How Much Will It Grow When It Gets Hot?
Every solid material changes size with temperature — bridges get expansion joints, pipelines get loops, and rails get gaps for exactly this reason. This free calculator applies the linear expansion formula ΔL = α × L₀ × ΔT and goes further than most: it can solve for any of the four variables — expansion, final length, temperature change, or the coefficient itself.
Pick from 8 built-in materials (or enter a custom α), choose your units, and get the answer with the full working shown. No signup, everything runs privately in your browser.
ΔL = α × L₀ × ΔT
Please check your inputs: length and coefficient must be positive, and ΔT cannot be zero when solving for α.
Change in length
Free-expansion estimate only. If the member is restrained (bolted, welded, embedded), the blocked expansion becomes thermal stress instead — a separate calculation an engineer must check. Coefficients vary by alloy and temperature range; confirm critical designs against supplier data.
How to Use the Calculator
- Choose what to solve for. Most people want ΔL (how much it grows), but you can also find the final length, back out the temperature change from a measured expansion, or determine a material’s coefficient from test data.
- Select the material — its α fills in automatically — or choose Custom and enter your own coefficient.
- Enter the known values in any units; the calculator converts internally and shows every step.
The Formula and Its Rearrangements
ΔT = ΔL ÷ (α × L₀)
α = ΔL ÷ (L₀ × ΔT)
Lfinal = L₀ + ΔL
Worked example: a 10 m carbon-steel beam heated from 20°C to 70°C (ΔT = 50 K). ΔL = 12×10⁻⁸ × 10 × 50 = 0.006 m = 6.0 mm. Final length: 10.006 m.
Coefficients of Linear Expansion (α)
| Material | α (×10⁻⁸/°C) |
|---|---|
| Aluminum | 23.1 |
| Brass | 19.2 |
| Stainless steel | 17.3 |
| Copper | 16.5 |
| Carbon steel / concrete | 12.0 |
| Glass (soda-lime) | 9.0 |
Where Thermal Expansion Matters
- Bridges & railways: expansion joints absorb seasonal movement — a 100 m steel bridge deck can move ~6 cm between winter and summer.
- Piping: long hot-water and steam runs need loops or bellows, or supports take the load.
- Precision work: machining, surveying and optics all correct for temperature because microns matter.
- Homework: the classic physics problem — now with the working shown.
Important caveat
This is the free-expansion result. If the member is restrained — bolted, welded, or embedded at both ends — the blocked expansion becomes thermal stress instead, which can buckle, crack or shear the assembly. That is a separate calculation for an engineer.
Beyond Length: Area and Volume Expansion
Objects expand in every direction at once, so surfaces and volumes follow from the same coefficient. For small temperature changes, the standard approximations are:
Volume: ΔV ≈ 3α × V₀ × ΔT (for an isotropic solid)
Why 2 and 3? Each dimension grows by the factor (1 + αΔT); an area multiplies two such factors and a volume three — and because αΔT is tiny, the cross-terms are negligible. For example, a 2 m² aluminum sheet (α = 23.1×10⁻⁶/°C) warmed by 50°C grows in area by ΔA = 2 × 23.1×10⁻⁶ × 2 × 50 = 0.00462 m² — about 46 cm², roughly the area of a credit card appearing from nowhere. The calculator above solves the linear case; use these extensions when a hole, a plate or a tank volume is what actually matters.
Frequently Asked Questions
What is the thermal expansion formula?
ΔL = α × L₀ × ΔT, where ΔL is the change in length, α the material’s coefficient of linear expansion, L₀ the original length, and ΔT the temperature change in °C or K.
Do materials shrink when cooled?
Yes — a negative ΔT gives a negative ΔL, i.e. contraction. The calculator handles cooling automatically; just enter a negative temperature change.
Why do bridges have expansion joints?
Because the deck genuinely moves. A 100-meter steel span warming 50°C grows about 6 cm — without joints, that movement would crack the deck or shear its supports.
Is the coefficient the same in °F?
The α values are per °C (same as per kelvin). For a ΔT in °F, convert first: Δ°C = Δ°F × 5/9. The calculator does this conversion for you.
Can I find an unknown material’s coefficient?
Yes — set “Solve for” to Coefficient, enter the measured length change, original length and temperature change, and the calculator rearranges the formula to α = ΔL ÷ (L₀ × ΔT).
Does thermal expansion apply to liquids and gases too?
They expand as well, but by volume rather than length — this calculator covers linear expansion of solids only.
What are the formulas for area and volume expansion?
For an isotropic solid, area grows by ΔA ≈ 2α × A₀ × ΔT and volume by ΔV ≈ 3α × V₀ × ΔT, where α is the same linear coefficient used for length. The factors 2 and 3 simply count the dimensions being multiplied, and the approximations hold whenever αΔT is small — which covers almost all everyday engineering.
Final Thoughts
Thermal expansion is easy to overlook until it causes real trouble — a buckled rail, a cracked tile bed, a jammed assembly. The math takes ten seconds; the rework takes ten days. When in doubt, leave the joint.
Try our concrete block calculator for masonry planning.