Thermal Expansion Calculator

About the Thermal Expansion Calculator

Almost everything expands when it warms up and shrinks when it cools. The change is usually too small to see, but it adds up over long lengths and large temperature swings. Bridges, railway lines, pipelines, concrete pavements and window panes must all be designed to cope with it, and liquids such as petrol and water need room to swell in their tanks.

This thermal expansion calculator works out how much a length of solid material or a volume of liquid changes with temperature. It includes typical expansion coefficients for steel, aluminium, copper, brass, ordinary and borosilicate glass, concrete and the low-expansion alloy Invar, and for water, petrol, ethanol and mercury — or you can enter your own coefficient. It gives the change, the new size and the percentage change.

How to Use the Thermal Expansion Calculator

Choose Length (solids) or Volume (liquids).

Choose the material or liquid, or enter a custom coefficient in units of 10⁻⁶ per K.

Enter the starting length or volume and its unit.

Enter the starting and final temperatures in °C. A lower final temperature gives a contraction.

The Formulas

  linear expansion   ΔL = α × L₀ × ΔT
  volume expansion   ΔV = β × V₀ × ΔT
  for solids         β ≈ 3α

  α = linear expansion coefficient (per K)
  β = volume expansion coefficient (per K)
  ΔT = change in temperature (°C or K)

Step-by-Step Examples

A 100 m steel bridge from 0 °C to 40 °C.

  ΔL = 12 × 10⁻⁶ × 100 × 40 = 0.048 m = 48 mm

A 1 m aluminium rod heated from 20 °C to 100 °C.

  ΔL = 23 × 10⁻⁶ × 1 × 80 = 0.00184 m = 1.84 mm

A 25 m steel rail from −10 °C to 40 °C: ΔL = 12 × 10⁻⁶ × 25 × 50 = 0.015 m = 15 mm.

60 litres of petrol warming by 15 °C.

  ΔV = 950 × 10⁻⁶ × 60 × 15 = 0.855 L = 855 mL

Typical Expansion Coefficients

  Solid (α, × 10⁻⁶ per K)        Liquid (β, × 10⁻⁶ per K)
  aluminium          23          ethanol        1,100
  brass              19          petrol           950
  copper             17          water (20 °C)    207
  steel              12          mercury          181
  concrete           12
  ordinary glass      9
  borosilicate glass  3.3
  Invar               1.2

Coefficients vary with temperature and composition; these are typical room-temperature values.

Why Materials Expand

As a material warms, its atoms and molecules vibrate more energetically and, on average, sit a little further apart. In a solid this makes every dimension grow by the same fraction, so the volume grows by about three times the linear fraction. Liquids expand more than solids, because their molecules are less tightly bound, and gases expand far more still. Water is unusual: between 0 and 4 °C it contracts as it warms, which is why ice floats and lakes freeze from the top down.

Engineering for Expansion

Engineers leave room for movement wherever expansion could cause damage. Bridges have expansion joints — interlocking steel fingers or rubber-filled gaps — that open and close with the seasons. Long pipelines include expansion loops or bellows. Concrete roads and pavements are laid in slabs separated by joints. Older railways left small gaps between rails, producing the familiar clickety-clack; modern continuous welded rail is instead laid under tension and anchored firmly so that it can expand and contract without buckling in summer heat.

Useful Uses of Expansion

Thermal expansion is also put to work. A bimetallic strip, two metals with different coefficients bonded together, bends as it warms and was long used in thermostats, kettles and fire alarms. Engineers fit tight parts together by shrink fitting: heating a ring so that it expands, sliding it over a shaft, and letting it cool to grip tightly. Liquid-in-glass thermometers rely on alcohol or mercury expanding far more than the glass tube. Borosilicate glass, used in laboratory glassware and ovenware, expands so little that it resists cracking when heated unevenly.

Expansion in the Home

Thermal expansion is at work around the house. A tight metal jar lid can often be loosened by running it under hot water, because the metal expands more than the glass. Hot-water pipes creak and tick as they warm and cool, sliding slightly against their clips. Central heating systems and hot water cylinders include an expansion vessel to absorb the extra volume of heated water, which would otherwise raise the pressure dangerously. Pouring boiling water into a cold, thick glass can crack it, because the inner surface expands before the outer surface has warmed; that is why ovenware is made from low-expansion borosilicate glass.

Expansion and Temperature Measurement

Many thermometers rely on thermal expansion. In a liquid-in-glass thermometer, the liquid in the bulb expands far more than the glass, pushing a thin thread up a narrow tube where even a small increase in volume produces a visible rise. Dial thermometers in ovens and on barbecues use a coiled bimetallic strip that winds or unwinds as the temperature changes, turning a pointer. The same principle once controlled most household thermostats, switching heating on and off as a strip bent to make or break an electrical contact.

Understanding Your Result

The headline is the change in length or volume, positive for expansion and negative for contraction.

The new size line gives the starting and final sizes and the percentage change.

The coefficient line gives the coefficient used and the temperature change.

When Should You Use This Calculator?

Use it for physics homework on thermal expansion.

Use it to size expansion gaps in building, plumbing and engineering work.

Use it to estimate how much fuel or water will swell in a tank.

Common Mistakes

Forgetting the 10⁻⁶. Coefficients are tiny numbers, usually quoted in millionths per kelvin.

Using the linear coefficient for volume. For solids, β is about three times α.

Ignoring the container. Tanks expand too, but usually much less than the liquid.

Assuming water always expands when warmed. Between 0 and 4 °C it contracts.