Bolt Elongation Calculator

Elastic bolt stretch from preload, grip length, tensile stress area and Young’s modulus. Useful for torque-to-yield checks, preload measurement and long-bolt joints. Metric and imperial. Free, no signup.

Inputs

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Preload (F)

Clamp force / tensile load in the bolt.

Stressed length (L)

Effective elastic length under tension. Often grip length plus a portion of the engaged threads and head/nut compliance.

Nominal diameter (d)

Nominal bolt diameter.

Thread pitch (P)

Thread pitch, used for tensile stress area when the threaded section controls.

Area basis

Use tensile stress area for threaded stretch, or shank area for an unthreaded reduced model.

Young’s modulus (E)

Steel is about 200 GPa; titanium about 110 GPa; aluminum about 69 GPa.

GPa

Results

Default result

Edit inputs

Elastic elongation(δ)

0.1078mm

Pass

elastic range for most steel bolts

Also computed

Bolt stress(σ)431.1MPa

σ = F/A

Elastic strain(ε)0.002156

ε = σ/E

Area used(A)57.99mm²

tensile stress area

Method notes 3 notes

Elastic stretch δ = F·L/(A·E). The model assumes the bolt remains elastic and the load is axial.
The effective stressed length is not always just the grip: head, nut and engaged-thread compliance can add elastic length.
Use the bolt proof/yield strength to judge whether the stress is acceptable for the joint.

Elastic bolt elongation is δ = F·L/(A·E), where F is preload, L is the effective stressed length, A is the tensile stress or shank area, and E is Young's modulus. Because stretch is tied directly to clamp force while the bolt remains elastic, it is often a better preload indicator than torque. This calculator also returns stress, strain and the area used.

How to use this calculator

Enter preload. Use the target clamp force or measured tensile load.
Enter stressed length. Estimate the effective elastic bolt length under tension.
Choose area basis. Use thread tensile stress area for threaded stretch or shank area for an unthreaded section.
Read elongation and stress. Check stretch, stress, strain and the area used.

How it works

A preloaded bolt acts like an axial spring while it remains elastic: δ = F · L / (A · E) where F is preload, L is effective stressed length, A is the tensile stress area or shank area, and E is Young’s modulus. Stress is σ = F/A, and strain is ε = σ/E.

Worked example

Verified against the live calculator

A default M10 × 1.5 steel bolt at 25 kN preload over 50 mm effective length uses tensile stress area A ≈ 58.0 mm². Stress is about 431 MPa, strain is 0.00216, and elastic elongation is about 0.108 mm.

Frequently asked questions

How do you calculate bolt elongation?

Use the elastic stretch formula δ = F·L/(A·E), where F is preload, L is effective stressed length, A is tensile stress area or shank area, and E is Young’s modulus.

Why measure bolt stretch instead of torque?

Torque is dominated by thread and under-head friction. Elastic elongation is more directly tied to preload because the bolt behaves like a spring while it remains below yield.

What area should I use?

Use tensile stress area when the threaded section is the controlling elastic section. Use shank area only for an unthreaded or reduced-shank model where the shank controls the stretch.

What is effective stressed length?

It is the elastic length of bolt participating in stretch. It is often grip length plus a portion of the engaged threads and head/nut compliance, not just the visible unthreaded length.

Method & assumptions

Assumes axial elastic stretch only; bending, embedment and joint compression are separate effects.
Thread area uses the standard tensile stress area approximation At = π/4 · (d − 0.9382P)².
Verify stress against bolt proof/yield strength before using stretch as a preload target.