Select a model, provide coefficients and temperatures, then enter the initial size. The calculator returns the change, final value, strain, and percent change.
- Linear: ΔL = α L0 ΔT, and Lf = L0 + ΔL
- Area: ΔA = β A0 ΔT, and Af = A0 + ΔA
- Volume: ΔV = γ V0 ΔT, and Vf = V0 + ΔV
- Approximations: β ≈ 2α and γ ≈ 3α for isotropic solids.
- Strain: ε = ΔL / L0 (similarly for area and volume ratios).
- Select the expansion model: length, area, or volume.
- Enter the linear coefficient α. Keep auto coefficients enabled for typical solids.
- Choose temperature inputs and set the correct unit.
- Provide the initial length, area, or volume and its unit.
- Press Calculate to see results above the form.
- Use Download CSV or Download PDF for reports.
| Case | Model | Coefficient | Initial | ΔT | Change | Final |
|---|---|---|---|---|---|---|
| 1 | Linear | α = 12e-6 1/C | L0 = 2.00 m | 100 C | ΔL = 0.0024 m | Lf = 2.0024 m |
| 2 | Area | β = 24e-6 1/C | A0 = 1.50 m2 | 80 C | ΔA = 0.00288 m2 | Af = 1.50288 m2 |
| 3 | Volume | γ = 36e-6 1/C | V0 = 0.50 m3 | 60 C | ΔV = 0.00108 m3 | Vf = 0.50108 m3 |
1) Why thermal expansion matters
Thermal expansion is the size change caused by temperature. Millimeters can matter: rails can buckle, pipe supports can bind, and tight fits can seize. This calculator estimates movement so you can set gaps, choose joints, and check strain early.
2) Inputs used in the calculations
Select a model, enter the initial value, an expansion coefficient, and the temperature change. You may use T1 and T2 or enter ΔT directly. Choose units and significant digits to match your drawings and reports.
3) Typical coefficients for common materials
For many solids near room temperature, linear coefficients are in the range of 1–30×10-6 1/°C. Invar is about 1×10-6, common glass ~9×10-6, concrete ~10×10-6, steel ~12×10-6, copper ~17×10-6, and aluminum ~23×10-6. Polymers can be much higher (often 50–200×10-6).
4) Temperature change and reference units
Expansion depends on ΔT, not the absolute temperature scale. A change of 1 K equals a change of 1 °C, while a 1 °F change equals 5/9 °C. For outdoor equipment, ΔT values such as 30–80 °C are common; for industrial heaters, ΔT can exceed 150 °C. Use realistic service temperatures for dependable estimates.
5) Linear, area, and volume models
Linear expansion uses ΔL = α·L0·ΔT. For isotropic solids, area and volume changes are approximated by β ≈ 2α and γ ≈ 3α, giving ΔA = β·A0·ΔT and ΔV = γ·V0·ΔT. These relations are accurate for small strains and uniform heating.
6) Engineering checks: strain and clearance
The calculator reports strain ε = ΔL/L0, a key value for stress checks when expansion is restrained. As a quick example, a 10 m steel member with ΔT = 60 °C and α = 12×10-6 expands by 7.2 mm (ε = 7.2×10-4). Clearances, slots, and expansion joints should exceed expected movement plus tolerance.
7) Typical applications and practical data
Use cases include pipe runs, bridges, machine frames, glazing, and precision stages. Long members amplify movement: 50 m of aluminum at ΔT = 40 °C expands about 46 mm. For dissimilar materials, compare movements to protect fasteners, seals, and adhesives.
8) Interpreting results for documentation
Use the change and final outputs to set fit-up gaps and end-stops; percent change helps compare sizes. Exported reports capture the model, coefficient, and ΔT for traceability. If coefficients vary with temperature, calculate in smaller ranges using updated values.
1) What is the difference between α, β, and γ?
α is the linear expansion coefficient. β is the area coefficient and is often about 2α for isotropic solids. γ is the volume coefficient and is often about 3α. Use measured values when material data provides them.
2) Can I enter temperatures in Fahrenheit?
Yes. Select °F and enter T1 and T2, or enter ΔT in °F. The calculator converts differences correctly using 5/9 to match °C-equivalent changes.
3) Why are β and γ auto-filled?
For many isotropic solids and small strains, β ≈ 2α and γ ≈ 3α. Auto-filling reduces input errors when only α is known. Disable auto mode if your material datasheet lists β or γ explicitly.
4) Is this suitable for liquids or gases?
The formulas here match solids well under uniform heating. Liquids and gases use volumetric expansion relationships that can be strongly temperature-dependent and pressure-dependent. Use verified volumetric data for fluids and enter γ directly if appropriate.
5) What if the coefficient changes with temperature?
Many coefficients vary across wide temperature ranges. For better accuracy, compute in segments (for example, 20–80 °C and 80–140 °C) using updated coefficients for each segment, then add the changes.
6) What units are supported?
Length supports m, cm, mm, in, and ft. Temperature supports °C, K, and °F. Area and volume fields accept numeric values; enter them in your chosen unit system and keep it consistent for interpretation and reporting.
7) How accurate are the results?
Accuracy depends on coefficient quality, uniform temperature assumptions, and whether the material is isotropic. For typical engineering estimates with small strains, results are reliable. For precision designs, validate against certified material data and operating conditions.