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Gearbox Ratios Calculator

Computes a gear pair or train ratio from tooth counts with output speed and torque, and the vehicle overall ratio, tyre diameter from the size code, road speed at an engine speed and engine speed at a road speed using exact NIST unit constants.

Gear ratio (driven / driver)
3.0000
Gear Ratio Calculator
Ratio as n:1
3:1
Output speed
575.00 rpm
Input torque (selected unit)
182.68
Output torque (selected unit)
548.05
Torque unit
lb·in
Output torque
61.92 N·m
Input power
3,728.5 W
Output power
3,728.5 W
Worked out from Carnegie Mellon University, Introduction to Mechanisms, Chapter 7 Gears (velocity ratio is the inverse tooth ratio; train ratio = product of driven / product of driver teeth) and 7 other sources.
Torque is the ideal (100 % efficient) figure; real gear sets lose a few percent per mesh, and worm drives considerably more.

Your figures

Updates as you type
One number per mesh, in order, e.g. "20" or "20, 15" for a two-stage train. Idlers appear in both lists and cancel out.
Same number of entries as the driver list, e.g. "60" or "60, 45".
Leave at 0 to use the tooth counts. Enter e.g. 5 for a 5:1 reduction or 0.582 for an overdrive.
Used when the input load is given as torque.
100 % is the ideal (lossless) case and the default. Indicative ranges from a continuing-education course, not AGMA: spur and helical 94-98 %, bevel 93-99 %, worm 50-90 %.

How this is worked out

5 steps
  1. Ratio i = driven teeth / driver teeth = 60 / 20 = 3
  2. Output speed = 1725 / 3 = 575 rpm
  3. Input torque from power: T = P x 60 / (2 pi n) = 3728.499 W x 60 / (2 pi x 1725) = 20.6403 N·m = 182.6822 lb·in (equivalently 5 hp x 63,025.36 / 1725)
  4. Output torque = T_in x i x eta = 182.6822 x 3 x 1 = 548.0466 lb·in (ideal, lossless)
  5. Output power = P_in x eta = 3728.5 x 1 = 3728.5 W

Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed

Sources and references

8 sources
Carnegie Mellon University, Introduction to Mechanisms, Chapter 7 Gears (velocity ratio is the inverse tooth ratio; train ratio = product of driven / product of driver teeth)
Mustansiriyah University, Mechanical Engineering lecture 8: Gears (efficiency = output power / input power; worked example 20 kW, ratio 5, 70 %)
CED Engineering course M06-031, Basic Fundamentals of Gear Drives (20-tooth pinion to 60-tooth gear at 1725 rpm; indicative efficiency ranges)
NIST SP 811 Appendix B.8, conversion factors (inch = 2.54 E-02 m exact; mile = 1.609344 E+03 m exact; horsepower (550 ft lbf/s))
Bridgestone, How to Read Tire Size (width in mm, aspect ratio as a percentage, rim diameter in inches)
Tire Rack, How Do I Calculate Tire Dimensions? (overall diameter = 2 x sidewall + rim; nominal versus actual caveat) and What Is the Revolutions Per Mile of a Tire?
Tire Rack, Racing and Rally Motorsport Tire Size Formats (flotation format 35x12.50R17: diameter x width R rim, inches)
Mazda USA, 2020 MX-5 Miata Features and Specs (6MT ratios, final drive 2.866, P205/45R17)
2020

What this calculator does

Computes a gear pair or train ratio from tooth counts with output speed and torque, and the vehicle overall ratio, tyre diameter from the size code, road speed at an engine speed and engine speed at a road speed using exact NIST unit constants.

How to use Gearbox Ratios Calculator

Enter Driver (input) gear tooth counts, Driven (output) gear tooth counts, Known ratio (optional, overrides tooth counts), Input (driver) speed, Input load given as, Input power, Power unit, Input torque, Torque unit and Gear-set efficiency. The calculator checks the values, applies the stated method, and updates the result without saving your figures.

What the result means

The result includes Gear ratio (driven / driver), Ratio as n:1, Output speed, Input torque (selected unit), Output torque (selected unit), Torque unit, Output torque, Input power, Output power, Overall ratio (gear x final drive), Tyre sidewall height, Tyre diameter (nominal, unloaded), Tyre diameter (nominal, unloaded), Tyre circumference, Revolutions per mile used, Road speed at the engine speed, Road speed at the engine speed, Same speed by the approximate "336" shortcut, Wheel speed at the engine speed and Engine speed at the road speed. Review the visible working and any warnings before using the answer for a decision.

Method and checks

The method cites Carnegie Mellon University, Introduction to Mechanisms, Chapter 7 Gears (velocity ratio is the inverse tooth ratio; train ratio = product of driven / product of driver teeth); Mustansiriyah University, Mechanical Engineering lecture 8: Gears (efficiency = output power / input power; worked example 20 kW, ratio 5, 70 %); CED Engineering course M06-031, Basic Fundamentals of Gear Drives (20-tooth pinion to 60-tooth gear at 1725 rpm; indicative efficiency ranges), among others. Its 5 built-in worked examples are checked on every full test run. The initial answer and working are rendered on the server, so they remain readable without JavaScript.

Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.

Embed this calculator on your website

Copy this code into any page. The calculator appears with the figures currently entered, sizes itself to fit, and a small credit line links back here. Free, no account, no ads inside it, no tracking of your readers. Set your own figures and fixed fields; Personal removes the credit line, sets your colour and shows you which sites use it.

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