Gear ratio calculator: speed and torque after every stage, startup and heat
Set a motor and the stages of the drive and get the gear ratio, speed, torque, power and loss after each stage, then the startup torque and whether the housing can shed the heat. The calculation runs in your browser.
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- 5 kindsof stage in one chain
- Startuptorque from the load inertia
- 5 profilesbelts from GT2 to HTD 8M
- 3 facesNEMA 17, 23 and 34
What a gear ratio is
This gear ratio torque calculator from EduFacturing is a free online tool that works out speed, torque, power and loss after each stage of a drive between a motor and a load. There are five kinds of stage: gear pair, toothed belt, chain, worm and planetary.
Besides steady running it shows the startup torque from the load inertia, whether the housing can shed the lost heat, how a belt closes and how many steps per millimetre a stepper gives.
Gear ratio calculator: speed, torque, power and loss
Calculates gear ratio and torque stage by stage
For each stage: i, efficiency, speed, torque, power and loss. The reverse problem returns the motor for a set torque and speed at the output.
Checks the startup and the motor
The load inertia is reflected to the motor and gives a startup torque. Derating and starting current follow IEC 60034-1, NEMA MG-1 and IEC 60034-17.
Measures belt, planetary and worm stages
Belt: diameters, standard length, centre distance, meshing teeth. Planetary: ring gear and assembly. Worm: whether it self-locks.
Works out heat and steps per millimetre
Housing temperature and the area needed. Steps per millimetre, smallest step and top speed.
When to use a gear ratio calculator for a drive
A drive that is right on paper can still fail to start, fail to assemble or overheat.
Choosing a motor
For 90 N·m at 30 min⁻¹ through 30:1 at 0.9 efficiency, the answer is a motor of 3.33 N·m at 900 min⁻¹.
3D printer and CNC
How many steps per millimetre a 20-tooth GT2 belt gives, and whether the driver reaches the speed you want.
Mounting the drive
NEMA 17, 23 and 34 faces and bearing fits from the EDi Brain rules.
How to calculate gear ratio and torque
Each stage is a multiplication by i and by efficiency; the rest follows from the torque and speed.
Stage and chain
i = output/input, the speed is n/i, the torque M·i·η. The total i and η are products: three stages at 0.90 give 0.73. A warning appears above i = 8 in a gear pair and above 5 in a belt.
Startup
The load inertia is reflected to the motor: J/(i²·η). The total inertia times the angular acceleration is added to the running torque. A load to motor ratio above 10 is flagged unstable.
Geometry
A belt has a whole number of teeth, so the centre distance is solved for the standard length; below 6 meshing teeth it skips. The ring gear of a planetary stage follows from the teeth.
Heat and motor
The loss leaves through the housing. The nameplate power needed is the shaft power divided by the strictest of three derating factors.
| Applies to | Formula | Meaning |
|---|---|---|
| Stage and power | i = z₂/z₁; M₂ = M₁·i·η; P = M·2πn/60 | n in min⁻¹, M in N·m; a worm takes its starts as z₁ |
| Startup | M_start = M_run + J_total·α; J_r = J/(i²·η) | α = 2πn/(60·t); t is the time to accelerate |
| Planetary stage | z_r = z_s + 2·z_p; i = 1 + z_r/z_s | with the ring fixed; (z_s + z_r) divides by the number of planets |
| Worm stage | self-locks when γ < arctan μ; η = tan γ / tan(γ + φ) | tan γ = starts·module / worm Ø; φ = arctan μ |
| Housing heat | ΔT = P_loss / (h·A) | h is 12 to 15 W/m²K in still air, 40 to 80 with a fan |
Derating that follows the standards
Derating comes from the standards
Above 1000 m and above 40 °C the tool applies a flat 0.9 (the core has about 1% per 100 m above 1000 m), and 0.85 for an inverter under NEMA MG-1 Part 31 and IEC 60034-17; the strictest applies.
It does not check tooth strength, shafts or bearing load capacity. The efficiencies are selectable typical values, the heat balance is for steady state, and backlash and positioning error are not counted.
For a stepper the speed ceiling is the driver's, and the motor's torque and speed curve is not calculated. Self-locking is a guide: under vibration a brake is still fitted.
Questions about gear ratio and torque
How to calculate torque from gear ratio?
i = z₂/z₁, and the torque is M₂ = M₁·i·η. With several stages the total i and efficiency are products: three stages at 0.90 give 0.73. With the defaults, i is 6, the total efficiency is 93.1% and the output is 11.2 N·m at 242 min⁻¹, with 21 W lost.
Why does startup need more than running?
A 5 kg disc of 80 mm radius (J = 0.016 kg·m²) feels like 4.8·10⁻⁴ kg·m² through i = 6 at a total efficiency of 93.1%. With a motor of J = 0.0002 kg·m² accelerating to 1450 min⁻¹ in 0.5 s, startup needs 2.21 N·m against 2 N·m running.
Are all worm gears self locking?
No. A worm self-locks when γ is below arctan μ. A worm with 1 start, module 2 mm, Ø28 mm and μ = 0.1: γ = 4.1°, φ = 5.7°, it self-locks, but forward efficiency is 41%. With 2 starts γ is 8.1° and it does not. Within 0.5° of the boundary the tool says borderline.
Why does a planetary stage sometimes not assemble?
The ring is z_s + 2·z_p, and (z_s + z_r) must divide by the number of planets. With a 24-tooth sun and an 18-tooth planet the ring is 60 and the sum 84 divides by 2, 3, 4 and 6, but not 5.
How many steps per millimetre does a stepper give?
Full steps per turn times microsteps, divided by travel per turn. 200 steps with 16 microsteps and a 20-tooth GT2 pulley give 80 steps/mm, an 8 mm screw gives 400, a 2 mm screw gives 1600. The speed ceiling is the driver's, not the motor's.
Is the gear ratio calculator free, and do I need an account?
Yes, it is free. Without an account it opens 3 times a day. A free account removes the limit.
The gear ratio calculators is free. Pro opens the rest
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