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Bolt Tensile Stress Area Calculator

Work out a metric bolt's tensile stress area — the thread area that carries tension — and its proof load, using the ISO 898 formula Aₜ = (π/4)(d − 0.9382·p)².

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How to use this calculator

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How to use this calculator

  1. Enter the bolt's nominal diameter and thread pitch (mm).
  2. Optionally add the proof strength to get the proof load.
  3. Read the tensile stress area and proof load.

How it works

The Bolt Tensile Stress Area Calculator finds the effective area a metric bolt uses to carry tension. It's smaller than the plain shank because the load passes through the threaded section, not the full diameter.

Aₜ = (π/4)(d − 0.9382·p)² from ISO 898-1, where d is the nominal diameter and p the thread pitch in mm. Multiply Aₜ by a stress to get a force: proof load = Aₜ × proof stress, and the tensile (breaking) capacity ≈ Aₜ × the ultimate tensile strength Rm.

Standard coarse-pitch tensile stress areas: M6 ≈ 20.1, M8 ≈ 36.6, M10 ≈ 58.0, M12 ≈ 84.3, M16 ≈ 157, M20 ≈ 245, M24 ≈ 353 mm². Proof stress depends on the property class — about 580–600 MPa for 8.8, 830 MPa for 10.9 and 970 MPa for 12.9.

Worked example

M10 × 1.5, class 10.9. Aₜ = (π/4)(10 − 0.9382×1.5)² ≈ 58.0 mm²; proof load = 58.0 × 830 ÷ 1000 ≈ 48.1 kN (using the 830 MPa proof stress for class 10.9).

Common mistakes

  • Using the plain shank area (π·d²/4) instead of the tensile stress area — that overestimates the bolt's tensile capacity.
  • Using the wrong pitch. Fine-pitch threads have a larger stress area than coarse threads of the same diameter, so enter your bolt's actual pitch.
  • Confusing proof strength with ultimate tensile strength — proof stress is close to the elastic limit, so don't size a joint to the breaking strength.

Frequently asked questions

How do you calculate the tensile stress area of a bolt?

Use Aₜ = (π/4)(d − 0.9382·p)² from ISO 898-1, where d is the nominal diameter and p the thread pitch in millimetres. For an M10 coarse bolt (p = 1.5): Aₜ = (π/4)(10 − 0.9382×1.5)² ≈ 58.0 mm².

What is the tensile stress area of an M8, M10 or M12 bolt?

For standard coarse pitch: M8 ≈ 36.6 mm², M10 ≈ 58.0 mm² and M12 ≈ 84.3 mm². Larger sizes are M16 ≈ 157, M20 ≈ 245 and M24 ≈ 353 mm². Fine-pitch threads are slightly larger.

How do you work out a bolt's proof load and tensile strength?

Multiply the tensile stress area by a stress. Proof load = Aₜ × proof stress; the tensile (breaking) load ≈ Aₜ × the ultimate tensile strength Rm. An M10 class 10.9 bolt (Aₜ ≈ 58.0 mm², proof ≈ 830 MPa) has a proof load of about 48 kN.

What proof stress should I use for grade 8.8, 10.9 and 12.9 bolts?

Approximate ISO 898-1 proof stresses are 580–600 MPa for class 8.8, 830 MPa for 10.9 and 970 MPa for 12.9. Their ultimate tensile strengths Rm are about 800, 1040 and 1220 MPa.

Why not just use the shank area?

A bolt fails through its threads, where the effective area is smaller. The tensile stress area accounts for the thread profile, so tensile strength is based on it, not the plain shank.

Can I use these results for final design?

No. These calculators are for first-pass sizing, checking and learning. They assume ideal supports, static loads and elastic behaviour, and they don't apply load factors, member capacity, buckling or connection checks. Always verify against the relevant design code (e.g. AS 4100, AS 1170, Eurocode) and have a qualified engineer sign off structural work.

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Cite this tool

Zerdly. (2026). Bolt Tensile Stress Area Calculator. Retrieved from https://www.zerdly.com/tools/bolt-tensile-stress-area-calculator/

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