Linear Thermal Expansion Calculator

About the Linear Thermal Expansion Calculator

Most materials expand when heated. The increase in length equals the original length times the linear expansion coefficient times the temperature change.

Enter the original length (m), the linear expansion coefficient α (per °C, steel ≈ 12×10⁻⁶, aluminium ≈ 23×10⁻⁶) and the temperature change (°C). The change in length is returned in metres.

How to use this calculator

1. Enter the original length of the object, usually written as \(L_0\).
2. Enter the coefficient of linear expansion, \(\alpha\), for the material.
3. Enter the temperature change, \(\Delta T\), in degrees.
4. Read the change in length, \(\Delta L\), from the result.

The formula explained

The formula \(\Delta L = \alpha L_0 \Delta T\) computes the change in length caused by heating or cooling. A positive \(\Delta T\) usually gives a positive length change, and a negative \(\Delta T\) gives contraction.

• \(\Delta L\) = change in length
• \(\alpha\) = coefficient of linear expansion
• \(L_0\) = original length
• \(\Delta T\) = change in temperature

Step by step method

1. Write down the values for \(\alpha\), \(L_0\), and \(\Delta T\).
2. Multiply \(\alpha\) and \(L_0\) first, then multiply by \(\Delta T\).
3. Check the sign of \(\Delta T\), because cooling makes \(\Delta L\) negative.
4. Add \(\Delta L\) to \(L_0\) if you want the final length.

Worked example

Problem. A steel rod is \(2\) m long, has \(\alpha = 12 \times 10^{-6}\) per degree, and its temperature rises by \(50\) degrees. Find the change in length.

1. Use the formula \(\Delta L = \alpha L_0 \Delta T\).
2. Substitute the values, \(\Delta L = (12 \times 10^{-6})(2)(50)\).
3. Compute \(\Delta L = 0.0012\) m, so the rod length increases by \(1.2\) mm.

Tips and common mistakes

• Make sure the temperature change is a difference, not the starting temperature itself.
• Keep units consistent, because \(L_0\) and \(\Delta L\) must use the same length units.

Frequently asked questions