Calculate tensile stress area Aₛ and associated basic diameters from nominal diameter and pitch.
Set the inputs and run the calculation.
Determine the equivalent area used for bolt tensile and preload calculations.
Nominal diameter and pitch define pitch/root diameters and Aₛ for the metric ISO thread.
Aₛ is an equivalent area for nonuniform thread geometry, not a visible circular area. Use it for tensile stress and proof force, not for under-head or nut bearing pressure.
Aₛ is a geometric equivalent between pitch and root diameters and is used for tensile stress F/Aₛ.
10 kN on Aₛ = 58 mm² gives 172 MPa mean tensile stress.
Sources and limits: ISO 724 basic profile; actual tolerance and property class come from ISO 965 and ISO 898-1.
Determine the equivalent area used for bolt tensile and preload calculations.
Bolt calculations describe a joint through geometry, preload, friction and material limits. Preload clamps the parts; external load, embedding and temperature change the reserve.
Aₛ = π/4 · ((d₂ + d₃) / 2)²
d₂ = d − 0.649519 · Pd₃ = d − 1.226869 · Pσ = F / Aₛ| Symbol / input | Meaning |
|---|---|
| d | Nominal thread diameter, for example 10 mm for M10. |
| P | Pitch, the axial distance between two adjacent thread turns. |
| d₂ | Basic pitch diameter to ISO 724. |
| d₃ | Basic minor diameter of the external thread to ISO 724. |
| Aₛ | Tensile stress area: circular area over the mean of d₂ and d₃. |
| σ | Tensile stress in the thread from axial force F and Aₛ. |
Nominal diameter and pitch define pitch/root diameters and Aₛ for the metric ISO thread. Aₛ is an equivalent area for nonuniform thread geometry, not a visible circular area. Use it for tensile stress and proof force, not for under-head or nut bearing pressure.
Pick the standard designation at the top, for example M10 × 1.5 – nominal diameter and pitch are then set together. For combinations outside the standard series, fill in the two fields below directly; the picker falls back to "Free entry". The calculator derives pitch and minor diameter and the tensile stress area Aₛ from them.
10 kN on Aₛ = 58 mm² gives 172 MPa mean tensile stress.
Aₛ is an equivalent area for nonuniform thread geometry, not a visible circular area. Use it for tensile stress and proof force, not for under-head or nut bearing pressure. A passing result means only that the selected model stays within the entered limits. Tightening scatter and real contact surfaces may govern residual clamp force.
Diameter and pitch in millimetres (inches in the US unit system), Aₛ in square millimetres or square inches. Aₛ is shown to three significant digits because ISO 724 tabulates the nominal value at that precision.
Providing the tensile stress area as an input for tensile-stress, preload and proof-force calculators, or cross-checking standard values from supplier tables.
ISO 724 basic profile; actual tolerance and property class come from ISO 965 and ISO 898-1.
Common mistake: Don't confuse Aₛ with the circular area from the nominal diameter – it is a smaller, geometrically defined equivalent value. Aₛ is not the right reference area for bearing pressure under the head or nut; use the actual bearing area for that.
For tensile stress F/Aₛ, proof force and preload calculations per ISO 16047/VDI 2230 – anywhere the load-bearing thread area, not the full nominal cross-section, matters.
Yes. A finer pitch slightly increases pitch and minor diameter and therefore Aₛ compared with the coarse thread of the same nominal size.
No, this calculator models only the metric ISO basic profile per ISO 724; inch threads (UN/UNC/UNF) follow a different profile standard.
The tensile stress area is used for bolt tensile stress, proof load, and preload calculations and links thread geometry to the existing bolt tools.
Thread-root concentration, tolerances, load distribution, fatigue, and material strength are outside this geometry-only calculation.