Gear calculators and data
Calculators for gear dimensions, mesh and tooth thickness, plus module and accuracy-grade tables. Formulas and values come from gear makers’ published technical data and public information on the standards, with numbered sources.
Module and teeth
give you every
gear dimension!
Spur gears
From module, number of teeth and profile shift coefficients: reference, tip, root and base diameters, working pressure angle, center distance and transverse contact ratio.
⫽Helical gears
From normal module, helix angle, teeth and profile shift: transverse module and pressure angle, diameters, center distance and contact ratios (transverse and overlap).
↔Span measurement
From module, pressure angle, teeth and profile shift (plus helix angle for helical gears): the number of teeth to span and the span measurement W. For checking tooth thickness.
◎Over pins
The dimension M measured over pins (balls for helical gears) placed in the tooth spaces. Leave the pin diameter blank to use the ideal pin diameter.
▦Gear cutting methods compared
Hobbing, shaping, skiving, shaving, grinding, broaching and more: 10 methods compared for internal and shoulder gears, accuracy and before/after hardening.
⛭Gear cutting tools and conditions
Hobs, pinion cutters, skiving cutters, shaving cutters and broaches; tool materials and coatings; makers’ published cutting examples.
🏭Gear cutting tool makers
Makers of gear cutting tools and gear machines in Japan, Korea, China, Europe and the US: product types, tool materials and coatings.
▦Standard modules (spur and helical gears)
JIS B 1701-2:1999 Cylindrical gears – Involute gear tooth profile – Part 2: Modules (values of 1 and above are the same as ISO 54:1996; values below 1 are specified in a normative annex of this standard). Applies to: Spur and helical gears for general and heavy machinery (for helical gears, the normal module). In mm.[1][2]
| Series I (preferred) | 0.10.20.30.40.50.60.811.251.522.5345681012162025324050 |
|---|---|
| Series II | 0.150.250.350.450.550.70.750.91.1251.3751.752.252.753.54.55.5(6.5)7911141822283645 |
One pitch of the basic rack profile (20° pressure angle) for modules 1 to 6, all at the same scale. Doubling m doubles both the pitch p (= πm) and the tooth depth (= 2.25m); for the same number of teeth the gear diameter (= z × m) doubles too.
- Use series I (first series) wherever possible
- Avoid module 6.5 (series II) as far as possible (shown in parentheses in the table)
- ISO 54:1996 specifies values of the normal module for spur and helical gears (2 pages, reaffirmed in 2022). Modules below 1 are not specified in ISO 54 and are covered by an annex of JIS B 1701-2.[3][2]
Modules for straight bevel gears One source / reference
JIS B 1706-2:1999 Straight bevel gears – Part 2: Modules and diametral pitches (values below 1 in an annex; corresponds to ISO 678)[2]
| Series I | 0.30.40.50.60.811.251.522.53456810 |
|---|---|
| Series II | 0.350.450.550.70.750.91.1251.3751.752.252.753.54.55.5(6.5)79 |
The Kyoiku Gear source lists values up to 10 as an "excerpt". Values above 10 and the DP table have not been checked.
⇄Diametral pitch (DP) and module conversion
Inch gears are specified by diametral pitch (teeth per inch of pitch diameter). m = 25.4 ÷ DP.[2][4][1][5]
| DP | m (mm) | Circular pitch (mm) | Nearest series I module |
|---|---|---|---|
| 2 | 12.7 | 39.898 | 12 |
| 3 | 8.467 | 26.599 | 8 |
| 4 | 6.35 | 19.949 | 6 |
| 5 | 5.08 | 15.959 | 5 |
| 6 | 4.233 | 13.299 | 4 |
| 8 | 3.175 | 9.975 | 3 |
| 10 | 2.54 | 7.98 | 2.5 |
| 12 | 2.117 | 6.65 | 2 |
| 16 | 1.588 | 4.987 | 1.5 |
| 20 | 1.27 | 3.99 | 1.25 |
| 24 | 1.058 | 3.325 | 1 |
| 32 | 0.794 | 2.494 | 0.8 |
| 48 | 0.529 | 1.662 | 0.5 |
Table values are calculated from the formula. DP gears and metric module gears do not mesh even when the values are close (e.g. DP10 is m2.54, not m2.5).
◎Accuracy grades (old and new JIS, ISO)
Tolerance tables for each grade belong to the standards themselves and are not reproduced here. This section sorts out the editions and how the grades are numbered.
| Standard | Grades | Confidence |
|---|---|---|
| JIS B 1702-1:2016 Cylindrical gears – ISO system of flank tolerance classification – Part 1: Definitions and allowable values of deviations relevant to flanks of gear teethCorresponds to: ISO 1328-1:2013 (MOD)1998-03-20 established → reaffirmed 2003, 2008, 2013 → 2016-04-20 revised → 2021-10-20 reaffirmed[6][7][8] | ISO 1328-1:2013 has 11 grades, 1–11 (the larger the number, the larger the tolerance)The number of JIS grades, the notation (handling of N-prefixed grades) and the correspondence of grades with the 1998 edition could not be confirmed in public sources (only the standard itself exists). Not filled in by guesswork. | Agrees in 2+ sources |
| JIS B 1702-1:1998 Cylindrical gears – System of accuracy – Part 1: Definitions and allowable values of deviations relevant to corresponding flanks of gear teethCorresponds to: ISO 1328-1:1995 (revised in 2016; on the ISO side it was also replaced by the 2013 edition)[9][10][2] | 13 grades from grade 0 (highest) to grade 12 (lowest). Written with an N prefix, as in grade N4, to distinguish them from the old standard | Agrees in 2+ sources |
| JIS B 1702-2:1998 Cylindrical gears – System of accuracy – Part 2: Definitions and allowable values of deviations relevant to radial composite deviations and runout information[9][2] | 9 grades from grade 4 (highest) to grade 12 (lowest) | Agrees in 2+ sources |
| Old JIS B 1702-1976 (Accuracy for spur and helical gears; reaffirmed in 1995, withdrawn in 1998)[9][10][2] | 9 grades, 0–8Old JIS classifies helical gears by the transverse module, new JIS by the normal module (convert with mt = mn/cosβ when comparing) | Agrees in 2+ sources |
| JIS B 1704:1978 Accuracy for bevel gears[11] | 9 grades, 0–8. Four items: single, adjacent and cumulative pitch deviation, and tooth space runout (formulas for the tolerances are in bevel_accuracy_jis1704 in formulas.json) | One source / reference |
Old JIS (1976) vs new JIS (1998): rule of thumb
New JIS (1998) accuracy grade ≈ old JIS (1976) accuracy grade + 4 (e.g. old grade 0 ≈ N4, old grade 4 ≈ N8)[10][2][12]
- A detailed correspondence is not possible because the module and reference diameter ranges differ
- The rule does not hold in some ranges, where the number of teeth is relatively small or large
- When a conversion is needed, see JGMA/TR0001 (2000) "Comparison Table of Standard Values between Old and New JIS Gear Accuracy" by the Japan Gear Manufacturers Association (as introduced by KHK; the table itself has not been consulted)
- The correspondence between the 2016 edition (grades 1–11), the 1998 edition (N0–N12) and the old JIS could not be confirmed in public sources and is not recorded
≋Gear deviations (symbols and meaning)
| Symbol | Name | Meaning |
|---|---|---|
| fpt (fp in ISO 1328-1:2013) | Single pitch deviation | The difference between the actual pitch and the theoretical pitch on the pitch circle, for adjacent flanks on the same side (Mitutoyo: the maximum of its absolute value)[9][13][8] |
| fu (fpu) | Adjacent pitch deviation | The maximum absolute value of the difference between two adjacent pitches[13][14][8] |
| Fp | Cumulative pitch deviation (total cumulative pitch deviation) | The total amplitude of the cumulative pitch deviation curve over all flanks (the maximum minus the minimum of the difference between the sum of actual pitches from a reference tooth to any tooth and the theoretical value)[9][13][8] |
| Fα | Total profile deviation | Within the profile evaluation range, the distance between the two design profiles that enclose the actual profile[9][13][8] |
| ffα / fHα | Profile form deviation / profile slope deviation | ffα: the width of the actual profile enclosed between lines parallel to the mean line. fHα: the distance, in the design profile direction, between the points where the mean line meets the start and end of the evaluation range[13][8] |
| Fβ | Total helix deviation | Within the helix evaluation range, the distance between the two design helix lines that enclose the actual helix. If large, the contact concentrates at the ends of the face width, so crowning and end relief are used as countermeasures[9][13][8] |
| ffβ / fHβ | Helix form deviation / helix slope deviation | The same idea as ffα and fHα for the profile, applied to the helix[13][8] |
| Fr | Tooth space runout | The difference between the maximum and minimum radial positions when a probe (ball or pin) is inserted in turn into every tooth space. Includes eccentricity. Strongly affected by runout of the fixture. Moved back to Part 1 in ISO 1328-1:2013[9][13][8] |
| Fi″ / fi″ | Double flank composite deviation (total / tooth-to-tooth) | The difference between the maximum and minimum center distance when the gear under test is meshed in double-flank contact with a master gear and turned one revolution (specified in JIS B 1702-2 / ISO 1328-2)[9][2][8] |
| Fis / fis | Single flank composite deviation (total / tooth-to-tooth) | An item in the terms table of ISO 1328-1:2013 (the text of the definition has not been checked)[8]One source / reference |
| Fpk / FpSk | Pitch deviation over a sector (k pitches) | The cumulative pitch deviation over a sector of k pitches (terms table of ISO 1328-1:2013; the text of the definition has not been checked)[8]One source / reference |
📚Sources
- Kohara Gear Industry (KHK) — Gear technical data (web version) 3.1 Gear tooth profile and dimensions (basic rack, standard module values)
- Kyoiku Gear Industry (KG) — Technical data (PDF, 176 pages: gear basics, profile shift, contact ratio, tooth thickness measurement, accuracy, calculations for various gears)
- ISO — ISO 54:1996 Cylindrical gears for general engineering and for heavy engineering — Modules (standard introduction page)
- Kohara Gear Industry (KHK) — Formulas, units and other data 7 Gear pitch comparison table (m, CP, DP)
- Tokyo University of Science (Noda) — Design and Drafting, Chapter 8: Gears (lecture material s2-2.pdf)
- Japanese Standards Association (JSA) — JIS B 1702-1:2016 standard introduction page (publication date, reaffirmation date, corresponding international standard, history)
- ISO — ISO 1328-1:2013 Cylindrical gears — ISO system of flank tolerance classification — Part 1 (standard introduction page: overview and status)
- iTeh Standards (preview page of an official distribution site for ISO standards) — ISO 1328-1:2013 preview (foreword, introduction, scope, terms table)
- Kohara Gear Industry (KHK) — Gear technical data (web version) 7.1 Accuracy of spur and helical gears
- Kohara Gear Industry (KHK) — JIS standards related to gears 1. Accuracy of spur and helical gears (excerpt of JIS B 1702-1/-2:1998, comparison of old and new)
- Kohara Gear Industry (KHK) — Gear technical data (web version) 7.2 Accuracy of bevel gears
- Kyoiku Gear Industry (KG) — General catalog reference material (KG4001WEB-10, PDF)
- Mitutoyo — Gear terms and definitions of deviations
- Kohara Gear Industry (KHK) — Gear technical data (web version) 1.2 Gear symbols and terms