Dr Ratio 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.
Your figures
Updates as you typeHow this is worked out
6 steps
- Overall ratio = gear 1 x final drive 2.866 = 2.866
- Tyre 205/45R17: sidewall = 205 x 45/100 = 92.25 mm; diameter = 17 x 25.4 + 2 x 92.25 = 616.3 mm = 24.2638 in
- Road speed = 3000 rpm x 24.2638 in x pi x 60 / (2.866 x 63,360 in/mile) = 75.56 mph; in metric 3000 x 616.3 mm x pi x 60 / (2.866 x 1,000,000) = 121.601 km/h
- Approximate "336" shortcut: 3000 x 24.2638 / (2.866 x 336) = 75.59 mph (63,360 / 60 pi is really 336.1352, so the shortcut reads about 0.04 % high)
- Engine speed at 70 mph = 70 mph x 2.866 x 63,360 / (24.2638 x pi x 60) = 2779.3 rpm
- Wheel speed = 3000 / 2.866 = 1046.76 rpm
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
8 sources
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 Dr Ratio Calculator
Enter Transmission ratio in the selected gear, Final drive (axle or differential) ratio, Tyre size code, Manufacturer revolutions per mile (optional), Engine speed for the road-speed result, Road speed for the engine-rpm result, Road speed unit and Headline result. 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.
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