Linear Expansion Calculator
Enter the expansion coefficient, original length and temperature change to compute the change in length ΔL = α·L₀·ΔT.
Input Data
Results
At a glance:Linear thermal expansion describes how a solid's length changes with temperature: ΔL = α·L₀·ΔT, where α (1/K) is the linear expansion coefficient, L₀ the initial length and ΔT the temperature change. The final length L = L₀·(1 + α·ΔT). α is material-specific: steel ~12×10⁻⁶/K, aluminum ~23×10⁻⁶/K, invar ~1.2×10⁻⁶/K. For area and volume, use 2α and 3α respectively (small-α approximation). Expansion joints in bridges and railways accommodate this; bimetallic strips use differing α to bend. This tool gives ΔL and L.
Formula
ΔL = α·L₀·ΔT
L = L₀·(1 + α·ΔT)
$$\Delta L = \alpha L_0 \Delta T$$How to Use
- Enter the expansion coefficient α (1/K).
- Enter the original length L₀ (m) and temperature change ΔT (K).
- The calculator returns ΔL and L.
Case Studies
Rail expansion
L₀ = 100 m, α = 12e-6/K, ΔT = 40 K.
ΔL = 12e-6×100×40 = 0.048 m (48 mm).
Expansion joints/pre-stress prevent buckling.
FAQ
Does α have units?
α is per kelvin (or per °C; the increment is the same). For small changes ΔL/L₀ = α·ΔT regardless of length units.
Why do bridges have expansion joints?
To absorb ΔL = α·L₀·ΔT as temperature varies, preventing buckling. A 100 m steel rail at ΔT=40 K expands ~48 mm.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.