CALCULATOR · INSTANT · FREE

Gear Ratio CalculatorGEAR RATIO

Enter driver and driven tooth counts for 1–3 gear stages plus input speed and torque to get each stage ratio, the total ratio, output speed, output torque and rotation direction (98% efficiency per stage by default).

Stages1–3
Efficiencyη 0.98 / stage
Outputsrpm · torque · centre distance

RESULT

Live

Total gear ratioi

9.0000: 1

Reduction train: speed drops to 1/9.000 and torque rises about 9.000× (before losses).

GEAR TRAIN · 2 STAGES

Details

Stage 1 ratio (15→45)i1: 3.0000
Stage 2 ratio (12→36)i2: 3.0000
Output speedn out: 333.33rpm
Output torque (incl. losses)T out: 4.322N·m
Overall efficiencyη: 96.04%
Output rotationdir: Same as input
Stage 1 centre distance (module m)a1: 30.00mm
Stage 2 centre distance (module m)a2: 24.00mm

Open in 3D generator

Opens the generator pre-filled with these values, ready to download STEP / STL.

INPUTS

Inputs

Quick picks

Number of stages

Compound train: each stage's driven gear shares a shaft with the next stage's driver.

Stage 1 driver teeth z16–300

Gear on the motor (input) shaft.

Stage 1 driven teeth z26–300

Stage 2 driver teeth z36–300

On the same shaft as z2.

Stage 2 driven teeth z46–300

Input speed0–100000 rpm

rpm

Speed of the motor or input shaft.

Input torque0–100000 N·m

N·m

Torque on the input shaft, used to estimate output torque.

Efficiency per stage50–100 %

Ground steel spur gears ≈ 98–99%; 3D-printed plastic gears ≈ 90–95%.

Module m0.1–20 mm

Only used for stage centre distances and the generator links; it does not change the ratio.

HOW-TO

How to use the Gear Ratio Calculator

1Choose the number of stages (1–3).
2Enter the driver and driven tooth counts for every stage.
3Enter motor speed and torque, and adjust the per-stage efficiency for your gear material.
4Enter the module to also get the centre distance of each stage.
5Use the “Generate gear” links to open the spur-gear generator with these teeth and module and download STEP / STL.

Worked example (default inputs)

Item	Value
Number of stages	2 stages
Stage 1 driver teeth z1	15
Stage 1 driven teeth z2	45
Stage 2 driver teeth z3	12
Stage 2 driven teeth z4	36
Input speed	3000 rpm
Input torque	0.5 N·m
Efficiency per stage	98 %
Module m	1 mm
Total gear ratio(i)	9.0000 : 1
Stage 1 ratio (15→45)(i1)	3.0000
Stage 2 ratio (12→36)(i2)	3.0000
Output speed(n out)	333.33 rpm
Output torque (incl. losses)(T out)	4.322 N·m
Overall efficiency(η)	96.04 %
Output rotation(dir)	Same as input
Stage 1 centre distance (module m)(a1)	30.00 mm
Stage 2 centre distance (module m)(a2)	24.00 mm

Compound gear trains and ratio

The most common multi-stage reducer is a compound train: the large gear of stage one and the small gear of stage two are fixed to the same intermediate shaft, so the total ratio is the product of the stage ratios. Small gears can therefore achieve large reductions — three stages of 1:4 give 1:64. Keep stage ratios similar and increase the module towards the output, because torque grows at every stage and the low-speed teeth need to be stronger.

Speed, torque and efficiency

In an ideal train power is conserved: speed divided by i, torque multiplied by i. Real meshes lose about 1–2% each for precision metal gears and 5–10% for printed or dry plastic gears. When sizing a motor, take the output torque including losses and apply a safety factor of 1.5–2. To make the gears, follow the links under the result to the spur-gear generator, or send the parts to Orinovate for printing in wear-resistant materials such as nylon (MJF/SLS).

Formulas

i_k = z_driven / z_driver (per stage)
i = i1 × i2 × i3
n_out = n_in / i
η_total = η^stages
T_out = T_in × i × η_total
a_k = m × (z_driver + z_driven) / 2

Results are for design reference only; confirm against supplier catalogues and the applicable standards before manufacturing.

FAQ

How is gear ratio calculated?

For one stage, i = driven teeth ÷ driver teeth. For a compound train the total ratio is the product of the stage ratios, e.g. 45/15 × 36/12 = 3 × 3 = 9.

Why is output torque less than input torque × ratio?

Every mesh loses some power to friction. The tool applies the per-stage efficiency η: overall efficiency = η^stages and output torque = input torque × ratio × overall efficiency.

Which way does the output shaft turn?

Two external gears turn in opposite directions, so an odd number of stages reverses the rotation and an even number keeps it. An idler gear reverses it again without changing the ratio.

What is the maximum practical ratio for one stage?

Keep a single spur stage below roughly 1:6 to 1:8. Larger ratios force a pinion with too few teeth (undercut) or a very large wheel. Use more stages, a planetary set or a worm drive instead.

What efficiency should I use for 3D-printed gears?

PLA or PETG gears have rough flanks and backlash; 90–95% per stage is realistic. Grease, nylon or POM improve efficiency and wear life.

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Standards

η 0.98 / stage
ISO 54 module