Thermal Expansion Calculator (linear & volume)

Understanding the thermal expansion calculator — concept and principle

Most materials grow when heated and shrink when cooled. This calculator finds how much a bar, pipe, rail or beam changes in length for a given temperature change, its new length, and the approximate change in volume. Engineers use these numbers to size expansion joints in bridges and pipelines, leave gaps in flooring and cladding, and check fits between parts made of different metals.

Only 4.8 mm over 10 m, but enough that bridges and rails need expansion gaps.

How it is calculated

Length change: ΔL = α × L₀ × ΔT, with α entered in units of 10⁻⁶ per K, L₀ in metres, and the result shown in millimetres.
New length: L = L₀ × (1 + αΔT).
Volume change: ΔV/V ≈ 3αΔT, shown as a percentage.

Typical α values (×10⁻⁶/K): steel about 12, concrete 10–12, copper about 17, aluminium about 23.

The principle

Heating makes atoms vibrate with larger amplitude. Because the force between atoms is not symmetric (easier to pull apart than to push together), the average spacing increases slightly as vibration grows, so the whole object lengthens. For small temperature changes this growth is very nearly proportional to both the original length and the temperature change, which gives ΔL = αL₀ΔT. An isotropic solid expands this way in all three directions, so its volume becomes (1 + αΔT)³ ≈ 1 + 3αΔT; the squared and cubed terms are negligible because αΔT is tiny.

Worked example

Inputs: L₀ = 10 m, α = 12 × 10⁻⁶ /K (steel), ΔT = 40 K.
ΔL = 12 × 10⁻⁶ × 10 × 40 = 0.0048 m = 4.8 mm.
New length = 10 × (1 + 0.00048) = 10.0048 m.
Volume change = 3 × 12 × 10⁻⁶ × 40 = 0.00144 = 0.14% (0.144%).

Each point is the calculator re-run with only “Original length (m)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Original length (m)	Length change (mm)
2.5	1.2
5	2.4
7.5	3.6
10	4.8
12.5	6
15	7.2
20	9.6

How to read the result

4.8 mm over 10 m sounds small, but if the steel is prevented from moving, the expansion becomes stress. For a fully restrained bar, σ = E·α·ΔT; with E ≈ 200 GPa for steel this example gives roughly 96 MPa, a large fraction of the yield strength of ordinary structural steel. That is why long structures need joints, rollers or loops. Pairs of materials with different α, such as aluminium on steel, will slide or bow as temperature changes.

Common mistakes

Entering α as 0.000012 when the field expects 12 (it is already scaled by 10⁻⁶).
Using the seasonal average instead of the full range between coldest and hottest conditions.
Applying 3α to liquids, whose volume coefficient is measured directly and is not linked to a linear α.

Keep in mind: These are linear, unrestrained estimates. α varies with alloy and temperature, and composite or anisotropic materials behave differently. Real expansion joints and structural designs must follow local codes and be checked by a qualified engineer.

Frequently asked questions

How much does a 30 m steel rail expand from −10 °C to 40 °C?

ΔT = 50 K, so ΔL = 12 × 10⁻⁶ × 30 × 50 = 0.018 m, about 18 mm.

Why do glass jars crack in hot water?

The outside heats and expands before the inside, creating stress across the thickness; glass with low α, like borosilicate, resists this better.

Do any materials shrink when heated?

A few do over certain ranges, for example water between 0 °C and 4 °C and some special ceramics.

Sources: D. Halliday, R. Resnick and J. Walker, Fundamentals of Physics, Wiley, section on thermal expansion · CRC Handbook of Chemistry and Physics, CRC Press (thermal expansion coefficients)

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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