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đŸ”„ Thermal Expansion Calculator

Calculate the linear thermal expansion of a material due to temperature changes.

đŸ”„ Thermal Expansion Calculator

Calculate the linear thermal expansion of a material due to temperature changes.

✅ Calculation Result

Change in Length (ΔL)- in
Final Length (L₁)- ft

Thermal Expansion Diagram

L₀

Calculator Description

Linear thermal expansion is the change in length of most solids as temperature changes, because the average interatomic spacing grows with temperature. It is a behavior that must be accounted for in piping, bridges, rails and structures.

What this calculator finds

Given the linear expansion coefficient α, initial length L₀ and the initial/final temperatures (T₁, T₂), it returns the length change ΔL and the final length L₁. Built-in coefficients are provided for common materials (steel, aluminum, copper, etc.).

Why it matters

  • Sizing expansion joints and support spacing for piping
  • Temperature stress and expansion gaps in rails and bridges
  • Thermal compensation in precision machines and instruments
  • Preventing expansion cracks in façades and glazing

Formula

Linear Thermal Expansion

The length change is proportional to the initial length and the temperature difference, with the proportionality constant being the material's linear expansion coefficient α.

ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta T
L1=L0+ΔLL_1 = L_0 + \Delta L
  • ΔL — Change in length [m or ft]
  • α — Linear expansion coefficient [1/°C or 1/°F]
  • L₀ — Initial length [m or ft]
  • ΔT — Temperature change (T₂ − T₁) [°C or °F]
  • L₁ — Final length [m or ft]

How the formula works

  • A longer L₀ gives a larger ΔL for the same temperature change.
  • A larger ΔT increases expansion/contraction proportionally.
  • Materials with larger α (aluminum 23 > steel 12 > glass 9, ×10⁻⁶/°C) change more.
  • In imperial units, α is converted to 1/°F basis (Ă·1.8).

Worked example

A 10 m steel pipe (α = 12×10⁻⁶/°C) heated from 20°C to 100°C has ΔT = 80°C, so ΔL = 12×10⁻⁶ × 10 × 80 = 0.0096 m = 9.6 mm, giving a final length of about 10.0096 m.

Useful Tips

Practical tips

  • Use expansion joints or loops to absorb ΔL in long piping runs.
  • For fully restrained pipes, evaluate temperature stress σ = E·α·ΔT rather than ΔL.
  • Composite materials can warp due to differing α across layers.

Limitations & cautions

  • This is a linear approximation; over a wide temperature range α itself varies with temperature.
  • Near phase transitions, volumetric expansion becomes non-linear and inaccurate.
  • For volumetric expansion of isotropic solids, use roughly 3α.