This thermal expansion calculator finds how much a material grows (or shrinks) with temperature change: ΔL = α·L·ΔT, with coefficients for common engineering materials built in.

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α Is a Material’s Personality Trait

Twenty-three millionths per degree (aluminum) vs one (Invar, engineered for metrology) — expansion mismatch bends bimetallic strips into thermostats and cracks mismatched assemblies. The heat that drives it is quantified on our Specific Heat Calculator. Part of our Physics Calculators collection.

Worked Example (Verified)

  • Steel, L = 10 m, ΔT = +50 °C (defaults): ΔL = 12×10⁻⁶ × 10 × 50 = 6.0 mm — a bridge deck’s daily breathing room, supplied by expansion joints and roller bearings
  • Same conditions in aluminum: 11.5 mm — nearly double; PVC pipe runs need expansion loops for their ~35 mm over 10 m
  • Railroad logic: continuously welded rail must be installed at a “neutral temperature” — the formula above, run backwards, schedules the work crew’s season
  • The Eiffel Tower grows ≈ 15 cm taller in summer (iron, 330 m, ΔT swinging) — α at architectural scale stops being a footnote

Designing With Expansion

  • Match α in joined materials (concrete ≈ steel is not an accident — reinforced concrete works because they expand together).
  • Give long runs somewhere to go: joints, loops, sliding supports — restraint converts ΔL directly into stress.
  • Shrink fits exploit the reverse: heat the outer ring, cool the shaft, let contraction do the clamping.
  • Precision instruments choose low-α materials (Invar, fused silica, Zerodur) — stability is a coefficient choice.

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Frequently Asked Questions

How do you calculate thermal expansion?

ΔL = α × L × ΔT, with α from the material table (steel 12×10⁻⁶/°C). A 10 m steel member heated 50 °C grows 6.0 mm. Negative ΔT (cooling) shrinks by the same arithmetic. This calculator covers nine common materials.

Why do bridges have expansion joints?

A 100 m steel span swelling through a 60 °C seasonal swing moves ≈ 72 mm. Restrained, that movement becomes stress σ = EαΔT — enough to buckle decks or crack abutments. Joints and bearings spend the movement cheaply before stress collects it expensively.

Which materials expand the least and most?

Among common solids: Invar (~1.2×10⁻⁶/°C) and fused silica near the bottom; engineering plastics (PVC ≈ 70, HDPE up to 200 ×10⁻⁶) at the top — an order of magnitude above metals, which is why plastic plumbing and siding detailing obsess over movement.

How does volume expansion differ?

For isotropic solids the volume coefficient β ≈ 3α (each dimension contributes). Liquids use measured β directly (water ≈ 207×10⁻⁶/°C near room temperature — with its famous 4 °C anomaly: water contracts cooling from 4 °C to 0 °C, which is why ice floats and lakes freeze top-down).

Why does a jar lid loosen under hot water?

The metal lid’s α exceeds the glass’s, and its diameter (an area/length effect) grows faster than the jar mouth — plus heat softens the seal. The same differential-expansion principle drives bimetallic thermostat coils.

Is this thermal expansion calculator free?

Yes — free, instant, no sign-up.