Spline Torque Capacity Calculator

First-pass spline torque capacity from pitch diameter, tooth count, flank height, engagement length and allowable bearing pressure. Metric and imperial. Free, no signup.

Inputs

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Pitch diameter (d)

Pitch or mean load radius diameter of the spline.

Number of teeth (z)

Number of spline teeth sharing the load before applying the load factor.

Effective tooth height (h)

Effective loaded flank height, not necessarily full tooth depth.

Engagement length (L)

Axial length over which the spline teeth carry load.

Allowable bearing pressure (p)

Allowable compressive pressure on the spline flanks.

MPa

Load distribution factor (K)

Fraction of the theoretical flank area assumed effective. Use less than 1 for misalignment and uneven tooth sharing.

Results

Default result

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Torque capacity(T)

450N·m

Also computed

Tangential force capacity(F_t)30,000N

30 kN · 6,744 lbf

Effective bearing area(A)375mm²

Method notes 3 notes

This is a flank bearing-pressure check: T = p_allow · z · h · L · K · d / 2.
Use a conservative load distribution factor when tooth contact, fit, lead error or shaft alignment are uncertain.
Final spline design should also check tooth-root shear/bending, shaft strength, hub hoop stress, fatigue and the applicable spline standard geometry.

How to use this calculator

Enter spline geometry. Enter pitch diameter, tooth count, effective tooth height and engagement length.
Set allowable pressure. Enter the allowable flank bearing pressure for the material and duty.
Apply load distribution. Reduce the area with a load distribution factor for imperfect tooth sharing.
Read torque capacity. Read torque capacity, tangential force and effective bearing area.

How it works

This screening check treats the spline flanks as loaded bearing area: A = z · h · L · K where z is tooth count, h is effective loaded height, L is engagement length and K is the load distribution factor. Allowable tangential force is F = p_allow · A, and torque follows from the pitch radius: T = F · d / 2

Worked example

Verified against the live calculator

A 30 mm pitch-diameter spline with 10 teeth, 2 mm effective flank height, 25 mm engagement, 80 MPa allowable bearing pressure and K = 0.75 has an effective area of 10 × 2 × 25 × 0.75 = 375 mm². Force capacity is 80 × 375 = 30,000 N, so torque is 30,000 × 30 / 2 / 1000 = 450 N·m.

Frequently asked questions

How do you estimate spline torque capacity?

For a first-pass flank-pressure check, effective bearing area is z·h·L·K. Tangential force is allowable pressure times that area, and torque is tangential force times pitch diameter divided by 2.

What is the load distribution factor?

It reduces the theoretical flank area for uneven tooth sharing, misalignment, lead error and fit clearance. Use less than 1 unless contact is very well controlled.

Does this check tooth-root stress?

No. This calculator checks flank bearing pressure only. Final spline design should also check tooth-root shear/bending, shaft strength, hub stress, fatigue and the applicable spline standard.

What diameter should I enter?

Use the pitch diameter or a defensible mean load diameter for the spline. The result is directly proportional to that diameter.

Method & assumptions

Flank bearing-pressure check only; it does not replace an involute spline standard calculation.
Effective tooth height should exclude chamfers, clearance and unloaded root/tip regions.
Use a conservative load factor when alignment and tooth contact pattern are unknown.