Nominal relations · controlled inputs · no strength verdict

Nominal Involute-Spline Reference Geometry Worksheet

Calculate three preliminary involute reference quantities from a documented metric module, integer tooth count and pressure angle.

d = mzPoint or commaNo design presets

Not a complete ISO 4156 spline calculator. This worksheet does not determine limiting diameters, tooth thickness, effective or actual tolerances, fit, fundamental deviation, inspection dimensions, root/tip form, load capacity or compliance. Use the current licensed ISO 4156 parts, the controlled drawing and a qualified spline designer for those decisions.

Documented inputs and traceability

Metric module m (mm) positive controlled nominal value

Number of teeth z positive integer from the controlled drawing

Documented pressure angle α (degrees) strictly between 0° and 90°; no allowed ISO set is inferred

Calculation / drawing record ID

Internal/external members and spline configuration

Module source, drawing and revision

Tooth-count source and revision

Pressure-angle source and revision

Applicable standard part, edition and licensed clause/table

Fit, fundamental deviation, tolerance class and centring basis

Inspection dimensions, gauges and acceptance plan

Source uncertainty and reporting precision

Responsible designer / reviewer

Review date

Notes and exclusions Optional: profile shift, manufacturing process, root form, material, lubrication, load spectrum and mating-member controls

The module, tooth count and pressure angle were copied from one controlled, mutually compatible spline definition; the worksheet must not choose them.
The application is a straight cylindrical involute spline, and the applicable ISO 4156 part/edition, member type, fit and tolerance data are controlled outside this arithmetic.
No root/tip diameter, tooth thickness, backlash, tolerance, gauge dimension, contact stress, torque capacity or safety factor will be inferred from these three relations.
Manufacturing and acceptance will follow the controlled drawing, licensed standard, inspection plan and qualified design review—not the displayed nominal quantities alone.

Preliminary reference quantities

Nominal reference diameter d

—

Base-circle diameter dᵦ

—

Circular pitch p

—

Formula, units and classification

d = m · z [mm]
d_b = d · cos(α) [mm], with α converted from degrees to radians for cos()
p = π · m [mm per tooth]

Σύμβολο	Quantity and unit	Όριο
m	documented metric module, mm	controlled nominal input; no series or preferred value selected
z	documented number of teeth, integer	no ISO range, undercut or mating compatibility inferred
α	documented pressure angle, degrees	no allowed ISO angle set or tolerance inferred
d	nominal reference diameter, mm	not a limiting tip, root, form, effective or inspection diameter
d_b	base-circle diameter, mm	generic involute reference relation, not an inspection result
p	circular pitch, mm per tooth	nominal reference relation only

These are general involute-geometry relations, not a verbatim ISO 4156 tolerance table and not a load-capacity method. All calculated lengths scale linearly with module; only the base-circle result depends on the supplied pressure angle.

Model boundary and removed unsupported outputs

No false complete ISO geometry. The former page accepted a pressure angle but ignored it in every result while advertising “ISO 4156 geometry.” It now affects the base-circle relation, and the page explicitly excludes the standard’s controlled limiting/tolerance/fit data.
No universal root diameter. The former d − 2.5m shortcut was presented as a spline root diameter. Actual internal/external spline form and limits depend on the specified system, coefficients, deviations, tolerances and manufacturing/inspection requirements.
No invented capacity model. The former bearing-pressure and torque-capacity outputs assumed effective height h = 0.9m, load factor K = 0.75 and uniform sharing by every tooth without a controlled source.
No “OK” safety verdict. Strength needs material properties, member geometry, root stress, wear/contact criteria, load spectrum, misalignment, lubrication, manufacturing deviations and an approved method.
No generic design advice. Universal K values, engagement-length ratios, hardness, “stronger angle” and spline-versus-key claims were removed because their validity depends on the application and source.
No hidden state. Defaults, presets, auto-calculation, local history, clipboard output, dynamic FAQ HTML and external KaTeX were removed.

Current ISO 4156 series status

Μέρος	Publicly verified scope/status	Evidence
ISO 4156-1:2021, Edition 2	Generalities for design/manufacture of straight, non-helical, side-fitting cylindrical involute splines; limiting dimensions, tolerances and deviations are defined by formulas/tables. Published; confirmed in 2026.	Official ISO card
ISO 4156-2:2021, Edition 2	Geometry and inspection dimensions; tables for external fundamental deviation h have a stated scope, while other deviations require formulas from Parts 1 and 3. Published and under review.	Official ISO card
ISO 4156-3:2021, Edition 2	Inspection data, guidance and requirements. Published and under review; corrected English and French versions issued December 2025.	Official ISO card

Accessed: 15 July 2026. The former undated “ISO 4156” reference omitted the three current parts and their 2021 editions. Exact formulas, tables, limits, permitted parameter sets, deviations, tolerances, fits and inspection requirements remain NEEDS_LICENSED_SOURCE.

Open formula evidence

Claim	Ταξινόμηση	Evidence
Metric module m = d/z, base-circle diameter d_b = d cos α and circular pitch p = πm.	University mechanical-engineering teaching material; page 3 visually inspected	Fairfield University ME 312, Gears, p. 3
Reference diameter d = zm and base diameter d_b = d cos α for standard involute gear geometry.	Gear manufacturer technical reference; corroborating public source	KHK Gear Technical Reference

These public sources support only the displayed generic involute relations. They do not substitute for licensed ISO 4156 spline dimensions, tolerances, fits or inspection rules.

Reference checks

For m = 2 mm, z = 20 and α = 30°, d = 40 mm, d_b = 34.641016151… mm and p = 6.283185307… mm. For m = 1.5 mm, z = 30 and α = 45°, d = 45 mm, d_b = 31.819805153… mm and p = 4.712388980… mm.

Questions

Can I manufacture a spline from these three outputs?

No. A manufacturing definition needs the applicable ISO 4156 part/edition, member types, fit, deviations, tolerance class, tooth/root form, inspection dimensions and drawing controls.

Why is torque capacity absent?

ISO 4156’s public scope concerns geometry, tolerances, fits and inspection. A defensible strength calculation needs a separately validated load-capacity method and many more controlled inputs.

Why is root diameter absent?

A single d − 2.5m rule is not a universal ISO 4156 spline root-diameter calculation. Use the applicable licensed tables/formulas for the exact internal/external member and specification.