# Thermal Stress Calculator (σ = E·α·ΔT)

Thermal stress in a fully constrained member under a uniform temperature change: σ_th = E·α·ΔT. Built-in typical Young's modulus E and expansion coefficient α for carbon/alloy steel, aluminum, copper, austenitic stainless and titanium, plus custom values. ΔT in K or °C (same magnitude), result in MPa. Heating (ΔT>0) → compressive stress in the member.

> Canonical page: https://elysiatools.com/en/tools/thermal-stress-calculator

- **Category:** Math & Numbers

- **Keywords:** thermal stress, sigma = E·alpha·dT, temperature stress, coefficient of thermal expansion, Young's modulus, constrained expansion, heating stress, mechanical design

## Overview

Calculate thermal stress in a fully constrained member using σ_th = E·α·ΔT. Choose a material preset or enter custom Young's modulus and thermal expansion values, then get the stress in MPa with compression or tension identified.

## Inputs

- **Material** (select): Material preset supplies typical E and α. Choose 'Custom' to enter both yourself.
- **Young's Modulus E (MPa)** (number): Young's modulus E in MPa. Required only when Material is 'Custom'.
- **Thermal Expansion α (1/K)** (number): Coefficient of linear thermal expansion α in 1/K. Required only when Material is 'Custom'. Typical: steel ≈ 12e-6, aluminum ≈ 23e-6.
- **Temperature Change ΔT (K)** (number): Temperature change ΔT in K or °C (same magnitude). Positive = heating (→ compressive thermal stress), negative = cooling (→ tensile).
- **Decimal Places** (number)

## When to use

- Estimate stress caused by uniform heating or cooling when expansion is fully constrained.
- Compare thermal stress for steel, aluminum, copper, stainless steel, or titanium.
- Use custom material properties when the built-in presets do not match your design material.

## How it works

- Select a material preset, or choose Custom and enter Young's modulus E in MPa and thermal expansion coefficient α in 1/K.
- Enter the temperature change ΔT in K or °C; use a positive value for heating and a negative value for cooling.
- The calculator applies σ_th = E·α·ΔT.
- The JSON result reports stress in MPa, the selected material properties, ΔT, and the loading direction.

## Use cases

- Check thermal loading in restrained steel, aluminum, copper, stainless steel, or titanium members.
- Estimate whether heating or cooling produces compression or tension in a constrained component.
- Run quick mechanical design comparisons using preset or custom material properties.

## Frequently asked questions

### What formula does the calculator use?

It uses σ_th = E·α·ΔT for a fully constrained member under a uniform temperature change.

### Can I enter temperature change in Celsius?

Yes. A temperature difference in °C has the same numerical magnitude as in K.

### What does a positive ΔT mean?

A positive ΔT represents heating and is reported as compressive thermal stress.

### What does a negative ΔT mean?

A negative ΔT represents cooling and is reported as tensile thermal stress.

### What units are required and returned?

Enter E in MPa, α in 1/K, and ΔT in K or °C. The stress result is returned in MPa.

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