Calculating Speed and Gear Ratios

Determining the required gear ratio or maximum speed is not always intuitive. Many factors have to be taken into account. This page is particularly useful for electric or motor-driven locomotives.

The ratios and speed required can be determined from the calculator below:-

These calculations are applicable to models with mechanical transmission systems, either petrol engine powered or electric motor powered. Allowance is also made for up to 3 stages of gearing, often required due to space limitations.


Chain & Sprocket
Single stage
Single stage gears
Two stage gears
Three stage gears
Gear ratio/speed Calculator
Enter either English or Metric values
below and press 'Calculate'.

Select English or Metric units for each input parameter
The equivalent converted unit is shown in the other (grey) box

Motor speed (max RPM): rpm
Wheel Dia: ins mm
1st stage: no of teeth [driving]
no of teeth [driven]
Intermediate shaft (1-2) Speed: ? rpm
2nd stage: no of teeth [driving]
no of teeth [driven]
Intermediate shaft (2-3) Speed: ? rpm
3rd stage: no of teeth [driving]
no of teeth [driven]
Axle Speed ? rpm
Overall ratio: ? : 1
Resultant (max) Speed: ? km/h
(= ? mph)

Note: Simple formulas using +-*/() may be entered if desired, not just straight plain numbers.
(for example, 43/16 is entered as 4+(3/16) [=4.1875])

If 2nd or 3rd stage is not used, use 1 for both no-of-teeth inputs.

Works for both step-up and step-down.

Note: The number of teeth does not have to be exact whole numbers. If, for example, a 2.35:1 gearbox is used for one of the stages, use 1 as the driving input, and 2.35 for the No of teeth (driven) input.

Example 1:
Motor speed is 5000 rpm (max),
Wheel diameter is 125mm.
1st stage reduction uses sprockets of 9T and 29T,
2nd stage reduction uses gears of 10T and 29T.
Resultant maximum speed is 12.6 kmph, overall reduction ratio 9.344:1
Example 2:
Motor speed is 2000 rpm (max)
Wheel diameter is 120mm
If stage 1 uses 11T and 16T sprockets, and a gearbox with a 2.35:1 ratio is used as stage 2 of the reduction, input 11T and 16T for stage 1, and 1T and 2.35T for stage 2. Overall reduction ratio ise 3.418:1
Resultant maximum speed is 13.2kmph
Example 3:
Motor speed is 2500 rpm (max)
Wheel diameter is 200mm
If stage 1 uses 11T and 15T sprockets, stage 2 uses 8T and 16T gears, and a gearbox with a 1.55:1 ratio is used for stage 3 (1T and 1.55T), overall reduction ratio would be 4.227:1 and maximum speed is 22.3kmph

Note the accuracy of these calculations is not necessarily exact, and figures calculated here may vary from actual results.
Results to be used at your own risk. Calculator provided for your personal use only.

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