Standard spline shaft dimensions

Standard spline shaft dimensions DEFAULT

What are splines and serrations?

shaft splines and serrations are ridges, or teeth type keys that are an integral part of the shaft that mesh with grooves in a mating hub to transfer torque and rotational motion. For example, a bevel gear mounted on a shaft might use a male shaft spline that matches the female spline on the gear as shown in Figure 1.

Spline shaft bevel gear connection

Although a splined shaft looks like having a series of shaft keyways with keys pushed in, splines are considerably stronger than the keyed joint as the keyways weaken the shaft and reduce its torque carrying capacity.

Application of splines and serrations

Although they look like gears, Splines are only used to transmit torque and rotation on the same axis. They are used mainly for the following reasons.

  1. Mechanical transmission element such as gears and pulleys might need removing from the shaft due to design for manufacture and assembly (DFMA) ie during assembly or to aid manufacturing.
  2. Relative axial movement of the mechanical transmission element is required for functional purposes such as speed reducers and clutches.
  3. High torque transfer is required.

Good spline joint provides very high secure torque transmission, little clearance, minimum backlash, good centring between the coupled components, low noise, low wear and small or no axial forces.

Surface wear, fretting corrosion, tooth breakage and fatigue failure are the most common failure modes associated with spline joints.

Types of Splines and Serrations

The term “spline” provides an umbrella term for all profiles and the splines can be divided into the following three groups based on their flank form.

  • Parallel-sided or straight-sided spline
  • Involute spline
  • Serration

Splines and serrations can also be grouped as fixed spline or flexible spline depending on their relative axial movement. Fixed spline as the name suggests is a joint which does not move axially such as gears, pullers, turbine wheels etc.

Flexible splines slide axially, mainly used between shafts couplings and do not carry much torque as fixed spline joint.

These have straight and parallel tooth flanks a shown in the figure below and as per various standards number of teeth can vary from 4 to 12. They can transmit higher torque compared to involute splines and serrations because of their large tooth thickness from minor to the major diameter of the profile. But might fail due to fatigue due to stress concentration in the root of the flanks.

Naturally, it lacks centring ability because of the straight flanks, therefore forces it to rely on the major and minor diameter fits to be able to manage the centring. Because of the straight-sided face, there will be a line of contact and surface contact will only exist after some wear.


Involute splines are very common and very similar to internal and external involute gear tooth. They are comparably stronger than the parallel spline because of the lower stress concentration factor and have better surface quality. Involute splines can be produced by gear manufacturing techniques and have the ability to self-centre under load.

Involute splines are made with pressure angles 30o, 37.5 and 45o and can include between 60 and 100 splines as per the American National Standard. Involute splines can be either Side fit or Diameter fit.


Serrations also have straight flanks, but they are angled as shown in the figure below. The biggest advantage of the serrations is that the angles flanks centre the shafts and the hub resulting in self-centring splines. Flank angles are generally between 50o and 90o.

The main disadvantages of serrations are due to comparably small teeth it can be only used for low torque applications. These are only used for the non-axial moving application. Like straight-sided splines, there will be line contact and wear.

Spline strength calculation

During the design of shaft splines and serrations, the following stresses have to be considered to evaluate the suitability of the spline joint strength.

  1. Spline shaft shear stress
  2. Spline teeth shear stress
  3. Spline teeth compressive stress

Generally, the shaft diameter is dictated by the overall design such as bearing arrangements, seals, elements etc.  In that instance, the spline strength calculations can be used in the following two ways

  1. Stress calculation can be used either to find the safety factor by calculating the stress involved and comparing it with the allowable stresses as per failure modes.
  2. Using the factor of safety, the spline connection can be defined using spline length, spline type, number of splines etc.

Spline shaft shear stress

Solid shaft stressesHollow shaft stresses
\( S_s = \frac{16T}{\pi{D_{re}}^{3}} \) \( S_s = \frac{16T{D_{re}}}{\pi ({D_{re}}^4-D_h^4)} \)
\(S_s\)  Shear stress
\({D_{re}}\)  Diameter of the spline
\(T\)  Torque
\({D_{h}}\)  Bore diameter of hollow shaft
[table “” not found /]

Calculated stress using the above equations  must not exceed the allowable stress (\(S^a\)) of the spline material and can be shown as follows

\(S^a_s \geq S_s \frac{{K_{a}}}{{L_{f}}}\)

Usually, the factor of safety is calculated using the allowable stress for various material using the following equations

Allowable shaft stress
\(S^a_s = {N_{sf}}S_s \frac{{K_{a}}}{{L_{f}}}\)\(S^a_s \geq S_s \frac{{K_{a}}}{{L_{f}}}\)
\(S_s\)  Shear stress
\(S^a_{s}\)  Allowable shear stress
\(T\)  Torque
\({L_{f}}\)  Life factor
\({N_{sf}}\)  Safety factor
\({K_{a}}\)  Application factor

Spline teeth shear stress

Shear stress in spline teeth
\(S_s = \frac{4T{K_{m}}}{DN{F_{e}}{t_{e}}}\) 
\(S_s\)  Induced shear stress in spines
\(D\)  Pitch diameter
\(T\)  Torque
\({K_{m}}\)  Load distribution factor
\({F_{e}}\)  Effective face width
\({t_{e}}\)  Chordal thickness at pitch line ( approximately equal to D/2N)
\(N\)  Number of spline teeth

Spline teeth compressive stress

Compressive stress on spline teeth
\( S_c = \frac{2T{K_{m}}}{DN{F_{e}h}} \) 
\(S_c\)  Compressive stress
\({K_{m}}\)  Load distribution factor
\(T\)  Torque
\({F_{e}}\)  Effective face width
\(h\)  Radial height of the tooth in contact

Again similar to shear stresses, calculated compressive stresses should be compared with allowable compressive stress and must not exceed them to avoid failure.

\(S^a_s \geq S_s \frac{{K_{a}}}{{L_{f}}}\) – Flexible splines\(S^a_s \geq S_s \frac{{K_{a}}}{{L_{f}}}\) – Fixed splines
Allowable shaft stress
Flexible splinesFixed Splines
\(S^a_c = {N_{sf}}S_c \frac{{K_{a}}}{{L_{w}}}\)\(S^a_c = {N_{sf}}S_c \frac{{K_{a}}}{{9L_{f}}}\)
\(S_s\)Shear stress
\({S^a_{s}}\)Allowable shear stress
\({L_{f}}\)Life factor
\({N_{sf}}\) Safety factor
\({K_{a}}\) Application factor

Spline stress factors

Allowable stress

The relationship between allowable stress and specified minimum yield strength as per AISC code.

Allowable stresses vs Yield strength
Allowable tensile stress\({0.45}S_{y}\leq S^a_{t}\leq {0.6}S_{y}\)
Allowable Shear stress (\({S^a_{s}}\))\(S^a_{s}= 0.4S_{y }\)
Allowable compressive/bearing stress (\({S^a_{c}}\))\(0.45S_{y}\leq S^a_{c} \leq 0.6S_{y}\)
Allowable bending stress (\({S^a{b}}\))\(0.6S_{y} \leq S^a_{b} \leq 0.75S_{y} \)
\({S_{y}}\)Material yield strength

Load distribution factor for splines Km

The load is equally distributed if the transferring load is purely radial torsion and the torsional radial load is in the middle of the spline length. But if for example, a bevel gear is used this will put some unwanted axial loads into the spline.

Misalignment of spline couplings has been recognized as harmful to splines because it causes significant load concentration on spline teeth, and accelerates the wear and fretting fatigue of splines.

Load distribution factor for splines Km
Effective face width (Fe)
Misalignment½-in. (12.7 mm)1-in. (25.4 mm)2-in. (50.8 mm)4-in. (101.6)
0.001 in. / in.
1111 ½
0.002 in. / in.
111 ½2
0.004 in. / in.
11 ½22 ½
0.008 in. / in.
1 ½22 ½3

The following two papers discuss the load distribution factor and how it can affect the life of the spline joint.

Fatigue life factor for splines- Lf

Number of torque cycles Fatugue Life Factor, Lf
UnidirectionalFully - reversed

Spline application factor – Ka

If there are any axial or radial shock loading on the element that is been connected, then care should be taken to support the external axial and radial shock loads to increase the joint life. This should also be considered during the calculations using the spline application factor.

The application factor compensates for any uncertainties in loads and impacts, where if everything is smooth and uniform then Ka is equal to 1.

Input source category
(Driving input or machine)
Type of Load
UniformLight shockIntermittent Shockheavy shock
Generators, FansOscillating pumpsActuatorsPresses, Shears
Uniform (Turbine, Motor)
light shock, (Hydraulic Motor)
Medium shock, (Internal combustion engine22.22.42.8

Table 1 Spline application Factor (Ka)

Wear life factor for splines Lw

Life factor for splines under wear conditions are based on the number of revolutions of the spline joint, not reversible cycles. Wear life factor only applies to flexible or sliding spline compressive stress calculations as each time the spline slide back and forth it wears the teeth.

No of revolutions of the splineWear life factor for splines (Lw )

#Productdesigntip Fixed spline can carry 9 times more compressive stresses than flexible spline


  • Society of Automotive Engineering standard parallel side splines SAE J 499-2014
  • The American standard for involute and straight-sided spline profile ANSI B92.1
  • IS 2610 – power transmission-straight sided splines for machine tools dimensions
  • IS 3665 – Dimensions for involute sided splines
  • IS 2327 – Straight-sided splines for cylindrical shafts
  • BS 2059 Straight-sided splines and serrations
  • DIN 5463 – spline shaft connections with straight flanks; medium series
  • DIN 5480 – Involute splines based on reference diameters
  • Some other standards – DIN 5480, DIN 5481, DIN 5482, ISO 4156, E22-141, E22-145, ANSI and SAE standards

References and recommended reading

  • Dudley, D. W. (n.d.). When splines need stress control.
  • Oberg, E., Jones, F. D., Horton, H. L., & Ryffel, H. H. (2016). Machinery’s handbook.
  • Lingaiah, K. (2007). Machine design databook. (Lingaiah, K.: Machine design databook.) Norwich, NY: Knovel.
  • Bhandari, V. B. (2017). Design of machine elements. New Delhi: McGraw-Hill Education (India).
  • British Standards Institution. 2059 (1953). Straight-sided splines and serrations. London: B.S.I.

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Related Articles


Splined Shafts for Rotary and Linear Motion

Splined on Both Ends

Splined End ×Step-Down End

Grooves on the surface of these shafts transmit rotary power while allowing bearings to move freely along the length of the shaft. The edges are chamfered to remove sharp corners, reducing damage to bearings,housings, and other components during installation. All are turned,ground, and polished to tight diameter and straightness tolerances.


Shafts with four splines work with ball spline bearings, which create relatively little friction.They're commonly found in robotic and other automated systems that require complex, fast movements. They don't transmit as much torque as shafts with six splines.

All four-spline shafts are 52100 alloy steel for high strength.They're case-hardened to increase hardness and wear resistance on the surface of the shaft while allowing the center to remain soft for absorbing stresses caused by shifting loads.

Some of our four-spline shafts have a step-down end, which has been ground smooth and round like a standard shaft. Mount bearings,gears, and other round-bore components.


Large, evenly spaced splines transmit high-torque loads, such as those found in hydraulic systems,drivetrains, and machine tools. These shafts work with plain bearings, which means they're not meant for high-speed positioning applications. Made of 1045 carbon steel,they're strong but also machinable, so you can modify the ends to fit into your mounting fixtures. All meet ISO 14-B (formerly DIN 5463-B) to ensure they work with bearings that meet ISO 14-A.

3D CAD models availableFor technical drawings and 3-D models, click on a part number.

4 Splines (Metric—52100 Alloy Steel)

Four Splines



Splined End × Splined End

4-0.01 to 0100-0.05 to 0.05100______16Chamfered57,500000000000000000
4-0.01 to 0150-0.05 to 0.05150______16Chamfered57,500000000000000000
4-0.01 to 0200-0.05 to 0.05200______16Chamfered57,500000000000000000
4-0.01 to 0300-0.05 to 0.05300______16Chamfered57,500000000000000000
6-0.012 to 0150-0.7874 to 0.7874150______16Chamfered63,00000000000000000
6-0.01 to 0200-0.05 to 0.05200______16Chamfered57,50000000000000000
6-0.01 to 0300-0.05 to 0.05300______16Chamfered57,500000000000000000
6-0.01 to 0400-0.05 to 0.05400______16Chamfered57,500000000000000000
8-0.015 to 0150-0.7874 to 0.7874150______16Chamfered63,0000000000000000
8-0.01 to 0200-0.05 to 0.05200______16Chamfered57,50000000000000000
8-0.01 to 0300-0.05 to 0.05300______16Chamfered57,500000000000000000
8-0.01 to 0400-0.05 to 0.05400______16Chamfered57,500000000000000000
8-0.01 to 0500-0.08 to 0.08500______16Chamfered57,500000000000000000
10-0.02 to 0300-0.05 to 0.05300______16Chamfered57,500000000000000000
10-0.02 to 0400-0.05 to 0.05400______16Chamfered57,500000000000000000
10-0.02 to 0500-0.08 to 0.08500______16Chamfered57,500000000000000000
10-0.02 to 0600-0.08 to 0.08600______16Chamfered57,500000000000000000
10-0.015 to 0200-0.7874 to 0.7874200______16Chamfered63,0000000000000000
13-0.02 to 0200-0.05 to 0.05200______16Chamfered57,50000000000000000
13-0.02 to 0500-0.08 to 0.08500______16Chamfered57,500000000000000000
13-0.02 to 0700-0.08 to 0.08700______16Chamfered57,500000000000000000
13-0.02 to 01,000-0.08 to 0.081,000______16Chamfered57,500000000000000000
13-0.02 to 01,500-0.08 to 0.081,500______16Chamfered57,500000000000000000
16-0.02 to 0200-0.05 to 0.05200______16Chamfered57,50000000000000000
16-0.02 to 0500-0.08 to 0.08500______16Chamfered57,500000000000000000
16-0.02 to 0700-0.08 to 0.08700______16Chamfered57,500000000000000000
16-0.02 to 01,000-0.08 to 0.081,000______16Chamfered57,500000000000000000
16-0.02 to 01,500-0.08 to 0.081,500______16Chamfered57,500000000000000000
20-0.02 to 0200-0.05 to 0.05200______16Chamfered57,500000000000000000
20-0.02 to 0500-0.08 to 0.08500______16Chamfered57,500000000000000000
20-0.02 to 01,000-0.08 to 0.081,000______16Chamfered57,500000000000000000
20-0.02 to 01,500-0.08 to 0.081,500______16Chamfered57,500000000000000000
20-0.02 to 02,000-0.08 to 0.082,000______16Chamfered57,500000000000000000
25-0.02 to 0200-0.05 to 0.05200______16Chamfered57,500000000000000000
25-0.02 to 0500-0.08 to 0.08500______16Chamfered57,500000000000000000
25-0.02 to 01,000-0.08 to 0.081,000______16Chamfered57,500000000000000000
25-0.02 to 01,500-0.08 to 0.081,500______16Chamfered57,500000000000000000
25-0.02 to 02,000-0.08 to 0.082,000______16Chamfered57,500000000000000000
30-0.02 to 0300-0.05 to 0.05300______16Chamfered57,500000000000000000
30-0.02 to 0500-0.08 to 0.08500______16Chamfered57,500000000000000000
30-0.02 to 01,000-0.08 to 0.081,000______16Chamfered57,500000000000000000
30-0.02 to 01,500-0.08 to 0.081,500______16Chamfered57,500000000000000000
30-0.02 to 02,000-0.08 to 0.082,000______16Chamfered57,500000000000000000
40-0.02 to 0400-0.05 to 0.05400______16Chamfered57,500000000000000000
40-0.02 to 0700-0.08 to 0.08700______16Chamfered57,500000000000000000
40-0.02 to 01,000-0.08 to 0.081,000______16Chamfered57,500000000000000000
40-0.02 to 01,500-0.08 to 0.081,500______16Chamfered57,500000000000000000
40-0.02 to 02,000-0.08 to 0.082,000______16Chamfered57,50000000000000000000
50-0.02 to 0500-0.08 to 0.08500______16Chamfered57,500000000000000000
50-0.02 to 01,000-0.08 to 0.081,000______16Chamfered57,500000000000000000
50-0.02 to 01,500-0.08 to 0.081,500______16Chamfered57,50000000000000000000
50-0.02 to 02,000-0.08 to 0.082,000______16Chamfered57,50000000000000000000
60-0.03 to 0500-0.08 to 0.08500______16Chamfered57,500000000000000000
60-0.03 to 01,000-0.08 to 0.081,000______16Chamfered57,50000000000000000000
60-0.03 to 01,500-0.08 to 0.081,500______16Chamfered57,50000000000000000000
60-0.03 to 02,000-0.08 to 0.082,000______16Chamfered57,50000000000000000000

Splined End × Step-Down End

18.2-0.021 to 0350-0.7874 to 0.787420015-0.018 to 015016Chamfered57,50000000000000000
23-0.021 to 0350-0.7874 to 0.787420020-0.021 to 015016Chamfered57,50000000000000000
28-0.021 to 0450-0.7874 to 0.787430025-0.021 to 015016Chamfered57,50000000000000000
37.4-0.025 to 0550-0.7874 to 0.787440030-0.021 to 015016Chamfered57,50000000000000000

6 Splines (Metric—1045 Carbon Steel)

Six Splines


Splined End × Splined End

20-0.07 to -0.0271,000Not Rated1,000Not RatedChamferedNot RatedISO 14-B, DIN 5463-B0000000000000000
25-0.07 to -0.0271,000Not Rated1,000Not RatedChamferedNot RatedISO 14-B, DIN 5463-B000000000000000
32-0.07 to -0.0271,000Not Rated1,000Not RatedChamferedNot RatedISO 14-B, DIN 5463-B000000000000000

Splined Rotary Shafts

Splined End × Straight End

With a splined profile on one end, these shafts transmit high rotational loads—good for hydraulic systems, machine tools, and other high-torque applications. Compared to keyed shafts, they last longer, handle higher torque, and do not require as tight of a fit. Shafts are 1045 carbon steel, a general purpose shafting material that balances high strength and good machinability. They are 48" long and have six 12"-long splined grooves on one end. The straight end is turned,ground, and polished for a smooth, round finish. The edges are chamfered to remove sharp corners, reducing damage to bearings,housings, and other components during installation.


Dia.Lg.No. of
End Dia.
Lg.Edge TypeHardness
Strength, psi

Inch—1045 Carbon Steel

3/4"12"61"48"ChamferedMediumRockwell C1585,0000000000000000
1"12"61.5"48"ChamferedMediumRockwell C1585,000000000000000
1 1/2"12"62"48"ChamferedMediumRockwell C1585,000000000000000
Sours: /spline-shafts/
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Standard Spline Shafts

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Grob Standard Spline Shafting has been designed to maximize torsional strength and contact area. Grob’s cold rolled spline shafts are made with an even number of teeth and are parallel over two or more teeth. When your project requires mating parts, look no further.

For your convenience we have off the shelf mating broached sleeves and flanged bushings to match our Grob Standard Spline shafts. We also offer custom broaching of your parts to match with our Grob Standard Splines.

  • Full Flank Fit
  • Large Contact Area
  • Equal size tooth to space ratio
  • The same pressure angle as parallel sided spline
  • 3 x’s the work surface of parallel sided spline
  • Mating sleeves or flanged bushings

Custom spline shafts & shapes are also available 


Spline Specifications

 Grob Spline #OD (Outside Diameter)
RD (Root Diameter)
Measurement (C)
OD/Root RadiusSpecs & CAD Link

Request Spline Shaft Quote Online – How To

When requesting a quote for cold-rolled spline shafts from Grob Inc., please include as much of the following as possible:

  • Spline Number
  • Material
    • All Grob Standard Splines are stocked in 1117 mild steel, but other materials are available
    • If you need a specific material, or would like to discuss with a Grob rep – just let us know!
  • Length
    • All Grob Standard Splines are sold by the foot
    • List the lengths & number of pieces you require in your request


  • Spline number: 0500-16-2
    • (specifications for each standard spline can be found in the table above)
    • this example is a nominal .500″ spline, with 16 teeth, and the chord measured over 2 teeth
  • Material: 1117 mild steel
  • Length & #: 2 pieces; 3ft each
  • Order: 2x, 3ft, 0500-16-2-1117

Placing all of this information in your quote request, which can be simplified: 2x, 3ft, 0500-16-2-1117 will ensure that our team can get you the most accurate quote as quickly as possible.

Ready to Request Your Spline Quote?


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Shaft dimensions spline standard

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Spline Shafts 101 — Grob, Inc.

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Now discussing:

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