Gear Ratio Calculator
Calculate gear ratio step by step: Ratio = driven teeth ÷ driving teeth.
In short
Formula: Ratio = driven teeth ÷ driving teeth. Output torque = input torque × ratio (ideal).
Gear ratio
3 : 1
- Speed change
- Output 3× slower
What this calculator does
Calculate gear ratio step by step: Ratio = driven teeth ÷ driving teeth. Worked example, questions and limitations included.
Use it to turn Driving gear teeth, Driven gear teeth, Input torque (optional) into a checked result you can compare, copy, or rerun with different assumptions.
The page shows the formula, a numeric worked example, and the assumptions that affect this mechanical calculation.
Inputs and what they mean
- Driving gear teeth
- — number value.
- Driven gear teeth
- — number value.
- Input torque (optional)
- — number value.
How to use it
- Enter each value in the unit shown next to the box (use the unit converter first if your numbers are in other units).
- Check the breakdown to see every intermediate step.
- Read the limitations before relying on the result.
Formula
Tooth counts must be positive whole numbers.
Ideal gears — no friction losses.
Idler gears do not change the ratio.
Ratio = driven teeth ÷ driving teeth. Output torque = input torque × ratio (ideal).
Inputs used: Driving gear teeth, Driven gear teeth, Input torque (optional).
Worked example
12-tooth pinion driving a 36-tooth gear
- Ratio = 36 ÷ 12 = 3 : 1.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
- Single stage.
- Friction losses ignored.
- Does not check gear strength or meshing.
- Results are estimates for planning and learning. Real designs, installations and bids must be checked by a qualified, licensed professional against the codes that apply where you work.
- The result depends on the values you enter for this gear ratio calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.
Common questions
Does a higher ratio mean more torque?
Yes. A 3 : 1 reduction triples torque (minus losses) and cuts speed to a third.
What about compound gear trains?
Multiply the ratio of each stage together to get the overall ratio. Check the formula, example, and limitations on this page before using the result for a real mechanical decision.
Do idler gears matter?
They reverse direction but do not change the overall ratio. Check the formula, example, and limitations on this page before using the result for a real mechanical decision.
How do I use the Gear Ratio Calculator?
Enter the required values for Driving gear teeth, Driven gear teeth, Input torque (optional). The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.
What formula does the Gear Ratio Calculator use?
Ratio = driven teeth ÷ driving teeth. Output torque = input torque × ratio (ideal). The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.
Can the Gear Ratio Calculator be used for exact decisions?
Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.
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