What is the linear thermal expansion formula?

ΔL = α × L₀ × ΔT, where α is the coefficient of linear thermal expansion (per °C or per °F), L₀ is the initial length, and ΔT is the temperature change. The final length is L₀ + ΔL.

What units does α use?

The coefficient α is expressed per degree Celsius (1/°C) in SI units, or equivalently per degree Fahrenheit (1/°F) in imperial — note that the numeric value of α in 1/°F is 5/9 of its value in 1/°C because a Fahrenheit degree is smaller.

Why is thermal expansion important in engineering?

Materials expand when heated and contract when cooled. Ignoring this can cause bridges to buckle, pipes to crack, or precision parts to seize. Expansion joints and clearance gaps are designed using this formula.

Can I enter a negative temperature change?

Yes. A negative ΔT means the material is cooling, which produces a negative ΔL (contraction). The final length will be shorter than the initial length.

What if my material is not in the preset list?

Select "Custom" and enter the α value directly in units of 10⁻⁶/°C (ppm/°C). Most engineering references list α in these units.

Linear Thermal Expansion Calculator

Name: Linear Thermal Expansion Calculator
Availability: InStock
Author: Nham Vu

Enter initial length, temperature change, and material to find how much it expands or contracts.

Calculator Inputs

Unit System

Material

Initial Length (L₀) mm

Temperature Change (ΔT) °C

Fill in the inputs and click Calculate.

Length Change (ΔL)

—

Positive = expansion, negative = contraction

Final Length (L)

—

Relative Change

—

Formula Applied

Common Coefficients (α)

Material	ppm/°C	ppm/°F

Summary

Enter initial length, temperature change, and material to find how much it expands or contracts.

How it works

Select a material or enter a custom expansion coefficient (α).
Enter the initial length of the object.
Enter the temperature change (ΔT) — positive for heating, negative for cooling.
Choose metric (mm/°C) or imperial (in/°F) units.
The calculator applies ΔL = α × L₀ × ΔT and displays the length change and final length.

Use cases

Estimating rail gap allowances for railroad tracks.
Designing expansion joints in bridges and concrete slabs.
Calculating pipe elongation in plumbing and HVAC systems.
Verifying fit tolerances for machined metal parts after temperature swings.
Academic and classroom physics problems on thermal expansion.
Engineering feasibility checks for structural steel in extreme climates.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu