MotionLab

Thermal Expansion Calculator

Why bridges have expansion joints and railroad tracks have small gaps — materials grow and shrink with temperature.

Original length (m)

Expansion coefficient (per °C)

Temperature change (°C)

Length change (m)

0.004

ΔL = L · α · ΔT

What you entered

Original length (m): 10Expansion coefficient (per °C): 0.000012Temperature change (°C): 30

1
ΔL = L × α × ΔT
10 × 0.000012 × 30= 0.0036 (length units)

Result

Length change (m): 0.004

A 10m length heated by 30°C expands by 0.004m.

Linear thermal expansion by material and temperature rise

Expansion is the original length times the coefficient times the temperature change.

Length (m)	Coefficient (per K)	Temp change (K)	Expansion (m)	Material
1	1.2e-5	100	0.001200	Steel
1	1.7e-5	100	0.001700	Copper
10	1.2e-5	50	0.006000	Steel
50	1.2e-5	30	0.018000	Steel rail
100	2.3e-5	40	0.092000	Aluminium span

The last row is why expansion joints exist: a 100 m aluminium span grows 9.2 cm over a 40 degree swing, and a bridge without room to move would buckle or tear its supports apart. Row four is the railway case - 1.8 cm on a 50 m rail, which is why continuous welded track is pre-stressed and why old track had gaps. Aluminium expands about twice as much as steel for the same rise, so joining dissimilar metals in something that gets hot builds in stress. The effect is linear in all three inputs.

Why expansion joints exist

A steel bridge or railroad track can change length noticeably between a cold winter night and a hot summer day — expansion joints and small gaps are engineered in specifically to absorb this movement without buckling or cracking the structure.

Different materials expand at different rates

The expansion coefficient (α) varies significantly by material — this is why bimetallic strips (two different metals bonded together) bend predictably with temperature, a mechanism used in old-style thermostats and circuit breakers.

Frequently asked questions

A 50 m steel bridge heats from -20°C to 40°C in summer. How much does it expand?

ΔL = L × α × ΔT = 50 × 12×10⁻⁶ × 60 = 0.036 m = 36 mm. That's about 1.4 inches — enough to buckle the bridge without expansion joints. Engineers design gaps at least this wide at each end.

Why do railroad tracks have small gaps between rails?

Steel rails expand in heat: a 12 m rail at α = 12×10⁻⁶/°C with a 50°C temperature swing expands by ΔL = 12 × 12×10⁻⁶ × 50 = 7.2 mm. Without gaps, the rails would buckle. Modern continuous-welded rail is pre-stressed to handle expansion without gaps.

Which materials expand the most and least?

High expansion: aluminum (23×10⁻⁶/°C), brass (19×10⁻⁶/°C). Low expansion: steel (12×10⁻⁶/°C), Invar alloy (1.2×10⁻⁶/°C — invented specifically for precision instruments). Glass: 3-9×10⁻⁶/°C, which is why Pyrex (low α) resists thermal shock better than regular glass.