Gear Ratio Calculator
Calculate one external gear pair’s ratio, output speed, torque and power. Enter tooth counts and your own efficiency to compare the two shafts.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Divide driven teeth by driver teeth for the reduction ratio. Output speed is input speed divided by that ratio. Multiply input torque by the ratio and entered efficiency for output torque. Power is torque times angular speed.
i=Z_driven/Z_driver; rpm_out=rpm_in/i; τ_out=τ_in×i×η; P=τ×rpm×2π/60
Worked example
A 20-tooth driver and 60-tooth driven gear give a 3:1 reduction. At 1200 rpm, 10 N·m and 90% entered efficiency, output is 400 rpm and 27 N·m. Output power is about 1130.97336 W.
Assumptions and input details
This models one pair of directly meshing external gears with fixed shafts. Output rotation is opposite to input. It is not an internal, planetary, worm, belt or compound train model. Tooth counts are integers from 1 to 10000; geometric compatibility and strength are not checked. Speed and torque are non-negative magnitudes. Efficiency is entered, not inferred, and may be 0–100%; 100% describes the ideal lossless model. No tooth module, load rating, inertia or dynamic stress is inferred.
References: KHK: speed ratio of gears
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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