Shaft Size Calculator

Calculate minimum shaft diameter based on torque, power, and allowable stress. ASME standard formula for solid shafts with safety factor.

Design Formula: d = [ (16 · T) / (π · τallow) ]1/3 (d in meters, T in N·m, τ in Pa).

Safety factor can be applied to allowable stress.

Typical mild steel: 40–60 MPa; alloy steel: 75–100 MPa.
Applied to allowable stress (τallow / SF).
Calculating...

Understanding Shaft Design

Torsion Formula Derivation

For a solid circular shaft, the shear stress at the outer surface is:

τ = (T · r) / J

where T = torque, r = radius, J = polar moment of inertia = πd⁴/32. Substituting r = d/2:

τ = (16 · T) / (π · d³)

Rearranged for diameter:

d = [ (16 · T) / (π · τallow) ]1/3

Power‑Torque Relation

For a rotating shaft, power P (kW) and torque T (N·m) are related by:

T = (9550 · P) / N

where N = rotational speed (RPM). This relation comes from P (W) = T · ω, with ω = 2πN/60.

This calculator uses this conversion when power mode is selected.

Allowable Stress & Material Selection

The allowable shear stress τallow depends on material yield strength and loading conditions. According to the maximum shear stress theory (Tresca), for ductile materials:

τallow = Sy / (2 · SF) (for pure torsion)

where Sy is the tensile yield strength. For brittle materials, use ultimate strength with appropriate factor.

Material Sy (MPa) τallow (MPa, static, SF=1.5) τallow (MPa, fatigue, SF=2.5) Common Applications
Mild steel (A36) 250 ~83 ~50 General purpose shafts, low stress
Alloy steel (4140 Q&T) 600 200 120 High strength, automotive
Stainless 304 210 70 42 Corrosive environments
Cast iron (grey) — 25 (ultimate) — Light duty, brittle
Aluminum 6061-T6 240 80 48 Lightweight applications

Additional Design Considerations

1

Keyways & stress concentrations: Keyways reduce shaft strength. Use a stress concentration factor Kt ≈ 2 for keyways in torsion. A common practice is to increase diameter by 20–25% or reduce allowable stress by 25%.

2

Combined bending and torsion: If the shaft carries transverse loads, use the equivalent torque approach per ASME code:

Te = √(M² + T²) (for maximum shear stress theory)

where M is the bending moment. Use Te in place of T in the diameter formula.

3

Fatigue loading: For fluctuating loads, use endurance limit (approx. 0.5·Sut for steel) and apply appropriate factors (size, surface, reliability).

4

Critical speed & deflection: Long, slender shafts may need analysis for lateral vibration and torsional deflection. Minimum diameter often governed by stiffness rather than strength.

Standard Shaft Sizes

After calculating the minimum diameter, select the next larger standard size from preferred numbers (ISO R20, R40). Common increments (mm): 10, 12, 14, 16, 18, 20, 22, 24, 25, 28, 30, 32, 35, 38, 40, 42, 45, 48, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, etc.

ASME Design Code (B106.1M): For commercial steel shafts, the allowable shear stress is often taken as 55 MPa for shafts without keyways and 41 MPa for shafts with keyways (based on 0.3·Sy or 0.18·Sut).

References: Shigley's Mechanical Engineering Design, 10th Ed.; ASME B106.1M-1985; DIN 743.

Frequently Asked Questions

Keyways create stress concentrations. A common rule is to multiply the calculated diameter by 1.2–1.25, or reduce the allowable stress by 25%. For example, if your design calls for 50 MPa, use 37.5 MPa. Alternatively, use the ASME recommendation: for shafts with keyways, limit shear stress to 41 MPa (for commercial steel). This calculator does not automatically apply this; you can increase the safety factor or lower the allowable stress manually.

Not directly. For hollow shafts, the torsion formula is τ = (16·T·do) / (π·(do⁴ - di⁴)). You can rearrange to solve for outer diameter given inner diameter and allowable stress. This calculator is for solid shafts only; for hollow shafts, use the equivalent torque approach or compute manually.

1 MPa = 1 N/mm² exactly. They are the same unit. In the formula, using τ in MPa and T in N·m yields diameter in mm because the factor 10 appears in the simplified equation: d(mm) = 10 * (16T/(πτ))^(1/3). This is what the calculator uses.

If bending moment M is present, compute the equivalent torque Te = √(M² + T²) (based on maximum shear stress theory). Then input Te as the torque in the calculator. For ductile materials, this gives a conservative diameter.