Gear Ratio Calculator | Spur, Compound and Planetary Gears
Calculate reduction ratio, output speed and direction from tooth counts and input rpm. Switch between a spur pair, compound train and planetary gears to compare motion and numerical results.
Mode
Driver Teeth N₁
Driven Teeth N₂
Input Speed
rpm
RPM
Module m
mm
mm
Stage 1 N₁ (driver)
Stage 1 N₂ (driven)
Stage 2 N₃ (driver)
Stage 2 N₄ (driven)
Input Speed
rpm
RPM
Sun Gear Teeth Zs
Planet Teeth Zp
Sun Input Speed
rpm
RPM
Fixed Member
Results
Velocity Ratio i
2.000
Output Speed
500RPM
Torque Ratio
1.96×
Total Efficiency
98.0%
d₁ Pitch Dia.
40mm
d₂ Pitch Dia.
80mm
Center Distance
60.0mm
Gear
Animation: each gear rotates at its correct angular velocity ratio
For a simple pair with N1=20, N2=40, input=1000rpm, module=2mm and no idler, ratio=2.000, output=500rpm and center distance=60.0mm. Ideal torque multiplication is 2.00; the displayed value is 1.96 after the assumed 98% efficiency.
For a simple pair, i=N2/N1, n2=n1/i, d=mN and a=m(N1+N2)/2. Compound ratios multiply. For a ring-fixed planetary train, Zr=Zs+2Zp and i=1+Zr/Zs. Efficiencies are fixed assumptions: 98%, 98% squared and 97% for the three modes respectively.
Questions and answers
Does adding an idler change the ratio?
In this model it changes output direction, not ratio magnitude. The center-distance card still describes the original gear-pair formula; it is not a complete idler shaft-layout dimension.
Is the torque ratio the same as the reduction ratio?
Define i as input speed divided by output speed. Without losses, output torque divided by input torque equals i. The displayed torque ratio also includes the assumed efficiency.
What does negative planetary output speed mean?
Rotation opposite to the input. Ring-fixed and carrier-fixed modes use different output members, so check member roles and direction as well as ratio magnitude.
Does the tool predict strength and actual efficiency?
No. Efficiency is not derived from load, lubrication or materials. Compound and planetary dimensions also use a fixed module of 2mm. Strength and durability require a separate assessment.
