Thermal Expansion Calculator
Most materials expand when heated and contract when cooled. This calculator computes linear and volumetric thermal expansion using the expansion coefficients for common materials, helping engineers account for temperature-induced size changes.
Advertisement
Calculator
See your Thermal Expansion Calculator results
Enter your email to unlock results — free forever.
No spam, ever. Unsubscribe at any time.
Advertisement
Formula
ΔL = α × L₀ × ΔT
Linear expansion ΔL = α × L₀ × ΔT, where α is the linear thermal expansion coefficient (per °C), L₀ is the original length, and ΔT is the temperature change. Volumetric expansion ΔV ≈ 3α × V₀ × ΔT. Common α values: steel 12×10⁻⁶/°C, aluminum 23×10⁻⁶/°C, concrete 12×10⁻⁶/°C, glass 9×10⁻⁶/°C.
How to use the Thermal Expansion Calculator
- 1
Enter your original length
Value should be in m.
- 2
Enter your temperature change (δt)
Value should be in °C.
- 3
Enter your linear expansion coefficient (×10⁻⁶/°c)
Value should be in ×10⁻⁶/°C.
- 4
Read your results instantly
Results update in real time as you type.
Advertisement
Why thermal expansion matters in engineering
Every material expands when heated and contracts when cooled. For small objects over small temperature ranges, this is negligible. For large structures over wide temperature ranges, it is significant and must be designed for.
Bridge expansion joints are the classic example: a 500 m steel bridge expands about 0.5 m × 12×10⁻⁶/°C × 40°C (summer/winter range) = 0.24 m = 24 cm of seasonal expansion. Without expansion joints, the bridge would buckle in summer and crack in winter. Rail buckling ('sun kink') occurs when continuous welded rail without expansion relief gets too hot and the track snaps sideways.
Expansion coefficients of common materials
Linear thermal expansion coefficients (α, ×10⁻⁶ per °C): - Invar (nickel alloy): 1.2 — used for precision instruments requiring dimensional stability - Glass (borosilicate/Pyrex): 3.3 — low expansion for thermal shock resistance - Concrete: 12 — matched to steel reinforcing bars (also ~12) to prevent cracking - Steel: 11-13 - Copper: 17 - Aluminum: 23 — highest among structural metals, relevant for aircraft and electronics - Rubber: ~200 — elastomers expand much more
Concrete and steel having nearly identical expansion coefficients is fortunate and essential for reinforced concrete structures.
Advertisement
Thermal expansion in everyday life
The gap between railroad tracks, the curved expansion loops in steam pipelines, the bimetallic strips in thermostats, the gaps between sidewalk slabs — all compensate for thermal expansion. Power lines are strung with sag in summer so they don't snap tight in winter. Glass thermometers and mercury barometers exploit differential expansion of liquids vs. glass.
Bimetallic strips — two metals bonded with different α values — bend when temperature changes. Brass (α ≈ 19) bonded to steel (α ≈ 12) bends toward the steel side when heated. This mechanical response powers thermostats, fire detectors, and circuit breakers.
Tips & Insights
Steel and concrete have matched expansion
Both have α ≈ 12×10⁻⁶/°C, which is why reinforced concrete works — they expand and contract together, preventing cracking at the interface.
Temperature change can be negative
For contraction (cooling), enter a negative ΔT. The expansion will be negative, giving a shorter final length.
Volumetric ≈ 3× linear
For isotropic materials, volumetric expansion coefficient β ≈ 3α. A cube expands similarly in all three dimensions.
Worked Examples
Steel bridge girder
ΔL = 100 × 12×10⁻⁶ × 40 = 0.048 m = 4.8 cm. A 100 m girder grows nearly 5 cm from winter to summer.
Aluminum engine block
ΔL = 0.5 × 23×10⁻⁶ × 150 ≈ 0.00173 m = 1.73 mm. Cylinder bore grows ~1.7 mm when engine reaches operating temperature.
Advertisement
Frequently Asked Questions
What is thermal expansion?
The increase in size of a material when its temperature rises. Most materials expand when heated due to increased atomic vibration spreading atoms further apart.
What is the thermal expansion coefficient?
A material-specific constant (α) expressing how much length changes per degree of temperature change per unit length. Unit: 1/°C or 10⁻⁶/°C (ppm/°C).
Does water expand when heated?
Mostly yes — but water is anomalous between 0°C and 4°C where it contracts as temperature rises. Above 4°C it expands normally. This is why ice floats and why water pipes burst when frozen.
What is Invar and why is it used?
Invar (64% iron, 36% nickel) has α ≈ 1.2×10⁻⁶/°C — nearly zero expansion. Used in precision instruments, clocks, telescope mirrors, and CRT shadow masks where dimensional stability over temperature is critical.
Why do expansion joints exist in bridges?
Bridges can change temperature by 40-60°C seasonally. Without joints, thermal expansion forces buckle or crack the structure. Joints allow the bridge to expand and contract freely.
Advertisement