Elongation Of A Bar Calculator

Work out elongation of a bar instantly with clear inputs, formula shown and shareable results.

About Elongation Of A Bar Calculator

Combining Hooke's law with the definitions of stress and strain gives the extension directly: delta = FL/(AE). A 3 m steel bar of 400 mm2 section under 40 kN stretches 1.5 mm at 100 MPa stress. Longer bars stretch proportionally more, and stiffer or fatter ones proportionally less.

Formulas

Elongation

delta = F L / (A E)

Underlying relations

sigma = F/A, epsilon = sigma/E, delta = epsilon L

Worked example

With the default values below, Elongation Of A Bar Calculator returns Elongation of 1.5000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Axial forceminimum 0 N: 40,000 N
Original lengthminimum 0 m: 3 m
Cross-sectional areaminimum 0 m2: 0.0004 m2
Young's modulusminimum 0 GPa: 200 GPa

Results

Elongation: 1.5000 mm
Same Elongation In Metres: 1.50000 × 10⁻³
Axial Stress: 100.000 MPa
Strain: 5.0000 × 10⁻⁴

Step by step

1Values used
2Elongation
3Underlying relations
4Elongation= 1.5000 mm
5Same Elongation In Metres= 0.00150
6Axial Stress= 100.000 MPa
7Strain= 0.0005

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Does this hold past yield?

No. Beyond the elastic limit the extension grows far faster and part of it is permanent, so the linear formula stops applying.

How do I handle a stepped bar?

Work out each section separately and add the extensions - stress differs in each because the area does.