📏 Thermal Expansion Calculator
Find how much a material expands when heated (ΔL = α·L₀·ΔT), or solve for the coefficient, original length or temperature change.
Expansion ΔL
0.006 m
Linear thermal expansion: ΔL = α·L₀·ΔT (α = coefficient, L₀ = original length, ΔT = temperature change). For area use 2α, for volume 3α. 🔒 Computed in your browser.
How the thermal expansion calculator works
Linear thermal expansion is ΔL = α·L₀·ΔT, where α is the coefficient of linear expansion, L₀ the original length and ΔT the temperature change. Enter any three and the tool solves for the fourth. For area expansion use 2α, and for volume use 3α.
Supply α for your material (steel ≈ 12×10⁻⁶ /°C, aluminium ≈ 23×10⁻⁶, glass ≈ 9×10⁻⁶), values vary, so we don’t bundle a table. This is why bridges have expansion joints and rails can buckle in heat.
Frequently asked questions
How do I calculate thermal expansion?
ΔL = α·L₀·ΔT: the change in length equals the expansion coefficient times the original length times the temperature change. A 10 m steel beam (α ≈ 12×10⁻⁶) heated 50 °C grows about 6 mm.
What is the coefficient of thermal expansion?
α, the fractional length change per degree of temperature. Typical values: steel ~12×10⁻⁶ /°C, aluminium ~23×10⁻⁶, glass ~9×10⁻⁶. Enter the value for your material.
What about area and volume expansion?
Area expands with ≈ 2α and volume with ≈ 3α, so ΔA = 2α·A₀·ΔT and ΔV = 3α·V₀·ΔT. Use those multiples of the linear coefficient.
Why do bridges and railways need expansion gaps?
Because materials lengthen when heated; without gaps, the thermal expansion force would buckle rails or crack structures. The gaps absorb ΔL.
Does the temperature scale matter?
A change of 1 °C equals a change of 1 K, so ΔT is the same in Celsius or kelvin, just be consistent.
Worked example: a heated rail
A 25 m steel rail (α ≈ 12×10⁻⁶ /°C) warmed by 40 °C expands by ΔL = α·L₀·ΔT = 12×10⁻⁶ × 25 × 40 = 0.012 m = 12 mm, which is why rails need expansion gaps.
What is the difference between linear, area and volume expansion?
Linear expansion uses α (change in length); area uses about 2α and volume about 3α, because expansion happens along each dimension. A solid heated uniformly grows in all three directions.
Why does water behave unusually when it cools?
Most materials contract as they cool, but water between 4 °C and 0 °C expands, so ice is less dense than liquid water and floats. Because of this anomaly, the simple ΔL = α·L₀·ΔT does not apply to water near freezing.
What is a bimetallic strip?
Two metals with different expansion coefficients bonded together. When heated they expand by different amounts, so the strip bends, the basis of older thermostats and thermal switches, a direct use of differing α values.