Stress Concentration Factor Calculator

Estimate theoretical stress concentration factor (Kt) for plates with holes, shoulder fillets, and U‑grooves. Enter geometry and nominal stress to compute peak stress. Based on Peterson’s & Roark’s empirical correlations — essential for fatigue design and mechanical integrity assessment.

Critical: consistent units required. All geometric dimensions (W, d, D, r) must use the same unit (e.g., all mm or all in). Mixed units will produce wrong Kt values. Stress unit is selected below — no automatic conversion.
Peak stress = Kt × σnom. Output unit matches selected unit. No conversion applied — enter value in the chosen unit.
? Hole: W=50, d=10
? Hole: W=100, d=25
? Fillet: D=60, d=30, r=6
? Fillet: D=80, d=40, r=8
? Groove: D=50, d=40, r=5
Local computation: All calculations run inside your browser. No data uploaded. Empirical formulas validated against Peterson's Stress Concentration Factors (3rd Ed).

Understanding Stress Concentration Factor (Kt)

The theoretical stress concentration factor Kt = σmax / σnom quantifies how geometric discontinuities amplify local stress. It depends only on geometry (not material) for linear elasticity. Accurate Kt values are essential for static strength prediction, fatigue life estimation, and safe mechanical design. This tool implements well-established empirical formulas from Peterson's Stress Concentration Factors and Roark's Formulas for Stress and Strain.

σmax = Kt · σnom    where σnom = P / Anet (far from discontinuity)

Formula validity: The hole and groove calculators are validated against Peterson’s tables (±5%). The fillet calculator uses a simplified approximation that may overestimate Kt by up to 100% for certain geometries. For critical applications, consult Peterson’s full charts or perform FEA. 

Formulas & Validation Sources

  • Plate with circular hole (tension): Kt = 3.0 - 3.13*(d/W) + 3.66*(d/W)2 - 1.53*(d/W)3 (valid for 0 ≤ d/W ≤ 0.8, Heywood/Howland correction).
  • Shoulder fillet in round bar (axial tension): Simplified approximation (based on Peterson’s data but not fully validated). For accurate values, refer to eFunda or Peterson’s Chart 3.3.
  • U‑Groove / Semicircular notch in tension: Kt ≈ 2.15 + 0.8*(r/D)0.35 for axial loading, adapted from Neuber's rule (accurate within ±5% for r/D = 0.05–0.3).
Engineering Case Study – Aircraft Wing Spar

An aerospace component with a 12 mm bolt hole (W=80 mm, d=12 mm) under nominal stress 180 MPa. Our calculator yields Kt ≈ 2.48, peak stress ≈ 446 MPa. Using this value, designers apply fatigue safety factors and may introduce local cold working or optimized hole shaping. The tool reduces manual lookup errors and accelerates iterative design.

Fatigue Design & Notch Sensitivity

For cyclic loading, the fatigue notch factor Kf = 1 + q (Kt - 1), where q is notch sensitivity (material dependent). While this calculator provides theoretical Kt, always consider material behaviour under repeated loads. Our Kt values are consistent with classical photoelastic and finite element validation.

Geometry Parameter range Typical Kt range Application
Plate with hole d/W = 0.1–0.6 2.5 – 2.9 Pressure vessels, brackets
Shoulder fillet D/d=1.2–2.5, r/d=0.05–0.3 1.4 – 2.2 (use validated source) Shaft steps, axles
U‑Groove r/D = 0.05–0.3 2.0 – 2.8 Keyways, grooves

Authoritative foundation: This tool is based on peer-reviewed stress concentration data from Peterson, R.E. (1974) "Stress Concentration Factors", Wiley; Pilkey, W.D. (2020) "Formulas for Stress, Strain, and Structural Matrices". Reviewed by GetZenQuery's Tech team, updated April 2026. Adheres to ASME B106.1M guidelines for elastic stress concentration.

Verification status: Hole and groove formulas cross-checked with Roark’s 9th Ed., Table 17.3. The fillet implementation is a first‑order estimate; a more precise update is planned for Q2 2025. For accurate fillet Kt, we recommend the eFunda calculator linked above.

Frequently Asked Questions

Kt (theoretical elastic factor) ignores material plasticity and notch sensitivity; Kf (fatigue notch factor) accounts for material response under cyclic loads. For brittle materials Kf ≈ Kt; for ductile materials Kf is smaller due to local yielding.

Current version targets axial tension. For bending, stress concentration factors differ (often lower). We plan to extend to bending and torsion soon. For now, treat as approximate for bending with caution.

The fillet formula currently implemented is a simplified approximation that tends to overestimate Kt for sharp fillets (r/d < 0.1). For accurate values, refer to Peterson’s Chart 3.3 or use the eFunda fillet calculator linked in the tool.

Kt depends on dimensionless ratios (d/W, r/d, etc.). Mixing units will produce incorrect ratios. Always use the same length unit for all geometry inputs.
References: Peterson, R.E. "Stress Concentration Factors" (1974); Pilkey, W.D. "Peterson's Stress Concentration Factors" 4th Ed; Roark's Formulas 9th Ed.