Axial Stress, Strain and Elongation Calculator

Find the stress, strain and elongation of a bar under an axial force, and the factor of safety against yield.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Axial stress is the force divided by the cross-section area: σ = F / A. Within the elastic range the strain is the stress divided by the elastic modulus, ε = σ / E, and the elongation is the strain times the original length.

The factor of safety against yield is the yield strength divided by the stress. A value below 1 means the bar is predicted to yield: it would stretch permanently. The calculator explains what that means and gives the smallest area, largest force or lowest yield strength that reaches the factor of safety you choose.

Formulas used

  • \sigma = F / A
  • \varepsilon = \sigma / E
  • \delta = \varepsilon L_0 = \frac{F L_0}{A E}
  • FoS = f_y / \sigma

Worked example

With the default numbers in the calculator above:

  1. Stress: 125 MPa
  2. Strain: 625 microstrain
  3. Elongation: 0.625 mm
  4. Factor of safety against yield: 2
  5. Smallest area that reaches FoS 1.5: 300 mm²
  6. Largest force the bar can take at FoS 1.5: 66.7 kN
  7. Lowest yield strength that reaches FoS 1.5: 188 MPa

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What does a factor of safety below 1 mean?

The stress is above the yield strength. The bar would deform permanently. Ductile steel does not snap straight away, but it is usually treated as failed because it no longer keeps its shape.

Is the elongation formula valid beyond yield?

No. The formula is elastic, so past yield the real elongation is larger than the formula shows.

Are stress concentrations included?

No. Holes, shoulders and notches raise the local stress and need a stress concentration factor.

Related calculators

Further reading: Hibbeler, Mechanics of Materials; Gere and Goodno, Mechanics of Materials; Shigley, Mechanical Engineering Design.

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