Quick answer
Gear ratio = driven teeth ÷ driving teeth, and output speed = input speed ÷ ratio. A 10 tooth driver turning a 40 tooth gear gives 4:1, so 1,200 rpm in becomes 300 rpm out.
Enter the driver and driven tooth counts and the input speed. The calculator returns the ratio and the output speed.
Related tools: Transmission Gear Ratio Calculator: Vehicle speed from engine rpm, gear ratio, final drive and tire size. Gear Speed Calculator: Output speed and ratio of a gear pair. Spring Constant Calculator: Hooke's law spring constant and stored energy.
How to use the Gear Ratio Calculator
- Enter driving gear teeth (a whole number, 1 or more).
- Enter driven gear teeth (a whole number, 1 or more).
- Optionally, enter input speed (rpm) (0 or more).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Driving gear teeth | A whole number | ≥ 1 |
| Driven gear teeth | A whole number | ≥ 1 |
| Input speed (optional) | A number, in rpm | ≥ 0 |
Formula and method
Formula
ratio = driven teeth ÷ driving teeth; output rpm = input rpm ÷ ratio
IEEE-754 double precision; shown to at most 6 decimal places.
Ideal gears; efficiency losses are ignored.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Driving gear teeth = 10; Driven gear teeth = 40; Input speed = 1200.
| Result | Value |
|---|---|
| Gear ratio | 4:1 |
| Output speed | 300 rpm |
Example 2
Inputs: Driving gear teeth = 30; Driven gear teeth = 20.
| Result | Value |
|---|---|
| Gear ratio | 0.6667:1 |
The first line is the headline result (gear ratio). Below it the gear Ratio Calculator lists output speed, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Speed and torque trade off
A ratio above 1 reduces speed and multiplies torque by the same factor (ignoring losses): 4:1 gives a quarter of the speed and four times the torque. A ratio below 1 is an overdrive.
Compound gear trains
For several meshing pairs, multiply their ratios. Idler gears change direction but not the ratio. Gears must have the same module or pitch to mesh.
How the result changes with driving gear teeth
Holding every other input at the first worked example, this table changes only driving gear teeth. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Driving gear teeth | Gear ratio | Output speed |
|---|---|---|
| 5 | 8:1 | 150 rpm |
| 10 | 4:1 | 300 rpm |
| 20 | 2:1 | 600 rpm |
| 40 | 1:1 | 1,200 rpm |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Driving gear teeth: entering "0" shows "Driving gear teeth must be at least 1." beside that field and no result.
Choosing between the Gear Ratio 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 |
|---|---|---|
| [Transmission Gear Ratio Calculator](/engineering/transmission-gear-ratio-calculator/) | transmission gear ratio, final drive ratio and tire diameter | Vehicle speed |
| [Gear Speed Calculator](/engineering/gear-speed-calculator/) | driver gear teeth, driven gear teeth and input speed | Output speed |
| [Spring Constant Calculator](/engineering/spring-constant/) | force and extension | Spring constant |
| [Ratio Calculator](/math/ratio-calculator/) | first number and second number | Simplified ratio |
| [Speedometer Gear Calculator](/engineering/speedometer-gear-calculator/) | teeth on the speedometer drive gear, axle ratio and tire diameter | Driven gear teeth |
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
- Ratio above 1 reduces speed and multiplies torque
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 driving gear teeth to confirm this.
Frequently asked questions
What is the gear ratio of 20 and 60 teeth?
A 20-tooth driver with a 60-tooth driven gear gives a 3:1 ratio, reducing speed to a third and tripling torque.
Does the driver or driven go first in the formula?
Driven divided by driver.
What is efficiency of a gear pair?
Typically 95 to 99%.
What does the Gear Ratio Calculator calculate?
Gear ratio, output speed and torque multiplication. It returns Gear ratio and Output speed.
What formula does the Gear Ratio Calculator use?
ratio = driven teeth ÷ driving teeth; output rpm = input rpm ÷ ratio. Ideal gears; efficiency losses are ignored.
What do I need to enter in the gear Ratio Calculator?
You enter Driving gear teeth and Driven gear teeth. Optional: Input speed (rpm).
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Ratio above 1 reduces speed and multiplies torque.
What is an example of a gear Ratio result?
With driving gear teeth 10, driven gear teeth 40 and input speed 1200, the gear ratio is 4:1.
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: Ratio above 1 reduces speed and multiplies torque.
Related calculators
- Transmission Gear Ratio Calculator — Vehicle speed from engine rpm, gear ratio, final drive and tire size.
- Gear Speed Calculator — Output speed and ratio of a gear pair.
- Spring Constant Calculator — Hooke's law spring constant and stored energy.
- Ratio Calculator — Simplify a ratio of two whole numbers.
- Speedometer Gear Calculator — Number of teeth for the speedometer driven gear after a tire or axle ratio change.
- K/D Ratio Calculator — Kill/death ratio.
- Transformer Turns Ratio Calculator — Secondary voltage from primary voltage and turns.
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.