MCPCalc

Thermal Expansion Calculator

Calculate linear or volumetric thermal expansion for any material — with material presets, reverse-solve mode, and instant unit conversion.

Scratchpad (not saved)

Select a material to auto-fill α, or choose Custom to enter manually.

m or m³

For linear mode enter length in m; for volumetric mode enter volume in m³.

Only used when Material Preset = Custom. Enter α in units of 10⁻⁶ per °C.

°C

Use negative values for cooling. For reverse-solve, this field is ignored.

m

The expansion you want to achieve or limit. Only used in reverse-solve mode.

What This Calculator Does

Thermal expansion occurs when a material changes length or volume in response to a temperature change. This calculator handles linear expansion (ΔL = α·L₀·ΔT), volumetric expansion (ΔV = γ·V₀·ΔT), and reverse-solve — finding the temperature rise needed to produce a target expansion. Material presets are built in for the most common engineering materials.

It combines Calculation Mode, Material Preset, Original Length / Volume (L₀ or V₀), Custom α (×10⁻⁶ /°C) to estimate Length Change (ΔL), Final Length, Expansion %.

Formula & Method

Linear thermal expansion: ΔL=α⋅L0⋅ΔT\Delta L = \alpha \cdot L_0 \cdot \Delta T where α\alpha is the coefficient of linear thermal expansion (per °C), L0L_0 is the original length, and ΔT\Delta T is the temperature change. Final length: L=L0+ΔLL = L_0 + \Delta L. Volumetric expansion uses: ΔV=γ⋅V0⋅ΔT\Delta V = \gamma \cdot V_0 \cdot \Delta T where for isotropic solids γ=3α\gamma = 3\alpha. Reverse solve for required temperature change: ΔT=ΔLα⋅L0\Delta T = \frac{\Delta L}{\alpha \cdot L_0}

Notation used in the formulas: RR = Length Change (ΔL); x1x_{1} = Calculation Mode; x2x_{2} = Material Preset; x3x_{3} = Original Length / Volume (L₀ or V₀); x4x_{4} = Custom α (×10⁻⁶ /°C); x5x_{5} = Temperature Change (ΔT); x6x_{6} = Target ΔL (reverse-solve only).

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Worked Examples

Steel pipe at 80 °C rise (Linear)

A DN100 steel pipe, original length L₀ = 12 m, heated from 10 °C to 90 °C (ΔT = 80 °C). α_steel = 12 × 10⁻⁶ /°C ΔL = 12 × 10⁻⁶ × 12 × 80 = 0.01152 m = 11.52 mm Final length L = 12.01152 m Expansion as % of original = 0.096%

Aluminium rod reverse-solve

An aluminium rod (α = 23 × 10⁻⁶ /°C) must not expand more than 1.5 mm over a 2.5 m span. ΔT = ΔL / (α × L₀) = 0.0015 / (23 × 10⁻⁶ × 2.5) = 26.1 °C The rod can safely withstand up to a 26 °C temperature rise.

Common Mistakes

  • Using the volumetric coefficient γ for linear calculations. For isotropic solids γ = 3α.
  • Mixing units — α is per °C, temperature change must be in °C (or K; the difference is the same).
  • Forgetting that ΔT is the change, not the absolute temperature.

Inputs Used

  • Calculation Mode: Used directly in the calculation.
  • Material Preset: Select a material to auto-fill α, or choose Custom to enter manually.
  • Original Length / Volume (L₀ or V₀): For linear mode enter length in m; for volumetric mode enter volume in m³.
  • Custom α (×10⁻⁶ /°C): Only used when Material Preset = Custom. Enter α in units of 10⁻⁶ per °C.
  • Temperature Change (ΔT): Use negative values for cooling. For reverse-solve, this field is ignored.
  • Target ΔL (reverse-solve only): The expansion you want to achieve or limit. Only used in reverse-solve mode.

See Also

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