Stress and Strain Calculator

What the stress and strain calculator shows

When you pull or push on a bar, the material inside carries the load as stress and stretches or squashes as strain. The stress and strain calculator gives both, plus Young's modulus, the stiffness that links them. Engineers use these numbers to check that a part stays well within the strength of its material.

Formulas for stress and strain

The formulas for stress and strain are simple ratios:

With force in newtons and area in mm², stress comes out directly in MPa. Strain has no unit, because it is a length divided by a length.

Stress and strain calculator example

A 10 kN pull on a bar of 100 mm², 1,000 mm long, that stretches 0.5 mm. The stress and strain calculator gives:

200 GPa is the modulus of steel, so this bar behaves like steel within its elastic range.

How to use the stress and strain calculator

Enter the axial force in newtons and the cross-section area in square millimetres to get stress. Add the original length and the change in length in millimetres to get strain and Young's modulus. The stress and strain calculator reports stress in MPa (N/mm²) and psi, so you can compare directly with material tables.

Reading the stress and strain calculator result

Compare the stress with the material's yield strength; mild steel yields around 250 MPa, so 100 MPa leaves a good margin. Strain shows how much the part stretches, and Young's modulus identifies the material's stiffness. These formulas hold in the elastic range, where the part returns to its original length when unloaded.

When to use the stress and strain calculator

• Checking a rod or bolt under tension with the stress and strain calculator
• Finding Young's modulus from a tensile test
• Comparing stress with yield strength
• Solving mechanics of materials problems

Common stress and strain calculator mistakes

• Mixing units. Newtons with mm² give MPa; newtons with m² give Pa.
• Using the wrong area. Use the cross-section perpendicular to the load.
• Going past yield. The modulus only applies in the elastic range.

Tips for accurate results

• Measure the cross-section at its smallest point.
• Keep a safety factor below the yield strength.
• Use early, straight-line test data for the modulus.

Related to the stress and strain calculator

Axial stress is one load case. The beam deflection calculator handles bending, and the moment of inertia calculator gives the section property bending stress depends on.

Formulas for stress and strain in the elastic range

Hooke's law says that, up to the elastic limit, stress is proportional to strain, and Young's modulus is the constant of proportion. Beyond the yield point the material deforms permanently and the formulas for stress and strain no longer predict behaviour with a single modulus. Springs are designed to work entirely in this elastic range, which the spring rate calculator describes as force per unit deflection.

Using the stress and strain calculator for test data

In a tensile test, a sample is pulled while force and extension are recorded. Feeding pairs of readings into the stress and strain calculator gives the slope of the stress-strain line, which is Young's modulus. Use readings from the straight early part of the curve for an accurate value.

Stress and strain calculator reference: Young's modulus

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