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Gear Tooth Span Calculator - Span Over Teeth Measurement

Gear Span Measurement Calculator ISO 1328 / ISO 21771
Important Notice: This calculator provides approximate results based on simplified ISO formulas. For critical applications, verify results with official ISO standards and specialized software. The tolerance calculations are simplified and may differ from exact ISO 1328-1:2013 values.
Basic Parameters
From 0.1 to 100 mm
From 6 to 1000
Profile Shift Parameters
From -1 to 1
From -0.5 to 0.5
Accuracy Parameters (ISO 1328)
Reverse Calculation
Measurement Settings
0 = flat anvils
Calculation Results
Calculation updates automatically when parameters change
-
Span measurement, mm
Number of teeth spanned: -
Inspection dimension:
-
- -
Upper deviation EsW: -
Lower deviation EiW: -
Tolerance TW: -
Measuring instrument: -

Calculation Details:

Calculation based on ISO 21771:2007 (simplified formulas)
Formula for spur gears:
W = m·cos(α)·[π·(k-0.5) + z·inv(α) + 2·x·tan(α) - z·Δy·tan(α)/cos(α)]
Formula for helical gears:
W = m·cos(α)·[π·(k-0.5) + z·inv(αt) + 2·x·tan(α) - z·Δy·tan(α)/cos(α)]
where αt - transverse pressure angle
tan(αt) = tan(α) / cos(β)
Number of teeth k in span:
k = z·α/(180°) + 0.5 (simplified ISO method)
Round to nearest integer
Note: This is a simplified formula. Exact ISO 21771 formula includes profile shift correction.
Measurement scheme:
W
ISO 1328 Tolerance System:

• Accuracy grades: 0 (highest) to 12 (lowest)
• Tolerance formula: TW = fpt × √(0.25 + 0.75×k)
• fpt depends on module and accuracy grade
• Tolerance positions: JS (symmetric), K/M (minus), H/G (plus)

ISO Standards:

• ISO 1328-1:2013: Accuracy system
• ISO 21771:2007: Span measurement
• ISO 1122-1: Vocabulary
• ISO 53: Cylindrical gears for general use

Calculation Accuracy:

Note: This calculator uses simplified formulas that provide approximate results:
• The k calculation is simplified (exact ISO formula is more complex)
• Tolerance values are approximated (exact ISO 1328-1 uses diameter-dependent formulas)
• Ball/pin measurement correction is simplified
• For production use, verify with official standards or certified software

Recommendations:

• For module m > 1 mm use vernier caliper
• For high accuracy use gear tooth vernier or CMM
• Measure at 3-4 positions around circumference
• Consider temperature compensation (20°C reference)
• Profile shift x affects tooth thickness
• For ball/pin measurement: contact should be on involute

⚠️ Important: For production or quality control, always verify calculations with:
• Official ISO standards documentation
• Certified gear measurement software
• Calibrated measurement equipment

Gear Tooth Span Measurement Table

Number of Teeth (z) Teeth in Span (k) Span Measurement (W/m)* Application
10-14 2 4.524 - 7.471 Small pinions
15-23 3 7.627 - 10.574 Standard pinions
24-32 4 10.730 - 13.677 Medium gears
33-41 5 13.833 - 16.780 Medium gears
42-50 6 16.936 - 19.883 Large gears
51-59 7 20.039 - 22.986 Large gears

* Values shown for module m=1 and pressure angle α=20°. Multiply by your gear's module for actual span measurement.

What is Gear Span Measurement

Gear span measurement (also known as span over teeth or base tangent length) is the distance between two parallel planes tangent to opposite tooth flanks. This gear tooth span measurement is one of the primary methods for quality control in gear manufacturing.

The measurement of span over teeth allows manufacturers to verify tooth thickness and detect deviations from nominal dimensions without measuring the complete tooth profile. This makes span measurement calculation an essential tool in gear inspection.

Gear Span Measurement Calculation

The gear span calculation is performed using the following formula:

W = m · cos(α) · [π·(k-0.5) + z·inv(α) + 2·x·tan(α)]
W
Span measurement over teeth (mm or inches)
m
Module of the gear (mm)
α
Pressure angle (typically 20°)
k
Number of teeth in span measurement
z
Total number of gear teeth
x
Profile shift coefficient

Gear Span Calculator Example

Given Data:

Module m = 2 mm, Number of teeth z = 20, Pressure angle α = 20°, Profile shift x = 0

1 Determine number of teeth k in span: k = z·α/180° + 0.5 = 20·20/180 + 0.5 ≈ 3
2 Calculate involute function: inv(20°) = tan(20°) - 20°·π/180° = 0.01490
3 Apply the span measurement formula:
W = 2 · cos(20°) · [π·(3-0.5) + 20·0.01490 + 0] = 2 · 0.9397 · 8.154 = 15.326 mm

Therefore, the gear tooth span measurement is 15.326 mm. This span measurement calculation provides the exact dimension needed for quality control inspection.

How to Measure Gear Span

To measure span over gear teeth, the following instruments are commonly used:

  • Vernier caliper - for gears with module larger than 1 mm
  • Gear tooth vernier - specialized instrument for precise measurements
  • Micrometer with flat anvils - for small module gears
  • Coordinate measuring machine (CMM) - for high-precision inspection

When measuring gear span, place the measuring instrument's anvils on opposite tooth flanks, spanning the calculated number of teeth k. Take measurements at several positions around the gear circumference to ensure accuracy.

Span Measurement Calculator Online

Our gear span measurement calculator provides instant calculation of span over teeth for various gear types, including spur and helical gears. The span calculator automatically updates results as you modify parameters, making it ideal for quick verification during design or inspection processes.

This online gear span calculator follows ISO standards and can be used for preliminary calculations in gear design and quality control. Whether you need to calculate span measurement for a new design or verify existing gears, this tool provides accurate results based on standard formulas.

ISO Standards for Gear Span Measurement

Gear tooth span calculation is governed by international standards that ensure consistency in measurement and manufacturing:

  • ISO 21771:2007 - Gears - Cylindrical involute gears and gear pairs - Concepts and geometry
  • ISO 1328-1:2013 - Cylindrical gears - ISO system of flank tolerance classification
  • DIN 3960 - Definitions, parameters and equations for involute cylindrical gears
  • AGMA 2000-A88 - Gear Classification and Inspection Handbook

These standards provide comprehensive gear span tables and formulas for accurate span measurement calculation across different gear specifications and quality grades.

Disclaimer

This gear span measurement calculator is provided "as is" and is intended for informational and educational purposes only. The author assumes no responsibility for any direct or indirect losses arising from the use of this calculator.

Calculations are approximate and based on simplified formulas. For production purposes and quality control, always refer to official ISO standards and certified software. Always verify calculation results using alternative methods and professional judgment.

References and Literature:
  • 1. ISO 21771:2007 - Gears - Cylindrical involute gears and gear pairs
  • 2. ISO 1328-1:2013 - Cylindrical gears - ISO system of flank tolerance classification
  • 3. AGMA 2000-A88 - Gear Classification and Inspection Handbook
  • 4. Dudley's Handbook of Practical Gear Design and Manufacture
  • 5. Machinery's Handbook - Industrial Press
  • 6. DIN 3960 - Definitions, parameters and equations for involute cylindrical gears
  • 7. Radzevich, S.P. - Gear Cutting Tools: Fundamentals of Design and Computation

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