# Thermal Stress Calculator

URL: https://speedycalculator.com/calculators/physics/thermal-stress/
Last updated: 2026-10-30

> The thermal stress calculator finds the stress in a fully restrained member when its temperature changes, from its coefficient of thermal expansion and Young's modulus, with presets for common materials.

## Inputs

- Material
- Thermal expansion coefficient α (10⁻⁶/K)
- Young's modulus E (GPa, MPa, Pa, psi, Mpsi)
- Initial temperature T_i (°C, °F, K)
- Final temperature T_f (°C, °F, K)

## Results

- Thermal stress σ
- Blocked thermal strain
- Type

## Formula

```
σ = −E·α·ΔT,  ΔT = T_f − T_i
```

## Explanation

Materials expand when heated. If they cannot – rails welded end to end, pipes fixed between walls – the blocked expansion turns into stress. Expansion joints in bridges and pipelines prevent it.

### How to use the Thermal Stress Calculator

- **Material**
- **Thermal expansion coefficient α (10⁻⁶/K)**
- **Young's modulus E**
- **Initial temperature T_i**
- **Final temperature T_f**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the material (or enter α and E) and the initial and final temperatures. Negative stress is compression (heating), positive is tension (cooling).

### Inputs explained

FieldWhat to enterMaterialChoose one: Aluminium, Brass, Copper, Gold …Thermal expansion coefficient α (10⁻⁶/K)A numberYoung's modulus EUnits: GPa, MPa, Pa, psi, MpsiInitial temperature T_iUnits: °C, °F, KFinal temperature T_fUnits: °C, °F, K

### What each result means

- **Thermal stress σ** = -[E]×[alpha]×([Final temperature T_f] - [Initial temperature T_i])
- **Blocked thermal strain** = [alpha]×([Final temperature T_f] - [Initial temperature T_i])

### Example values

How the main result changes when **Thermal expansion coefficient α** changes and everything else stays at the example values above:

Thermal expansion coefficient α (10⁻⁶/K)Thermal stress σ (MPa)6-969-9612-9615-9618-9624-96

## Worked example

Inputs — Material: Structural steel; Initial temperature T_i: 20 °C; Final temperature T_f: 60 °C.

Results — **Thermal stress σ = -96 MPa**; Blocked thermal strain = 0.00048; Type = Compression.

## Key terms

- **Coefficient of thermal expansion**: Fractional length change per degree.

## FAQ

**Why do railway tracks buckle in heat?**
Restrained expansion creates large compressive stress.

**How much stress per degree in steel?**
About 2.4 MPa per °C.

**Does an unrestrained bar have thermal stress?**
No – it simply expands freely.

**How are thermal stresses avoided?**
Expansion joints, loops and sliding supports.


## Sources

- [MIT OpenCourseWare – Mechanics of Materials](https://ocw.mit.edu/courses/2-001-mechanics-materials-i-fall-2006/)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)