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.
Results
| Thread | d (mm) | P (mm) | d₂ (mm) | d₃ (mm) | D₁ (mm) | H (mm) | Aₛ (mm²) | A₃ (mm²) |
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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 As (per ISO 898-1) and core area A₃ are:
ℹ️ Note: The stress area As 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
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
As = (π/4) × ((10.863 + 9.853)/2)² = 84.3 mm²
A₃ = (π/4) × 9.853² = 76.2 mm²
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. This formula (per ISO 898-1) uses the average of the pitch and minor diameters, giving an effective area that accounts for the stress concentration at the thread root.
Pitch diameter (d₂) is where the thread tooth width equals the groove width — it determines the fit between bolt and nut. It is the most critical dimension for thread gauging.
Minor diameter (d₃) is the smallest diameter at the root of the external thread. It determines the minimum cross-section and thus the core area of the bolt.
The pitch diameter is always larger than the minor diameter by 0.577 × P.
For the same nominal diameter, fine pitch threads have:
- Smaller pitch P — finer thread profile
- Larger pitch diameter d₂ — more material in the bolt
- Larger minor diameter d₃ — stronger core
- Larger stress area As — higher load capacity
Example: M12 coarse (P=1.75) has As=84.3 mm², while M12×1.25 fine has As≈92.1 mm² — about 9% more.
Fine pitch also offers better resistance to vibration loosening and finer tension adjustment.
The procedures described on this page were developed and field-tested by the Vibromera team using the Balanset-1A, a portable dual-channel balancer and vibration analyzer for on-site rotor balancing.
Professional field balancing instruments and software. Used in 50+ countries.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
