What this linear expansion calculator does
This calculator estimates how much a solid object changes length when temperature changes. It uses the standard engineering relation for linear thermal expansion and gives you:
- Temperature change, ΔT
- Length change, ΔL
- Final length, Lf
- Percent change in length
Linear expansion formula
ΔL = α · L₀ · ΔT
Where:
- ΔL = change in length
- α = coefficient of linear thermal expansion
- L₀ = original length
- ΔT = temperature change =
T₂ - T₁
A positive ΔT means heating (usually expansion), while a negative ΔT means cooling (usually contraction).
How to use the calculator
Step 1: Choose material (or custom)
Select a material to auto-fill a typical α value. If your project has a measured value from a datasheet, choose Custom and type it directly.
Step 2: Enter dimensions and temperatures
Provide the initial length and choose the unit you want the result reported in. Then enter starting and ending temperatures. This page assumes °C for temperature values.
Step 3: Calculate and interpret
Click Calculate. If ΔL is positive, the part expands. If ΔL is negative, it contracts. For long pipes, rails, machine shafts, and structural members, even small values can be important.
Typical coefficient values (quick reference)
Typical room-temperature values used in this tool:
- Aluminum: 23 × 10-6/°C
- Brass: 19 × 10-6/°C
- Copper: 16.5 × 10-6/°C
- Steel (carbon): 12 × 10-6/°C
- Stainless steel: 17 × 10-6/°C
- Concrete: 12 × 10-6/°C
- Glass (soda-lime): 9 × 10-6/°C
- Titanium: 8.6 × 10-6/°C
- PVC: 52 × 10-6/°C
- Invar: 1.2 × 10-6/°C
Real values vary with temperature range, alloy composition, moisture, and manufacturing method. For critical design work, always use material-specific datasheet values.
Worked example
Suppose a 10 m steel beam warms from 20°C to 80°C. For steel, α ≈ 12 × 10-6/°C.
ΔT = 80 - 20 = 60°C
ΔL = (12 × 10-6/°C) × 10 m × 60°C = 0.0072 m = 7.2 mm
The beam gets about 7.2 mm longer. If endpoints are constrained, thermal stress can also develop.
Design notes and limitations
- This is a linear model and is best for moderate temperature intervals.
- It assumes uniform temperature through the object.
- It does not compute thermal stress in restrained members.
- It does not include nonlinear material behavior at extreme temperatures.
Common applications
- Bridge expansion joints
- Railway tracks and gaps
- Piping supports and loops
- Precision instrument calibration
- Manufacturing tolerance stack-up under temperature drift
Final takeaway
Thermal expansion seems small, but across long lengths and changing environments it can become a major design factor. Use this linear expansion calculator as a fast planning tool, then validate against project standards and material data.