Thermal expansion compensation calculator

Measurements referenced to the 20 °C standard reference temperature. The differential case — part and gage expanding differently — is the primary mode. Companion to the three-wire, pre-plate, TAR/TUR, and process capability calculators.

Calculation aid. Material constants are nominal. Every expansion and thermal property in this page is a widely known nominal value that varies with alloy, temper, heat treatment, grade, and temperature range. They are provided as editable starting points only. For any critical measurement, take the coefficient from your material certificate or supplier data and enter it. This page assumes uniform temperature within each body, a coefficient constant over the range in use, and free unconstrained expansion; none of those hold exactly. Applying a thermal correction to a measurement result is a decision governed by your quality system and, where relevant, your accreditation scope — this page makes no determination about that. No warranty of any kind is made as to accuracy, completeness, or fitness for a particular purpose, and no liability is accepted for any loss or damage arising from its use. Version 1.0 · All values computed, none transcribed · Last reviewed August 2026

Measurement conditions

Identification, optional

Part or characteristic

Record reference

Date

Mode

Differential part and gage Single body

Length and units

Nominal length or diameter

Length units

Temperature units

Coefficient units

Display decimals

Part

Material

Coefficient

Nominal. Overwrite with certificate data.

Temperature

Gage or standard

Material

Coefficient

Nominal. Overwrite with certificate data.

Temperature

Tolerance and observed reading

Tolerance span

Total span, not ±. Used for the percentage and the thermal limits.

Fraction of tolerance for the limits

Observed reading, optional

Enter what the gage actually indicated to get the value referenced to 20 °C.

Uncertainty contribution from thermal effects

Input uncertainties, standard uncertainties at k = 1

u(α) part

u(α) gage

u(T) part, °C

u(T) gage, °C

Part and gage are the same material The two coefficients are then one quantity used twice, not two independent quantities, and the alpha terms collapse to a single term driven by the difference in temperature. Ignored if the two coefficients you entered do not match.

Both temperatures read with the same instrument The systematic part of the thermometer error is then common to both readings and acts on the difference of the coefficients — which is exactly zero when the materials match.

Both treatments are always shown side by side so the effect of the assumption is visible. Independent is the conservative default.

Soak time estimate

Body and environment

Material

Shape

Diameter, mm

Length, mm

Height, mm

Air movement

Dimensions in millimetres regardless of the length units chosen above. The convective coefficient is the largest single lever in this estimate, which is why it is a selection rather than a fixed assumption.

Formulas and material constants

Formulas

Indicated value, differential	`M = L₂₀ (1 + α_pΔT_p) / (1 + α_gΔT_g)`
Referenced to 20 °C	`L₂₀ = M (1 + α_gΔT_g) / (1 + α_pΔT_p)`
Single body	`L₂₀ = M / (1 + αΔT)`
First-order form, shown for comparison only	`e ≈ L(α_pΔT_p − α_gΔT_g)`
Uniform departure limit	`\|T − 20\| = budget / (L \|α_p − α_g\|)`
Body drift limit	`budget / (L α)` for each body
Uncertainty, independent	`√[ (LΔT_pu_αp)² + (LΔT_gu_αg)² + (Lα_pu_Tp)² + (Lα_gu_Tg)² ]`
Common coefficient term	`(L(ΔT_p − ΔT_g) u_α)²`
Common thermometer term	`(L(α_p − α_g) u_T)²`
Soak time constant	`τ = ρ c L_c / h`, `L_c = V/A`
Time to fraction f	`t = τ ln(1/(1−f))`
Biot number	`Bi = h L_c / k`, lumped model valid below about 0.1
Coefficient conversion	`µin/in/°F × 1.8 = µm/m/°C`

Nominal material constants

Material	α µm/m/°C	α µin/in/°F	ρ kg/m³	c J/kg·K	k W/m·K

These are nominal figures, not specifications. Expansion coefficients vary with alloy, temper, heat treatment, grade, and temperature range — the spread within a single material family can exceed ten percent, and for stainless and carbide it is wider than that. Every value here is editable and every one should be replaced with certificate or supplier data for a critical measurement. The thermal properties used for soak time are textbook nominals and are only ever used for an order-of-magnitude planning estimate.

Not covered

Temperature gradients within a body. Coefficient variation with temperature. Anisotropic expansion. Radiative exchange. Conduction into fixtures, benches, or hands. Measurement taken during stabilization rather than after it. Distortion from differential expansion within an assembly. Humidity effects on granite. Any determination of whether a thermal correction may be applied under a particular quality system or accreditation scope.