Splined Shaft Connection Calculator (DIN 5480)
Verify involute splined shaft connections per DIN 5480: from the reference diameter, module, load-carrying length and operating torque follow the number of teeth, mean load-carrying diameter, flank pressure and transmittable torque with a safety factor against the hub, live with every input.
Calculation
R_e and heat treatment follow the selected hub material, R_e for a steel also the outer diameter D_N. For your own values, select “Custom input” as the hub material above.
Results
DIN 5480: z = 24, d_m = 48 mm, h_tr = 0.9 mm
- Equivalent torque T_eq = K_A · T
- 1,000 Nm
- Transmittable torque T_allow
- 3,541.1 Nm
- Mean load-carrying diameter d_m
- 48 mm
- Load-carrying tooth height h_tr
- 0.9 mm
- Applied hub yield strength R_e
- 370 N/mm²
- Strength step
- over 40 up to 100 mm (D_N = 80 mm)
Simplified flank pressure verification per Niemann/Roloff-Matek, not an exact calculation per DIN 5480-1 (no tolerance class, no friction or wear analysis).
Root load capacity and the notch effect of the spline on the shaft are not covered here - use the DIN 743 shaft calculator for that.
DIN 5480 describes the involute spline; the older straight-sided spline per DIN ISO 14 is a separate connection type with a higher notch effect.
Cross-section: splined shaft profile with hub
Calculation in your browser, inputs go to our server only when you export or save.
Formulas and fundamentals
Geometry per DIN 5480
The splined shaft connection per DIN 5480 is an involute spline with many, evenly distributed teeth: the number of teeth follows from the reference diameter d_B and the module m using the DIN 5480 convention. If the result is not an integer, it is conservatively rounded up with a note - the chosen combination of d_B and m then does not correspond to a regular DIN 5480 size.
The mean load-carrying diameter and the load-carrying tooth height (guideline value for involute splines) follow as:
Equivalent torque and flank pressure
The operating torque is increased by the application factor to the equivalent torque and converted via the mean load-carrying diameter into a circumferential force, which is distributed over the load-carrying length, all z teeth and the load-sharing factor φ:
The load-sharing factor φ (default 0.75, range 0.5 to 0.8) accounts for the fact that manufacturing tolerances prevent a perfectly even load distribution across all teeth - similar to the load-sharing factor of a second parallel key.
Allowable flank pressure and safety factor
The flank pressure is allowable up to a value that depends on the hub's yield strength, its heat treatment and the required safety factor:
Here f_H is the hardness factor: f_H = 1.0 for quenched-and-tempered hubs, f_H = 1.5 for case-hardened hubs, which withstand a considerably higher flank pressure thanks to the hard surface layer. The safety factor S_F defaults to 1.3. The utilization is:
For a steel from the list, the calculator applies the minimum yield strength of the product standard for the hub outer diameter D_N. It falls with the dimension, for quenched-and-tempered C45 from 490 N/mm² up to 16 mm to 370 N/mm² over 40 up to 100 mm. Above the last documented step it continues with that step and flags it; without D_N it applies the smallest documented yield strength of the grade. D_N itself does not enter the pressure.
Transmittable torque
Rearranging the pressure formula for torque gives the nominal torque transmittable at the given geometry and safety factor - directly comparable to the operating torque T:
Worked example
Given: splined shaft connection per DIN 5480 with reference diameter d_B = 50 mm and module m = 2 mm (giving z = 24), load-carrying length l_tr = 40 mm, operating torque T = 800 Nm with application factor K_A = 1.25 (light shocks). Hub of quenched-and-tempered C45 with outer diameter D_N = 80 mm (R_e = 370 N/mm² for over 40 up to 100 mm; without D_N the calculator applies the same value as the smallest documented step), load-sharing factor φ = 0.75 and safety factor S_F = 1.3 (both defaults).
Calculation: d_m = 50 - 2 = 48 mm, h_tr = 0.45 · 2 = 0.9 mm, T_eq = 1.25 · 800 = 1000 Nm = 1,000,000 Nmm. Flank pressure p = 2 · 1,000,000 / (48 · 0.9 · 40 · 24 · 0.75) = 64.3 N/mm².
Verification: p_allow = 370 · 1.0 / 1.3 = 284.6 N/mm². Utilization = 64.3 / 284.6 = 0.226 (23%, pass, green rating). Transmittable torque T_allow = 284.6 · 48 · 0.9 · 40 · 24 · 0.75 / (2000 · 1.25) = 3541 Nm - well above the required 800 Nm.
Frequently asked questions
What is the difference between a splined shaft connection and a parallel key connection?
The splined shaft connection per DIN 5480 transmits torque through many evenly distributed teeth instead of a single parallel key. This gives the shaft a much lower notch effect, results in a low-backlash connection, and allows high alternating or shock torques as well as axially sliding hubs (sliding fit). The drawback is higher manufacturing cost compared to a simple keyway.
How much torque can a DIN 5480 splined shaft transmit?
The transmittable torque T_allow follows from the allowable flank pressure, the geometry (mean load-carrying diameter, load-carrying tooth height, number of teeth, load-carrying length) and the load-sharing factor φ. For the example W 50 × 2 × 24 with l_tr = 40 mm and a quenched-and-tempered C45 hub, T_allow ≈ 3541 Nm - the calculator outputs this value directly for any input.
What is the load-sharing factor φ in a splined shaft connection?
Manufacturing tolerances prevent all teeth of a splined shaft connection from carrying load perfectly evenly - some teeth take on more load than others. The load-sharing factor φ (default 0.75, typical range 0.5 to 0.8) accounts for this by reducing the theoretically available load-carrying area accordingly. A smaller value should be used for larger pitch deviation or a lower tooth count.
What do reference diameter, module and number of teeth mean in DIN 5480?
The reference diameter d_B is the spline's reference dimension, the module m determines the tooth size - together, via the DIN 5480 convention z = d_B/m - 1, they fix the number of teeth. A splined shaft W 50 × 2 × 24 therefore has d_B = 50 mm, m = 2 mm and z = 24 teeth. If a chosen combination does not give an integer tooth count, the calculator flags it and conservatively rounds up.
When should the hub be case-hardened instead of quenched-and-tempered?
Case-hardened hubs (e.g. of 16MnCr5) withstand a considerably higher flank pressure than quenched-and-tempered hubs thanks to the hard, wear-resistant surface layer - the calculator applies a flat hardness factor f_H = 1.5 for this. It pays off for highly utilized connections, sliding fits subject to wear, or whenever a quenched-and-tempered hub would exceed the allowable pressure.
Why does the hub's yield strength depend on its outer diameter?
Because the product standards grade the minimum yield strength by thickness: a thick section does not reach the same strength during rolling and quenching and tempering as a thin one. What counts is the bar stock the hub is turned from, and that has at least the outer diameter D_N; the reference diameter would be the unsafe side. The default is D_N = 80 mm at d_B = 50 mm; as long as you do not enter D_N yourself, it follows the reference diameter as D_N = 1.6·d_B. Without D_N the calculator applies the smallest documented yield strength of the grade. If the stock is thicker than the finished hub and lies above a step boundary, enter its yield strength directly. 16MnCr5 carries a fixed value.
How does DIN 5480 differ from the involute-free spline per DIN ISO 14?
DIN 5480 describes an involute spline with many, flat teeth and a low notch effect - the standard for highly loaded, low-backlash shaft-hub connections in mechanical engineering. The straight-sided spline per DIN ISO 14 (formerly DIN 5471/5472) instead has only a few straight driving splines with a considerably higher notch effect, and today is mainly used for simpler, lower-load applications or in legacy designs.
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