RPM → Linear Speed (Sprocket/Gear)

CE Style

Inputs

Use pitch diameter (not outside diameter)

Results

How to use this calculator

Boost Guide

Quick start

  1. Pick Units (SI or Imperial).
  2. Choose a Geometry Mode: Known pitch diameter, Sprocket (pitch & teeth), or Gear (module/DP & teeth).
  3. Enter the RPM and the requested geometry values.
  4. Click Calculate to see linear speed in multiple units.
Tip: Use pitch diameter, not outside diameter. For gears, use module (mm) in SI or DP (1/in) in Imperial.

Modes

  • Known pitch diameter (D): Linear speed = π · D · (RPM / 60).
  • Sprocket: Pitch diameter from chain pitch p and teeth Z using d = p / sin(π/Z).
  • Gear:
    • Metric: d = m · Z (module m in mm).
    • Imperial: d = Z / DP (DP in 1/in).

Inputs

  • RPM: Rotational speed of the sprocket/gear.
  • Pitch Diameter D: Use pitch circle, not OD.
  • Chain Pitch p: e.g., 6.35, 9.525, 12.7, 15.875 mm (¼″, 3⁄8″, ½″, 5⁄8″).
  • Teeth Z: Tooth count of the sprocket or gear.
  • Module / DP: Module in mm (SI) or DP in 1/in (Imperial).

Results

  • Linear speed: m/s, plus km/h, mph, ft/s.
  • Pitch diameter / circumference: Travel per revolution (π·d).
  • Source: Which geometry was used (D, sprocket, or gear).

Examples

  • Known D: RPM = 1200, D = 159 mm → v ≈ π·0.159·(1200/60) ≈ 9.99 m/s.
  • Sprocket: RPM = 900, p = 12.7 mm, Z = 19 → d ≈ 0.244 m → v ≈ 11.52 m/s.
  • Gear (metric): RPM = 600, m = 2.5, Z = 24 → d = 60 mm → v ≈ 3.14 m/s.

Notes & limits

  • Ideal kinematics (no slip, no compliance, no backlash).
  • Chain speed uses the pitch circle; roller/OD differences ignored.
  • Use correct module/DP and tooth count at the pitch circle.
  • For multi-stage reductions, apply the overall ratio to RPM before using this tool.
Need the reverse? RPM = 60·v / (π·d).
FAQ & Troubleshooting

Nothing shows in results

  • Check that all required inputs for the selected mode are filled.
  • RPM must be ≥ 0 and geometry must be positive.
  • For sprocket mode, Z should be ≥ 8 for realistic geometry.

Wrong units

  • Pick the correct Units first (SI vs Imperial).
  • In Imperial, enter DP (1/in), not module.

Diameter confusion

  • Use pitch diameter (PD), not outside diameter (OD).
  • For chains, PD is the pitch circle through chain joints.

Speed after gearbox?

  • Multiply motor RPM by each stage ratio to get output RPM, then use the calculator.

Copy-Paste Mini Workflow

1) Choose geometry mode: D / Sprocket / Gear
2) Enter RPM (n)
3) Enter geometry:
   • D mode: pitch diameter D
   • Sprocket: chain pitch p and teeth Z
   • Gear: module m (SI) or diametral pitch DP (Imperial) and teeth Z
4) Press Calculate
5) Read linear speed (m/s, km/h, mph, ft/s), pitch diameter and circumference