Gear Ratio CalculatorSpeed · torque · teeth
Gear ratio is the driven gear’s teeth divided by the driving gear’s teeth: GR = Nout ÷ Nin. Output speed is divided by that ratio and output torque is multiplied by it, minus losses. Enter tooth counts and input rpm and torque for a single pair or a two-stage train, or use bicycle mode to turn chainring, cog and cadence into road speed. The animated gears mesh at your actual ratio.
Formula verified against OpenStax — University Physics, Volume 1 · HyperPhysics, Georgia State University
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Gear set
Driver = input gear (on the motor). Driven = output gear (on the load).
Step-by-step working
What is gear ratio?
A gear ratio compares how fast two meshing gears turn. It equals the ratio of their tooth counts, and it sets how speed and torque change between the input and output shafts.
Gearboxes, bicycles, clocks, drills and wind turbines all use gear ratios to match a motor’s natural speed to the job, trading rpm for torque or the other way round.
Quick answers
How do you calculate gear ratio from teeth?
Divide the teeth on the driven gear by the teeth on the driving gear. A 15-tooth pinion driving a 45-tooth gear is 45 ÷ 15 = 3:1.
How do I find output rpm from a gear ratio?
Output rpm = input rpm ÷ gear ratio. A 3:1 reduction turns a 1,800 rpm motor into 600 rpm at the output shaft.
How does gear ratio affect torque?
Torque is multiplied by the ratio, less friction losses. A 4:1 reduction at 97% efficiency turns 5 N·m into 19.4 N·m. Check your units with the torque calculator.
How fast will I go in a bicycle gear?
Speed = cadence × (chainring ÷ cog) × wheel circumference. At 90 rpm in a 50 × 17 gear on 700c wheels, that is about 33 km/h. Use the Bicycle tab.
Gear ratio formulas
For a gear train, multiply the ratios of each meshing pair. Idler gears change direction but not the ratio.
| Symbol | Meaning | SI unit |
|---|---|---|
| GR | Gear ratio (reduction if > 1) | — |
| N | Number of teeth | — |
| ω | Rotational speed | rpm or rad/s |
| τ | Torque | N·m |
| η | Mechanical efficiency | % |
How to calculate gear ratio
- Count the teeth on the driving (input) gear and the driven (output) gear.
- Divide driven by driver: 60 ÷ 20 = 3, written 3:1.
- Divide input speed by the ratio for output speed.
- Multiply input torque by the ratio and the efficiency for output torque.
Worked example: a 20 → 60 tooth reduction
A motor turning at 1,500 rpm with 10 N·m drives a 20-tooth gear meshed with a 60-tooth gear at 98% efficiency.
Output speed = 1,500 ÷ 3 = 500 rpm
Output torque = 10 × 3 × 0.98 = 29.4 N·m
On a road bike, a 50 × 17 gear at 90 rpm cadence on 700×25c wheels (2,105 mm) moves you 6.19 m per pedal stroke, about 33.4 km/h.
Bicycle speed chart at 90 rpm (700×25c)
Speed for common chainring and cog pairs.
| Gear | Ratio | Development | Speed @ 90 rpm |
|---|---|---|---|
| 34 × 28 | 1.21 | 2.56 m | 13.8 km/h |
| 34 × 17 | 2.00 | 4.21 m | 22.7 km/h |
| 50 × 17 | 2.94 | 6.19 m | 33.4 km/h |
| 50 × 13 | 3.85 | 8.10 m | 43.7 km/h |
| 53 × 11 | 4.82 | 10.14 m | 54.8 km/h |
Common mistakes to avoid
- Dividing the wrong way. Ratio = driven ÷ driver. A small gear driving a big one gives a ratio above 1, a speed reduction.
- Counting idler gears in the ratio. They only reverse direction.
- Assuming torque is multiplied for free. Power out is at most power in; friction losses reduce it further.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who turned into a full-time tech geek, and for 13+ years I’ve designed and coded web tools. My pharmacy degree included physical pharmacy and pharmaceutics — states of matter, heat, flow and reaction kinetics — so the physics behind these tools is familiar ground, not a new hobby.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Gear Ratio Calculator: frequently asked questions
The ratio of teeth (or speeds) between two meshing gears. It tells you how many times the input gear must turn to rotate the output gear once.
The input turns three times for every single turn of the output. Speed drops to a third and torque roughly triples.
It depends on the convention. In cars, a ‘higher’ (numerically lower) final drive gives more top speed. A numerically larger ratio means more torque and acceleration but lower top speed.
Multiply the ratios of each meshing pair: (N₂ ÷ N₁) × (N₄ ÷ N₃) × … Idler gears cancel out.
No. Ideal gears trade speed for torque at constant power. Real gears lose 1–3% per mesh to friction, or more for worm gears.
References & sources
- OpenStax — University Physics, Volume 1 — Ch. 10, Rotational Motion
- HyperPhysics, Georgia State University — gears and mechanical advantage
- Sheldon Brown — Gear Calculator notes — bicycle gear inches and development
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.