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How much does a dimension change with temperature?

A fit at assembly temperature can change in operation. Check both the dimensional change and which locations can move.

Free thermal expansion of a bar: original length above, expanded length below with a common left reference and exaggerated length change.LT₀, αT₀ + ΔTΔLLeft reference
Free expansion of a bar referenced at its left end: original length L above, changed length below. Red ΔL is exaggerated. The left end is the positional reference; the right end can move axially.

What you will understand

  • Separate temperature from temperature difference
  • Read expansion, contraction and differential movement
  • Distinguish free movement from restraint

Blue: defined conditions · Red: calculated quantities. Diagrams are schematic.

  • L: length at reference temperature
  • α: linear expansion coefficient, ΔT: temperature difference
  • ΔL: length change (negative for cooling)

The examples below are illustrative. Each example button loads its fixed values, units and mode. Ordinary calculator links do not load an example.

Define reference length and temperature change

L is the length at reference temperature T₀. Enter ΔT=T−T₀. From 20°C to 60°C gives +40; from 20°C to 0°C gives −20.

  • Actual part temperature during assembly/measurement and use
  • Length direction and positional reference

Check coefficient and freedom to move

Choose α for the material, condition, direction and temperature range. Numeric values in μm/(m·K) differ by a factor of a million from 1/K. This is a uniform-temperature, free, linear expansion model.

For practical review

With end restraint or contacting parts, free expansion alone does not determine actual displacement or thermal stress. Temperature gradients, contact, joint slip, buckling, polymer anisotropy and creep require separate assessment.

ΔL=αLΔT, final L′=L+ΔL

Compare heating and cooling

For positive α, heating lengthens and cooling shortens the part. Check the sign and the motion relative to nearby components.

Example: heat a 1 m part from 20°C to 60°C

Inputs

  • L=1000 mm, α=12 μm/(m·K) (illustrative)
  • ΔT=+40 K (same interval as 40°C)

Results

  • Length change ΔL=+0.480 mm
  • Final length L′=1000.480 mm
  • With ΔT=−20 K, ΔL=−0.240 mm

α=12 is not a guaranteed product value. This example assumes constant α and free expansion; it does not calculate restrained thermal stress or deformation.

Load the fixed values, units and mode for this illustration. Then edit them for your conditions.

Check differential movement and clearance

For equal-length parts with the same reference end and temperature change, relative end movement is the difference between their free expansions. Whether a gap opens or closes depends on the arrangement.

  • Example: α₁=23, α₂=12 μm/(m·K), L=1 m, ΔT=40 K → difference 0.440 mm
  • Combine with assembly tolerances, initial gap, references and temperature extremes

For common L and ΔT, differential movement=(α₁−α₂)LΔT

Keep a review checklist

This checklist is a personal reminder, not a safety score or an automatic approval. It is not sent or saved.

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Reference information and illustrative calculations. This content does not guarantee suitability or safety of a design. Confirm the actual materials, component specifications and operating conditions.