Enrichment · STEM Explorations · Engineering

Why gutters
have slip joints
and bridges gaps.

Choose a material, type the length and the coldest and hottest temperatures it will see. The calculator shows how much each part grows and shrinks, how big a gap to leave, and why two materials joined together fight each other.

Work out the changeWhat you get

The thermal expansion calculator

The worked example is made up: a gutter, a drain pipe and a fence rail along a school garden. Nothing you type leaves this browser.

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What you get

Enrichment · STEM ExplorationsFree

What you finish with
The change in length of each part over its temperature swing, the gap to leave, the approximate change in volume and the steps. It prints as a summary and downloads as a spreadsheet.
Who it is for
Middle and high school physical science students, engineering and design classes, science teachers and families doing build projects.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Metric or US units. Up to 20 parts. Prints a summary; downloads a spreadsheet (.csv); export and import a file.
Access
Free. No account, no sign-in and nothing to install. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The STEM Explorations space in Caveat Enrichment.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Name the project and choose units.
  2. Add each part with its material, length and temperature range.
  3. Choose Other to type a coefficient from a data sheet.
  4. Read the change in length and the gap to leave.
  5. Print the summary or download the spreadsheet.

Work out the change

How the change is worked out

Coefficient, length, swing.

The worked example: the aluminum gutterα, aluminum0.0000231per °C, per meter× length× 12 mthe whole gutter× swing× 55°C−10°C to 45°CChange15.2 mm23.1 × 12 × 55 ÷ 1,000The worked example: the aluminum gutterα, aluminum0.0000231per °C, per meter× length× 12 mthe whole gutter× swing× 55°C−10°C to 45°CChange15.2 mm23.1 × 12 × 55 ÷ 1,000
Each meter of aluminum grows 0.0231 mm for every degree; twelve meters across a 55-degree swing grow 15.2 mm.

The arithmetic

Most solids grow by a nearly fixed fraction of their length for each degree of warming, the coefficient of linear expansion, α. Multiply α by the length and by the temperature swing to get the change in length. In Fahrenheit the coefficient is 1.8 times smaller per degree. A solid’s volume grows about three times as fast as any one length.

Using it in a build

The figures are typical; alloys, grades, moisture in wood and very hot or cold conditions change them. Dark surfaces in sun can run far hotter than the air, so use the temperature of the part, not the forecast. Where two materials are fastened together, the difference in their growth is what cracks joints and bends bimetal strips.

Sources

  1. OpenStax. College Physics 2e (2022), section 13.2, Thermal Expansion of Solids and Liquids, table of coefficients (openstax.org).
  2. CRC Handbook of Chemistry and Physics, thermal expansion of metals and alloys and of common materials.
  3. U.S. Department of Agriculture, Forest Products Laboratory. Wood Handbook (FPL-GTR-282, 2021), chapter 5: thermal expansion of wood parallel to grain.
  4. NIST Special Publication 811, Guide for the Use of the International System of Units (2008): temperature intervals and length conversions.

The worked example is made up. Coefficients are typical values; use a supplier’s data for real construction. Your figures stay in this browser. Support: team@caveatacademic.com.