Linear Speed Calculator
Parameters
Enter your gear and motor specifications below. The results will update automatically.
Calculation Breakdown
Practical Considerations
These calculations assume ideal conditions. For real-world applications, also account for:
- System inertia
- Acceleration/deceleration profiles
- Torque and load dynamics
- System efficiency and power losses
For critical designs, consult your vendor or use specialized motion control software for a full analysis.
Related Standards- DIN 780 / ISO 54 — Standard module series for cylindrical gears
- DIN 3960 / ISO 21771 — Involute gear geometry: definitions, parameters, formulas for reference diameter d = m · z
- DIN 3990 / ISO 6336 — Calculation of load capacity of spur and helical gears (bending, pitting, scuffing)
- DIN 3961–3964 — Tolerances for cylindrical gear teeth (quality grades, pitch, profile, lead deviations)
- ISO 1328 — Cylindrical gears: ISO system of flank tolerance classification
- DIN 3993 — Geometrical design of cylindrical internal gear pairs
- DIN 3967 — System of gear fits: backlash, tooth thickness allowances
Angle Conversion Guide
Gear catalogs often specify helix angles in degrees, minutes, seconds (DMS) format. This calculator requires decimal degrees.
Formula:Decimal° = Degrees + (Minutes / 60) + (Seconds / 3600)
Example: 19° 31' 42"
19 + (31 / 60) + (42 / 3600)
= 19 + 0.5167 + 0.0117 ≈ 19.53°
| DMS | Decimal | Usage |
|---|---|---|
| 8° 7' 48" | 8.13° | Light-duty gearboxes |
| 14° 0' 0" | 14.00° | Standard helical gears |
| 19° 31' 42" | 19.53° | SEW / Flender gearboxes |
| 20° 0' 0" | 20.00° | Common industrial standard |
| 23° 0' 0" | 23.00° | Automotive transmissions |
| 30° 0' 0" | 30.00° | High overlap, quiet operation |
Typical range for helical gears is β = 8°–30°. Higher angles increase axial thrust but improve contact ratio and reduce noise.
Linear Speed from Motor RPM
A rotating pinion or gear rack converts rotation into straight-line motion: the pitch line of the gear moves forward by the reference diameter times pi for every revolution. So the linear speed of a rack drive, conveyor drum, or pinion-on-rack axis is simply v = n × π × d, where n is the output speed in revolutions per minute and d is the pitch diameter in metres - giving the speed directly in m/min.
The Formula Step by Step
The calculator starts from the module m and tooth count Z to derive the reference diameter d = m × Z / cos(β), where the helix angle β widens the effective diameter for helical gears. It then divides the motor RPM by the reducer ratio i to get the pinion speed n₂, and finally computes v₂ = n₂ × π × d. Every stage - reference diameter, tip diameter, pinion RPM, and linear speed - is printed in the Calculation Breakdown box so you can verify the numbers for your drawing or report.
Why the Reducer and Helix Angle Matter
The reducer ratio scales the motor speed down before it reaches the pinion, so the linear speed at the rack is i times lower than it would be on a direct drive - the trade-off that lets a small high-speed motor move a heavy load slowly. The helix angle does the opposite effect on the geometry: it enlarges the pitch diameter at the same module and tooth count, which raises the linear travel per revolution while also improving quietness and tooth overlap. Both parameters are standard inputs on any gearbox datasheet, so they are built into the calculator.
Frequently Asked Questions
What does the Linear Speed Calculator do?
It calculates output linear speed in m/min from gear tooth count, module and motor RPM for conveyors, gear trains and gearboxes.
How do I use it?
Enter number of gear teeth (Z), gear module (m) and motor RPM. The calculator returns the output linear speed in m/min.
Is it free?
Yes. This Kod5 tool runs in the browser, requires no installation, and is free to use.