How do I format the tooth pairs for multiple stages?

Enter each stage on a new line or separate them with semicolons, using the format 'driver,driven' (for example, '20,60').

What formula is used to calculate the total gear ratio?

The total ratio is the product of the individual stage ratios, where each stage ratio is the number of driven teeth divided by the driver teeth.

Is the input speed required to calculate the gear ratio?

No, the input speed is optional. If omitted, the calculator will still compute the overall transmission ratio.

Can this calculator handle planetary or epicyclic gear systems?

No, this calculator is designed specifically for standard external or internal spur and helical gear trains in compound arrangements.

How does the calculator handle speed reduction versus overdrive?

A total ratio greater than 1 indicates speed reduction (torque multiplication), while a ratio less than 1 indicates overdrive (speed multiplication).

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Gear Train Speed Ratio Calculator

Calculate the overall ratio and output speed of a multi-stage gear train. i_total = i₁·i₂·…·iₙ (each i = z₂/z₁). Enter tooth pairs per stage and the input speed to get the final output speed.

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1 examples

Two-stage train: (20→60) then (15→45) at 1800 rpm

Stage 1 i = 3, stage 2 i = 3, i_total = 9, n_out = 1800/9 = 200 rpm.

{"result":"i_total = 3 · 3 = 9 over 2 stages. n_out = 1800 rpm / 9 = 200 rpm.","metadata":{"input":{"stageCount":2,"inputSpeed":1800},"result":{"stages":[{"stage":1,"driver":20,"driven":60,"ratio":3},{"stage":2,"driver":15,"driven":45,"ratio":3}],"totalRatio":9,"stageCount":2,"outputSpeed":200,"outputSpeedUnit":"rpm"}}}

Inputs

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3 options

ContentPaste or type the main input values.1

Tooth Pairs (one stage per line, 'driver,driven')textareaRequiredEach line is one stage: driver teeth, then driven teeth, separated by a comma. Separate stages with new lines or semicolons.

SettingsAdjust formats, ranges, numbers, and modes.2

Input Shaft Speed (rpm)numberOptionalOptional. If provided, the final output speed is computed.Decimal PlacesnumberOptional

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Gear Train Speed Ratio Calculator

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Key facts

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Use cases

Examples

1. Two-Stage Speed Reduction Gearbox

2. High-Speed Overdrive System

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