Quick answer
Output speed = input speed × driver teeth ÷ driven teeth. A 20 tooth driver at 1,800 rpm turning a 40 tooth gear outputs 900 rpm, a ratio of 2.
Enter the driver and driven tooth counts and the input speed. The calculator returns the output rpm and ratio.
Related tools: Gear Ratio Calculator: Gear ratio, output speed and torque multiplication. Transmission Gear Ratio Calculator: Vehicle speed from engine rpm, gear ratio, final drive and tire size. Spring Constant Calculator: Hooke's law spring constant and stored energy.
How to use the Gear Speed Calculator
- Enter driver gear teeth (above 0).
- Enter driven gear teeth (above 0).
- Enter input speed (rpm) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Driver gear teeth | A number | > 0 |
| Driven gear teeth | A number | > 0 |
| Input speed | A number, in rpm | > 0 |
Formula and method
Formula
output rpm = input rpm × driver teeth ÷ driven teeth
IEEE-754 double precision; shown to the decimals indicated.
Ratio is driven ÷ driver; torque scales by the same ratio, ignoring losses.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Driver gear teeth = 20; Driven gear teeth = 40; Input speed = 1800.
| Result | Value |
|---|---|
| Output speed | 900 rpm |
| Gear ratio (driven ÷ driver) | 2 |
Example 2
Inputs: Driver gear teeth = 60; Driven gear teeth = 15; Input speed = 500.
| Result | Value |
|---|---|
| Output speed | 2,000 rpm |
| Gear ratio (driven ÷ driver) | 0.25 |
Example 3
Inputs: Driver gear teeth = 12; Driven gear teeth = 36; Input speed = 3000.
| Result | Value |
|---|---|
| Output speed | 1,000 rpm |
| Gear ratio (driven ÷ driver) | 3 |
The first line is the headline result (output speed). Below it the gear Speed Calculator lists gear ratio (driven ÷ driver), which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Direction
External gears reverse rotation direction at each mesh. An even number of meshes returns the original direction. An idler between two gears flips the direction without changing speed.
Meshing requirements
Meshing gears must share a module or pitch, and the centre distance is (d₁ + d₂) ÷ 2. For belt or chain drives the same tooth ratio applies to the sprockets.
How the result changes with driver gear teeth
Holding every other input at the first worked example, this table changes only driver gear teeth. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Driver gear teeth | Output speed | Gear ratio (driven ÷ driver) |
|---|---|---|
| 10 | 450 rpm | 4 |
| 20 | 900 rpm | 2 |
| 40 | 1,800 rpm | 1 |
| 80 | 3,600 rpm | 0.5 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Driver gear teeth: entering "0" shows "Driver gear teeth must be greater than 0." beside that field and no result.
- Input speed: entering "0" shows "Input speed must be greater than 0." beside that field and no result.
Choosing between the Gear Speed Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Gear Ratio Calculator](/engineering/gear-ratio-calculator/) | driving gear teeth and driven gear teeth | Gear ratio |
| [Transmission Gear Ratio Calculator](/engineering/transmission-gear-ratio-calculator/) | transmission gear ratio, final drive ratio and tire diameter | Vehicle speed |
| [Spring Constant Calculator](/engineering/spring-constant/) | force and extension | Spring constant |
| [Speedometer Gear Calculator](/engineering/speedometer-gear-calculator/) | teeth on the speedometer drive gear, axle ratio and tire diameter | Driven gear teeth |
| [Speed Converter](/converters/speed-converter/) | value, from and to | Mile per hour (mph) → Kilometre per hour (km/h) |
Background: structural and wiring estimates
Structural and electrical results are only as good as their assumptions. Bending stress is the bending moment divided by the section modulus, and an allowable stress is the yield strength divided by a safety factor that depends on the governing design code and the type of load. For a single-phase or DC run the voltage drop uses the round-trip length: V = 2 × L × R per unit length × I.
Recommended limits, such as keeping branch-circuit voltage drop around 3%, differ between sources and code editions. These pages are estimates: follow the applicable code and a qualified engineer or electrician for real work.
Assumptions and limitations
- Meshing gears must share a module or pitch
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for driver gear teeth and input speed to confirm this.
Frequently asked questions
What if the driver has more teeth?
A driver with more teeth than the driven gear makes the output spin faster: 40 driver teeth to 20 driven doubles the speed.
Is rpm the same as rad/s?
No, 1 rpm is 0.1047 rad/s.
How do I find tooth count?
Count the teeth or use the specification.
What does the Gear Speed Calculator calculate?
Output speed and ratio of a gear pair. It returns Output speed and Gear ratio (driven ÷ driver).
What formula does the Gear Speed Calculator use?
output rpm = input rpm × driver teeth ÷ driven teeth. Ratio is driven ÷ driver; torque scales by the same ratio, ignoring losses.
What do I need to enter in the gear Speed Calculator?
You enter Driver gear teeth, Driven gear teeth and Input speed (rpm).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Meshing gears must share a module or pitch.
What is an example of a gear Speed result?
With driver gear teeth 20, driven gear teeth 40 and input speed 1800, the output speed is 900 rpm.
Can I rely on this calculator for a decision?
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them. For this calculator in particular: Meshing gears must share a module or pitch.
Related calculators
- Gear Ratio Calculator — Gear ratio, output speed and torque multiplication.
- Transmission Gear Ratio Calculator — Vehicle speed from engine rpm, gear ratio, final drive and tire size.
- Spring Constant Calculator — Hooke's law spring constant and stored energy.
- Speedometer Gear Calculator — Number of teeth for the speedometer driven gear after a tire or axle ratio change.
- Speed Converter — mph, km/h, knots, m/s and ft/s.
- Belt Length Calculator — Open-belt length for two pulleys.
- Cycling Speed Calculator — Average speed from a distance and a time.
Sources
- OpenStax, University Physics Volume 1 (Rice University): mechanics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.