How to calculate RC gear ratio: choosing pinion and spur gear

A new motor, a different battery, bigger tyres or different terrain: all of this changes how hard the drive has to work. With the gearing, the ratio of pinion to spur gear, you tune the drive to suit. It determines how quickly the model accelerates, how fast it gets and how warm motor and ESC run.

The terms

• Pinion: the small gear on the motor shaft.

• Spur gear: the large gear the pinion meshes with.

• Internal ratio: the fixed ratio in the vehicle’s gearbox and differentials. It is stated in the manual or data sheet.

• Final drive ratio (FDR): the overall ratio, in other words how many times the motor turns for one turn of the wheel.

Calculating the final drive ratio

Final drive ratio = (spur gear teeth ÷ pinion teeth) × internal ratio

Example: spur gear with 84 teeth, pinion with 24 teeth, internal ratio 2.6:1. 84 ÷ 24 = 3.5 and 3.5 × 2.6 = 9.10:1. The motor turns 9.1 times for each turn of the wheel.

A higher number means “shorter” gearing: more acceleration, less top speed, less load on the motor. A lower number is “taller”. Many manuals also include a table of final drive ratios for different pinions.

Calculating rollout

Rollout states how far the vehicle travels per motor revolution. It lets you compare vehicles with different tyre sizes, too.

Rollout = tyre diameter × π ÷ final drive ratio

Example with 85 mm tyres: 85 mm × 3.1416 = 267 mm circumference, divided by 9.10 gives 29.3 mm per motor revolution. It also follows that bigger tyres act like taller gearing.

Calculating top speed

Top speed in km/h = kV × battery voltage × rollout in mm × 0.00006

Example with a 3300 kV motor on 2S (7.4 V nominal): 3300 × 7.4 = 24,420 rpm, times 29.3 mm times 0.00006 gives about 43 km/h. That is a theoretical value. In practice the model is slower, because the voltage drops under load and the motor does not reach its no-load rpm. For comparing two gearings, though, the formula is ideal.

Gear chart: example for a 1:10 model

Calculated with: spur gear 84 teeth, internal ratio 2.6:1, tyres 85 mm, 3300 kV at 7.4 V.

Bigger or smaller pinion?

One tooth on the pinion changes the ratio much more than one tooth on the spur gear. For fine-tuning, the spur gear is therefore the better tool.

Pinion pitch and module: what fits together

Pinion and spur gear must have exactly the same tooth pitch. There are two systems: metric module (for example module 0.8 or module 1) and imperial diametral pitch (DP, for example 48dp). The smaller the module or the larger the DP number, the finer the teeth. The conversion is: module = 25.4 ÷ DP.

Never mix pitches, even if two values look similar. The pinion’s bore has to match as well: usually 3.175 mm (1/8 inch) on 1:10 motors, sometimes 5 mm on powerful motors for 4WD trucks, 5 mm on 1:8 motors and 8 mm on large 1:5 motors. The right spur gear for your model is quickly found with the spare-parts finder.

Setting the gear mesh

Pinion and spur gear need a little play. If it is too tight, the drive is noisy, loses power and gets warm. If it is too loose, the teeth can skip, which destroys the spur gear within seconds.

How to set the mesh with a strip of paper:

1. Slightly loosen the motor screws.

2. Place a narrow strip of ordinary paper between pinion and spur gear.

3. Push the motor against the spur gear and tighten the screws.

4. Turn the gears to run the paper out. What remains is exactly the right play.

5. Check at several points around the spur gear: there should be slight play everywhere and binding nowhere.

6. The pinion’s grub screw sits on the flat of the motor shaft and gets a drop of medium-strength thread lock.

Step by step to the right gearing

1. Start with the recommendation: the manual of the vehicle or motor gives a base gearing. If in doubt, start a little shorter, with a smaller pinion.

2. Drive for three to five minutes, the way you normally drive and on your usual surface.

3. Measure the temperature: check motor, ESC and battery directly after the run, most easily with an infrared thermometer. Hobbywing states 100 °C as the limit for its motors in its manuals; above that the magnets weaken and the windings can be damaged. With a safety margin, the motor should stay well below that.

4. Adjust step by step: if everything stays cool, you can try a pinion with one or two more teeth. If it gets too hot, use one with fewer teeth. Measure again after every change.

5. Mind the surface and weather: tall grass, sand, snow and big tyres load the drive more, so gear shorter there. On smooth tarmac, taller gearing is possible.

Read more about choosing the motor and kV in the guide Brushless motor and ESC.