DIN 5480 Spline Calculator: Dimensions & Measurement over Pins

How Is a DIN 5480 Spline Designated?

DIN 5480 builds every spline around a round reference diameter dB (the nominal size of the shaft), a module from the preferred series and a 30° pressure angle. A full designation reads DIN 5480 – W 30 × 2 × 30 × 14 × 8f: W for a shaft (N for a hub), 30 mm reference diameter, module 2, 30° flank angle, 14 teeth and tolerance class 8f. Because the teeth have to fit a round number, the standard applies a profile shift instead of changing the pitch: x₁·m = (dB − m·z − 1.1·m) / 2. For W 30 × 2 × 30 × 14 that gives x₁ = -0.050; for W 25 × 1.25 × 30 × 18 it is +0.450, which matches the values printed in the standard's size tables.

The international counterpart is ISO 4156-1 (metric-module involute splines), which uses the same involute geometry with flat-root and fillet-root options and 30°, 37.5° and 45° pressure angles; DIN 5480 keeps the 30° flank and the round reference diameter, which is why European gearbox and pump drawings usually call it out. When a drawing gives only "W 40 × 2 × 30 × 18", the reference diameter, module and tooth count are enough to rebuild every dimension below, because the standard fixes the rest. All dimensions are in millimetres, the SI unit used throughout the standard (NIST SI units).

What Are the Main Diameters?

• Pitch diameter d = m·z and base diameter dbase = d·cos 30° — the involute starts at the base circle.
• Shaft tip diameter da1 = dB − 0.2·m — slightly under the reference diameter so the shaft clears the hub root.
• Hub tip diameter da2 = dB − 2·m and hub root diameter equal to dB.
• Tooth thickness at the pitch circle s = m·(π/2 + 2·x₁·tan 30°), which the hub's space width matches before tolerances.

How Do You Measure a Spline over Pins?

Tooth thickness is checked indirectly with two hardened pins (or balls) placed in opposite spaces. The pin center lies on a circle whose pressure angle αM satisfies inv αM = s/d + inv 30° + DM/dbase − π/z for a shaft, where inv α = tan α − α. The calculator solves it with Newton's method and returns M = dbase/cos αM + DM; with an odd number of teeth the pins are not diametrically opposite, so it multiplies by cos(90°/z). Hubs are measured between pins with the mirror equation. The same method is used for gears in Machinery's Handbook (Industrial Press); online tools such as Kod5 and SplineGen list the dimensions but not the pin measurement you need at the bench.

Which Pin Diameter Should You Use?

Before measuring, clean the spaces and check the pins themselves with a micrometer: a 2 µm error in a pin becomes roughly 4 µm in the measurement over two pins, which is a sizable part of a fine tolerance class. For hardened shafts measure after grinding and at room temperature; our thermal expansion calculator shows how much a warm part grows. The default pins of 1.728·m (shaft) and 1.44·m (hub) touch the flanks near the pitch circle, where the measurement is most sensitive to tooth thickness. Use the nearest pin you actually have and type its diameter; the measurement changes accordingly, but the tooth thickness it represents does not. The values here are basic sizes: the tolerance class (8f, 9g, 9H…) shifts and widens them, so read the allowances from the standard or your drawing. For straight-sided keys see our keyway calculator, for gear sizes the gear module calculator, and for the fit of a shaft in its bore the ISO 286 tolerance calculator.