How It Is Calculated
The RC Gear Ratio Calculator determines the effective gear ratio, rollout, and expected speed of a radio-controlled vehicle based on the motor, battery, and drivetrain parameters. The calculations follow these steps:
Gear Ratio
The gear ratio (G) is the ratio of spur gear teeth (S) to pinion gear teeth (P):
G = S / P
Overall Ratio
The overall ratio (O) includes the internal gearbox ratio (I):
O = G × I
Rollout
Rollout (R) is the distance the vehicle moves per motor revolution, calculated from tire circumference divided by the overall ratio:
R = (π × D) / O
where D is the tire diameter in inches.
Motor RPM
Motor RPM (M) is the product of motor kV (K), battery voltage (V), and efficiency (E as a decimal):
M = K × V × (E / 100)
Speed
Speed (S) in miles per hour is derived from motor RPM and rollout:
S = (M × R × 60) / 63360
All intermediate values use full precision; final outputs are rounded as shown.
Assumptions
- Motor kV is the no-load RPM per volt.
- Efficiency accounts for motor and drivetrain losses; 85% is typical for brushless systems.
- Internal gear ratio is 1 if no additional gearbox is present.
- Tire diameter is the outer diameter under load (approximate).
- Battery voltage is nominal (e.g., 7.4V for 2S LiPo).
Worked Example
Using the default inputs:
- Spur gear teeth (S) = 100 teeth
- Pinion gear teeth (P) = 20 teeth
- Internal gear ratio (I) = 1 :1
- Tire diameter (D) = 4.0 in
- Motor kV (K) = 3000 RPM/V
- Battery voltage (V) = 7.4 V
- Efficiency (E) = 85%
Step 1: Gear ratio G = 100 / 20 = 5 :1
Step 2: Overall ratio O = 5 × 1 = 5 :1
Step 3: Rollout R = (π × 4.0) / 5 = 12.56637 / 5 = 2.51327 in (rounded to 2.51 in)
Step 4: Motor RPM M = 3000 × 7.4 × (85/100) = 3000 × 7.4 × 0.85 = 18870 RPM
Step 5: Speed S = (18870 × 2.51327 × 60) / 63360 = (18870 × 150.7962) / 63360 = 2845000 / 63360 ≈ 44.9 mph
Results: Gear ratio = 5 :1, Overall ratio = 5 :1, Rollout = 2.51 in, Speed = 44.9 mph, Motor RPM = 18870 RPM.
Practical Tips
- Use a motor torque calculator to check if your motor can handle the load at the chosen gear ratio.
- Smaller pinion gears increase torque but reduce top speed; larger pinions do the opposite.
- Always verify tire diameter under load, as it can differ from the nominal size.
- For multi-speed gearboxes, enter the internal ratio for the gear you plan to use.
- Efficiency varies with temperature and load; test your setup to fine-tune.
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