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Gear Ratio Calculator

Speed, torque, power, centre distance and tooth force for a gear pair.

Enter tooth counts and module, or a direct ratio, to get output speed, output torque after efficiency losses, and transmitted power. For spur and helical pairs defined by teeth, the calculator also gives pitch diameters, centre distance, pitch line velocity and tangential tooth force.

  • Live results
  • Full step-by-step working
  • PASS / FAIL checks
  • Free PDF report

Inputs

Results

Ratio i
3
Output speed
483.3 rpm
Output torque
29.4 N·m
Output power
1488 W
Centre distance
80 mm
Step-by-step calculation (7 steps)
  1. 1Gear ratio
    Formulai = Z2 / Z1
    Solutioni = 60 / 20
    Resulti = 3 (reduction)
  2. 2Output speed
    Formulan2 = n1 / i
    Solutionn2 = 1450 / 3
    Resultn2 = 483.3 rpm
  3. 3Output torque
    FormulaT2 = T1·i·η
    SolutionT2 = 10 × 3 × 0.98
    ResultT2 = 29.4 N·m
  4. 4Power
    FormulaP1 = T1·2π·n1 / 60, P2 = η·P1
    SolutionP1 = 10 × 2π × 1450 / 60
    ResultP1 = 1518 W, P2 = 1488 W, loss = 30.37 W
  5. 5Pitch diameters and centre distance
    Formulad = m·Z, a = m·(Z1 + Z2) / 2
    Solutiond1 = 2 × 20, d2 = 2 × 60, a = 2 × (20 + 60) / 2
    Resultd1 = 40, d2 = 120, a = 80 mm
  6. 6Pitch line velocity and tangential force
    Formulav = π·d1·n1 / 60 000, Ft = 2000·T1 / d1
    Solutionv = π × 40 × 1450 / 60 000, Ft = 2000 × 10 / 40
    Resultv = 3.037 m/s, Ft = 500 N
  7. 7Undercut check (20° pressure angle, no profile shift)
    FormulaZ1 ≥ 17
    SolutionZ1 = 20
    ResultNo undercutPASS

Engineering takeaways

  • Choose tooth counts with no common factor (hunting tooth ratio) so every pinion tooth meets every gear tooth, spreading wear evenly.
  • Ratio per spur stage is usually kept below 6:1. Use two or more stages for larger reductions.
  • Tooth strength (ISO 6336 bending and contact stress) must be checked separately for the tangential force.

The PDF report contains every input, formula, substitution and check shown above, in LTM calculation-sheet format.

Worked Example

An undercut check flags pinions below 17 teeth at a 20° pressure angle, and the efficiency options cover spur, helical, bevel, planetary and worm stages.

The calculator above opens with this example. Change any input to run your own case.

Inputs

Input methodNumber of teeth Z1 / Z2
Driver teeth Z120
Driven teeth Z260
Module m2 mm
Input speed n11450 rpm
Input torque T110 N·m
Gear type (efficiency per stage)Spur / helical η = 0.98

Results

Ratio i3
Output speed483.3 rpm
Output torque29.4 N·m
Output power1488 W
Centre distance80 mm

Gear Ratio Formulas Used

Ratio, speed and torque

i=Z2Z1,n2=n1i,T2=T1 i ηi = \frac{Z_2}{Z_1},\qquad n_2 = \frac{n_1}{i},\qquad T_2 = T_1\,i\,\eta
  • Z₁, Z₂driver and driven teeth
  • ηmesh efficiency

Power

P=T ω=T⋅2πn60P = T\,\omega = T\cdot\frac{2\pi n}{60}

Geometry

d=m Z,a=m (Z1+Z2)2d = m\,Z,\qquad a = \frac{m\,(Z_1 + Z_2)}{2}
  • mmodule (mm)
  • acentre distance

Tooth load

Ft=2000 T1d1,v=π d1 n160 000F_t = \frac{2000\,T_1}{d_1},\qquad v = \frac{\pi\,d_1\,n_1}{60\,000}

Basis: ISO 53 / ISO 54 standard module gearing relationships. Results are for preliminary design and should be confirmed against supplier data and the governing standard.

Gear Ratio Calculator FAQ

How do I calculate gear ratio?

Divide the number of teeth on the driven gear by the number on the driving gear. A 20-tooth pinion driving a 60-tooth gear gives 3:1, so output speed is one third and output torque is about three times input, less losses.

How efficient are gears?

A well-made spur or helical stage is about 98% efficient, bevel about 97% and a planetary stage about 95 to 97%. Worm gears range from 50% to 90% depending on ratio and lead angle.

What is a hunting tooth ratio?

A ratio whose tooth counts share no common factor, for example 19:58 instead of 20:60. Every pinion tooth then meets every gear tooth, which spreads wear and avoids repeating defects.

What is gear module?

Module is pitch diameter divided by number of teeth, in mm. Gears must have the same module and pressure angle to mesh. Common modules are 1, 1.5, 2, 2.5, 3, 4 and 5.

Does this check gear tooth strength?

No. It gives the tangential force needed for a strength check. Bending and contact stress should be checked to ISO 6336 or AGMA 2001 for the chosen material and face width.

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