and to calibrate odometry. It is also used in designing traction control systems and in estimating vehicle speed from wheel sensors. By understanding this relation, they can accurately track motion and control wheeled platforms. This formula is a basic building block for mobile robotics and automotive engineering.
- Calibration of wheel odometry for mobile robots
- Conversion of motor RPM to vehicle speed
- Speed control of wheeled vehicles
- Design of traction and braking systems
- Educational understanding of rotational‑linear motion mapping
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