Is this an ISO gear-rating calculation?

No. It is a transparent fixed-axis kinematic calculation. It does not rate tooth strength, durability, accuracy, backlash or ISO conformity.

When may stage ratios be multiplied?

Only when the entered stages form a sequential compound train and each driven shaft is rigidly connected to the next stage driver shaft.

How is output direction determined?

For the parallel-axis scope used here, each external mesh reverses direction and each internal mesh preserves it; the parity of external meshes therefore determines the output direction relative to the input.

Why is there no default efficiency?

Efficiency depends on the actual gears, bearings, seals, lubricant, speed, load and temperature. Torque is calculated only when a documented total efficiency is supplied.

Fixed-axis compound-train kinematics

Documented Compound Gear-Train Ratio Calculator

Calculate ratio magnitude, speed and rotation direction for a sequential parallel-shaft compound train. Optional power and torque results require a documented total train efficiency; no efficiency is assumed.

i=Π(Zdriven/Zdriver)External reversesNo default efficiency

Gear-train identifier

Configuration provenance

Sequential stages

Input speed (opcional)

Input speed unit (with speed)

Input shaft power (optional, kW)

Documented total efficiency η (0<η≤1)

Efficiency provenance

Estágio	Driver teeth Z₁	Driven teeth Z₂	Parallel-axis mesh
1	Driver teeth	Driven teeth	Mesh type
2	Driver teeth	Driven teeth	Mesh type
3	Driver teeth	Driven teeth	Mesh type
4	Driver teeth	Driven teeth	Mesh type
5	Driver teeth	Driven teeth	Mesh type

Scope boundary: stages must be sequential, fixed-axis, parallel-shaft gear meshes, with each stage’s driven shaft rigidly connected to the next stage’s driver shaft. Do not use this model for planetary/moving-carrier, differential, bevel, worm, crossed-axis, belt or chain arrangements. It does not check geometry, interference, strength, rating, heat, lubrication, backlash or accuracy.

Kinematic result

Total ratio magnitude i=|nin/nout|

—

Output/input speed multiplier

—

Output direction

—

Output speed

Not supplied

Per-stage ratios

—

Input torque

Não calculado

Output power

Não calculado

Output torque

Não calculado

Implemented kinematics

iⱼ=Z₂ⱼ/Z₁ⱼ=|n₁ⱼ/n₂ⱼ|
i=Πiⱼ
|nout/nin|=1/i

Each external mesh reverses rotation; each internal mesh preserves it. Direction is therefore based on the number of external meshes. The product rule applies only to the declared sequential compound arrangement.

Optional power and torque

ωin=2πfin
Tin=Pin/ωin
Pout=ηtotal Pin
ωout=ωin/i
Tout=Pout/ωout=Tin·i·ηtotal

The page never supplies η. Enter a total efficiency documented for the actual operating point; a per-mesh catalogue estimate is not silently exponentiated. Power/torque output is unavailable at zero speed.

Sources and classification

KHK Gear Technical Reference defines reference diameter from tooth count and module and documents gear transmission-ratio relationships. The NASA gear-mesh technical memorandum uses the tooth-count/speed equality for a fixed gear mesh. OpenStax University Physics, section 10.8 gives rotational power P=τω; section 10.1 defines angular speed and RPM conversion.

This is a general kinematic and power-balance calculation, not a formula claimed from ISO. It does not implement ISO 6336 gear load capacity, ISO 1328 accuracy, or a conformity decision.

Why former guidance was removed

The former page assumed 97% efficiency per stage, called broad spur/helical/worm ratio ranges typical, accepted fractional tooth counts and showed opposite rotation for every first mesh. Those statements were not tied to the entered gear geometry, duty or manufacturer data. Defaults and presets also produced an immediate apparently operational result. They were removed.