How is the stress area of a bolt calculated?

The tensile stress area As is calculated as As = (π/4) × ((d₂ + d₃)/2)², where d₂ is the pitch diameter and d₃ is the minor diameter of the external thread. This formula accounts for the thread root geometry and gives the effective cross-section for tensile loading per ISO 898-1.

What is the difference between pitch diameter and minor diameter?

The pitch diameter (d₂) is the diameter where the thread tooth width equals the space width — it's the key dimension for thread fit. The minor diameter (d₃) is the smallest diameter at the root of the external thread. The minor diameter determines the core cross-section of the bolt.

What is the difference between coarse and fine pitch thread dimensions?

For the same nominal diameter, fine pitch threads have a smaller pitch (P), resulting in a larger pitch diameter and minor diameter compared to coarse threads. This gives fine pitch bolts a larger stress area — for example, M12×1.25 fine has As ≈ 92 mm² versus M12 coarse (P=1.75) with As ≈ 84.3 mm². Fine pitch threads provide better resistance to loosening from vibration.

Free Engineering Tool

Metric Thread Dimensions Calculator

Look up all key dimensions for metric ISO threads — pitch diameter, minor diameter, stress area, core area — for M3 to M48 in coarse and fine pitch.

This calculator was developed and verified by the Vibromera engineering team, makers of the Balanset portable balancing instruments.

ISO 261 ISO 724 M3 – M48

Results

Thread Designation

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Nominal Diameter d

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Pitch P

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Pitch Diameter d₂

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Minor Diameter d₃ (bolt)

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Minor Diameter D₁ (nut)

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Thread Height H

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Stress Area Aₛ

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Core Area A₃

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Thread	d (mm)	P (mm)	d₂ (mm)	d₃ (mm)	D₁ (mm)	H (mm)	Aₛ (mm²)	A₃ (mm²)

ISO Metric Thread Geometry

Per ISO 261 and ISO 724, the basic profile of ISO metric threads is defined by the fundamental triangle height H₁ and the pitch P.

Pitch Diameter & Minor Diameter

The pitch diameter d₂ and minor diameter d₃ of the external (bolt) thread are derived from the nominal diameter d and pitch P:

The minor diameter D₁ of the internal (nut) thread:

Stress Area & Core Area

The tensile stress area A_s (per ISO 898-1) and core area A₃ are:

ℹ️ Note: The stress area A_s is the effective cross-sectional area used for calculating tensile and proof loads of bolts. It is larger than the core area A₃ because it averages the pitch and minor diameters.

Practical Example

Example — M12 Coarse Pitch

Given: d = 12 mm, P = 1.75 mm

H = 0.866025 × 1.75 = 1.5155 mm

d₂ = 12 − 0.6495 × 1.75 = 10.863 mm

d₃ = 12 − 1.2269 × 1.75 = 9.853 mm

A_s = (π/4) × ((10.863 + 9.853)/2)² = 84.3 mm²

A₃ = (π/4) × 9.853² = 76.2 mm²