Gear Ratio Calculator — RPM, Torque & Teeth Count in Seconds
Calculate gear ratios for any spur, helical, or bevel gear train. Input teeth counts or pitch diameters — get output speed and torque instantly.
Quick Answer
For a driver gear with 20 teeth at 1500 RPM driving a 60-tooth driven gear, you get: Gear Ratio = 3:1, Output Speed = 500 RPM, and Output Torque = 3x Input Torque (assuming 100% efficiency). Use the calculator above with your own values.
How Gear Ratio Calculations Work
Gear ratio is the heart of mechanical power transmission. It determines how speed and torque trade off between two meshing gears. Three things you need to know:
1. Gear Ratio from Teeth
Ratio = N₂ / N₁ where N₂ = driven gear teeth, N₁ = driver gear teeth. A 60-tooth driven gear and 20-tooth driver gives 3:1 — the output shaft turns at 1/3 the input speed but delivers 3x the torque (before efficiency losses).
2. Output Speed
n₂ = n₁ × (N₁ / N₂). Simply divide input RPM by the ratio. For compound gear trains, multiply the ratios of each stage.
3. Torque Multiplication
T₂ = T₁ × (N₂ / N₁) × η where η is gear efficiency (typically 0.94-0.98 for spur gears). This is why a small electric motor can lift heavy loads — gears amplify torque at the expense of speed.
Where Engineers Use This
- Designing gearbox reduction stages for industrial machinery
- Selecting motor-gearbox combinations for conveyor drives
- Calculating spindle speeds for lathe and milling operations
- Verifying replacement gear compatibility in maintenance
- Designing winch and hoist drive trains
Common Mistakes
- Confusing ratio direction — “3:1” means 3 turns of driver = 1 turn of driven (reduction). A “1:3” ratio means speed increase. Always confirm which shaft is input.
- Ignoring gear efficiency — Real gears lose 2-6% per mesh. A 3-stage gearbox at 96% per stage delivers only 88.5% of theoretical output torque.
- Forgetting backlash — Gears need clearance. For precision positioning (CNC, robotics), use anti-backlash gears or account for lost motion.
- Overlooking idler gears — An idler between two gears doesn’t change the ratio — it only reverses direction. Don’t include idler teeth in your ratio calculation.
- Mixing diametral pitch — Two gears must have the same DP (or module) to mesh properly. Different DP gears will bind or strip.
Frequently Asked Questions
What’s the difference between gear ratio and gear reduction?
Gear ratio describes any ratio, including speed-up (output faster than input). Gear reduction specifically means output speed is lower than input (ratio > 1:1). Our calculator handles both — just enter your teeth counts and it tells you whether you’re reducing or increasing speed.
Can I use this for worm gears?
No — worm gears have a fundamentally different ratio formula: Ratio = Number of teeth on worm gear (not the worm). For worm drive calculations, use our Worm Gear Efficiency Calculator.
How do I calculate compound gear train ratios?
Multiply the individual stage ratios. For a 2-stage train where stage 1 has ratio 3:1 and stage 2 has 4:1, the overall ratio is 12:1. Our calculator handles single-stage; for multi-stage, run each stage separately and multiply.
What if I only know pitch diameters?
Ratio = D₂ / D₁ works identically to the teeth count method (since teeth count is proportional to diameter for the same DP). Enter either value — the ratio is the same.
Why does output torque decrease at high speed?
It doesn’t decrease from the ratio — torque ratio is theoretically constant. But at high speeds, gear efficiency drops due to increased oil churning and windage losses. Above 20 m/s pitch line velocity, expect 1-3% additional efficiency loss.
What module or DP should I choose?
Module (metric) or DP (imperial) depends on torque requirements. Higher torque needs larger teeth (smaller DP number, larger module). Rough guide: <5 Nm → module 1-2, 5-50 Nm → module 2-4, >50 Nm → module 4-8. Use our Gear Strength Calculator for detailed sizing.
How does helical gear ratio differ from spur?
It doesn’t — the ratio formula is identical for spur, helical, and bevel gears. The advantage of helical is smoother engagement and higher load capacity, not a different ratio. For bevel gear angle considerations, see the Shaft Stress Calculator.
Can I reverse the ratio for a speed-up drive?
Yes. If you swap driver and driven (20 teeth driving 20 teeth → swap to 20 driving 20… well, same ratio). But if you make the smaller gear the driven, say 60 driving 20, your output runs 3x faster — great for generators, centrifugal pumps, and superchargers.