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Thermal Stress Calculator.

Calculate stress in a fully constrained uniaxial material.

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Thermal stress: 120,000,000 Pa

Thermal stress

120,000,000.000000Pa

Results update automatically as you type.

Use Cases

Engineering design of constrained components

Determine the stress that will develop in a component that is rigidly fixed at both ends when it experiences a temperature change, helping to assess if the material can withstand it.

Example: A steel rail with E=200 GPa, α=12e-6 1/K, ΔT=50 K → stress = 120 MPa.

Material selection for temperature-varying environments

Compare different materials to see which produces lower thermal stress under the same constraints and temperature change, aiding in material choice.

Example: Compare aluminum vs. steel for a fixed beam with a 30 K temperature rise.

Frequently Asked Questions

What is thermal stress?
Thermal stress is the internal stress that develops in a material when it is fully constrained and subjected to a temperature change. It is calculated as the product of Young's modulus, the expansion coefficient, and the temperature change.
How is thermal stress calculated?
The calculator uses the formula: Thermal Stress = Young's Modulus × Expansion Coefficient × Temperature Change. This assumes the material is fully constrained and cannot expand or contract freely.
What units should I use?
Enter Young's modulus in pascals (Pa), expansion coefficient in per kelvin (1/K), and temperature change in kelvin (K). The result will be in pascals (Pa).

Tips & Common Mistakes

Tips

  • Ensure the material is truly fully constrained; if it can expand partially, the stress will be lower.
  • Use consistent units: convert all inputs to SI units (Pa, 1/K, K) before calculating.
  • Remember that thermal stress is independent of the material's length or cross-sectional area.
  • For temperature changes, use the difference between final and initial temperatures in kelvin.

Common Mistakes to Avoid

  • Forgetting to convert temperature change from Celsius to Kelvin; the difference is the same, but ensure you use the correct value.
  • Using the expansion coefficient in per °C instead of per K; they are numerically equal for differences, but be consistent.
  • Assuming the material is not fully constrained when it is, leading to an underestimation of stress.

Last updated: August 13, 2026