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.

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

Metric Thread Dimensions Calculator | ISO 261/724

Published by Nikolai Shelkovenko on February 15, 2026 February 15, 2026