Gear Ratio Calculator

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 %.
e.g. 2020 MX-5 6MT: 1st 5.087 ... 6th 1.000. Overdrive ratios below 1 are fine.
Multiply in a transfer case or hub reduction as well if fitted.
Metric (205/45R17, P225/70R16 91S, LT265/70R17) or flotation (33x12.50R17). Gives the nominal unloaded diameter.
Leave at 0 to use the geometric diameter. A published figure accounts for the loaded rolling radius and is usually a few percent higher than geometry.
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.

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

Results are general information, not financial, tax, legal, medical or engineering advice.