📏 Thermal Expansion Calculator (ΔL=αLΔT)

Enter any 3 of Length Change (ΔL), Linear Expansion Coefficient (α), Original Length (L), and Temperature Change (ΔT), and this calculator instantly derives the missing 1 using ΔL=αLΔT. Pick a material preset to auto-fill α.

Fill in only 3 of the 4 fields. The other 1 will be calculated automatically. ΔL is in mm, L is in m.

Material preset (auto-fills α)

Length Change (ΔL) (mm)

Linear Expansion Coefficient (α) (×10⁻⁶ /°C)

Original Length (L) (m)

Temperature Change (ΔT) (°C)

Results

Length Change (ΔL)

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Linear Expansion Coefficient (α)

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Original Length (L)

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Temperature Change (ΔT)

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Linear Expansion Coefficient (α) Reference Table by Material

Material	α (×10⁻⁶/°C)
Steel	12
Aluminum	23
Copper	17
Concrete	12
Glass	8.5
PVC	52
Wood (along grain)	5
Brass	19
Glass (Pyrex)	3.3

※ Values below are typical figures from standard engineering handbooks (approximate, near 20°C, ×10⁻⁶/°C) and may vary with alloy composition and temperature range.

GUIDE

Learn more

What is Thermal Expansion? The ΔL=αLΔT Formula

Most solids lengthen when heated and shrink when cooled — this is linear thermal expansion.

ΔL = α × L × ΔT

ΔL is the length change, α is the material's linear expansion coefficient (expansion ratio per °C), L is the original length, and ΔT is the temperature change. This calculator derives any 1 of the 4 variables from the other 3.

Why Expansion Coefficients Differ by Material

The coefficient depends on atomic bonding strength and crystal structure. Weakly-bonded plastics like PVC (52×10⁻⁶/°C) expand a lot, while rigid inorganic materials like glass and concrete (about 8-12×10⁻⁶/°C) expand little. This is why bridges, railways, and building joints include expansion joints designed to absorb temperature-driven movement.

Worked Example

A 10m steel rail (α=12×10⁻⁶/°C) heated by 30°C in summer expands by ΔL = 12×10⁻⁶ × 10 × 30 = 0.0036m = 3.6mm. Rail and bridge designers use this exact calculation to size expansion joint gaps.

Frequently asked questions

Why do I only enter 3 values?

ΔL, α, L, and ΔT are linked by the single equation ΔL=αLΔT, so knowing 3 mathematically determines the 4th uniquely. That is why exactly 3 are required.

What happens when I pick a material preset?

The standard linear expansion coefficient (α, ×10⁻⁶/°C) auto-fills the input. To use your own value, choose "Custom" or clear the auto-filled field.

The units differ (mm vs m) — does that cause problems?

No. The calculator automatically handles the α ×10⁻⁶ scaling and the L(m)→ΔL(mm) unit conversion internally, so you can enter values directly in the displayed units.