Fareed Mohmed · Engineering
Shaft Design Calculator
Load · Combine · Size
Find the minimum solid shaft diameter for a section under combined bending and torsion, using the ASME shaft design code equation — with helper calculators for the two inputs it needs most often: torque from transmitted power, and bending moment from a point load.
This sizes a shaft against static/steady combined stress with the code's built-in shock and fatigue allowance factors (Kb, Kt) — it is not a full fatigue (Goodman/Soderberg) analysis. For a shaft under significant cyclic reversed bending in a fatigue-critical application, this is a first-pass sizing tool, not the final word.
Torque from Transmitted Power
T = 9550 × P / n
Copy this T value into section 03 below.
Bending Moment from a Point Load
M = F × L — a transverse force at a given distance from the section being sized.
For loads in two planes (e.g. a gear's tangential and radial force components), calculate the bending moment each produces separately, then combine as M = √(Mx² + My²) before using it below. Copy the result into section 03.
Shaft Diameter — Combined Bending & Torsion
d = [ 16 / (π · τallow) · √((Kb·M)² + (Kt·T)²) ]1/3 — the ASME shaft design code equation (maximum shear stress theory).
τallow = min(0.18·Sut, 0.30·Sy), reduced by 25% if a keyway is present at this section — per the ASME shaft design code. The standard diameter is rounded up from the same size series used across the bearing tools on this site, so the shaft you size here lines up with a standard bearing bore.
Reference Tables
| Loading Character (Rotating Shaft) | Kb Range | Kt Range | Value Used Above |
|---|---|---|---|
| Gradually Applied / Steady | 1.5 | 1.0 | Kb 1.5, Kt 1.0 |
| Suddenly Applied, Minor Shocks | 1.5 – 2.0 | 1.0 – 1.5 | Kb 1.75, Kt 1.25 (midpoint) |
| Suddenly Applied, Heavy Shocks | 2.0 – 3.0 | 1.5 – 3.0 | Kb 2.5, Kt 2.25 (midpoint) |
Per the ASME shaft design code (B106.1M) for a rotating shaft, as widely reproduced in machine design references. A stationary shaft uses different (generally lower) factors — consult a design text directly for that case. The calculator uses the midpoint of each shock range; override Kb/Kt directly above if your reference specifies a different point in the range.
Explanatory Notes
Why torque and bending combine the way they do
Bending produces a normal (tension/compression) stress that varies across the shaft's cross-section, while torque produces a shear stress. The code equation combines them through the maximum shear stress (Tresca) failure theory, which for a solid round shaft reduces neatly to a single closed-form diameter equation — this is why M and T appear inside one square root rather than being checked separately.
Kb and Kt are standing in for fatigue and shock, not just safety margin
A shaft that rotates under a steady transverse load sees fully-reversed bending stress at every point on its surface, once per revolution — even though the applied load itself never changes. The Kb/Kt factors are the code's way of building an allowance for that fatigue effect (and for shock loading) directly into a static-equivalent formula, without requiring a full S-N/Goodman fatigue analysis for a first-pass sizing.
A keyway is a stress concentration, not just a slot
The sharp corners of a keyway seat locally raise stress well above the nominal value calculated from the shaft's gross diameter. The code's blanket 25% reduction in allowable stress at a keyed section is a simplified way to cover this — a more detailed design would apply an actual stress concentration factor (Kt, in the fatigue sense — not to be confused with the torque factor above) from a stress concentration chart for the specific keyway geometry.
Related tools
For the material's actual yield and tensile strength by grade, see Mechanical Properties of Engineering Materials. Once the shaft diameter is set, the Bearing Size Finder shortlists a bearing at that bore, and the Bearing Load, Life & Static Capacity Calculator verifies it against the same loads. For the coupling on the other end of this shaft, see the Coupling Selection Calculator. If this shaft is driven by a servo axis, the Servo Motor Sizing Calculator checks the motor's inertia match and torque against the same load.