§1 — Why propagate uncertainties?
The pressure returned by every optical or diffraction gauge is derived from a measured quantity (a wavelength, a Raman shift, a unit-cell volume). Each measurement carries an uncertainty; the calibration itself carries an uncertainty; the sample environment (temperature, non-hydrostatic stress) contributes further. A pressure quoted as "P = 42 GPa" without a σ(P) hides all of this. This tool shows σ(P) for the four main gauge families of Wave Fit, and — more importantly — decomposes it into its individual contributions, so the dominant source becomes visible.

§2 — The formula
For P = f(x₁, x₂, …), assuming uncorrelated inputs, Gaussian propagation gives: σ(P)² = Σᵢ (∂P/∂xᵢ)² · σ(xᵢ)² Each squared term is a variance contribution. When one dominates, it is the one to reduce first. For the ruby and Sm:YAG power-law scales P = (A/B)·[(λ/λ₀)^B − 1], the wavelength derivative is analytical: ∂P/∂λ = A·(λ/λ₀)^(B−1) / λ₀. For the diamond Raman (Occelli 2003) ω = 1333.0 + 2.83·P − 3.65×10⁻³·P², the inverse gives ∂P/∂ω = 1/(2.83 − 7.30×10⁻³·P). For BM3 EOS gauges (Au, Pt, MgO, NaCl…) the volume derivative is computed numerically from the analytic P(V/V₀) at the working point.

§3 — Typical σ values in the literature
· σ(λ) — ruby R1: 0.02–0.05 nm for a well-calibrated spectrometer (Klotz et al. 2009: R1 position ±0.1 cm⁻¹ ≈ ±0.005 nm at 694 nm); routine work: 0.03 nm; noisy or fluorescence-perturbed conditions: 0.1 nm.
· σ(λ) — Sm:YAG: comparable to ruby (~0.03 nm) since the lines are equally sharp; broaden slightly at high T (Hess & Schiferl 1990).
· σ(ω) — Raman diamond edge: 1–2 cm⁻¹ typical (Akahama & Kawamura 2006); high-P edge asymmetry may push σ(ω) up to 3–5 cm⁻¹ above 200 GPa.
· σ(V/V₀) — XRD gauges: 0.1–0.5 % single-crystal, 0.5–1 % on powder rings (Fei et al. 2007 report typical 0.3 % on Au / MgO).
· σ(T): 1 K in stable thermostated setups, 5–10 K under laser heating gradients.

§4 — Non-hydrostatic contribution (medium-dependent)
When the pressure-transmitting medium leaves its hydrostatic regime, a deviatoric stress appears and the extracted pressure becomes anisotropic. Klotz et al. (2009) report macroscopic uniaxial stress σ(P) reaching, above the hydrostatic limit: He 0.15 GPa at 40 GPa, Ne 0.20 GPa at 20 GPa, N₂ 0.50 GPa at 10 GPa, Ar 0.80 GPa at 10 GPa, MeOH:EtOH 4:1 ≈ 1 GPa above 10 GPa. This tool adds the selected medium's hydrostaticity term in quadrature with the wavelength/volume/frequency contributions.

§5 — How to read the result
Each gauge card shows σ(P) as a total, then breaks it down as "λ contribution", "medium contribution", "thermal contribution". Look at the dominant term. If λ dominates → improve spectrometer calibration or acquisition time. If the medium dominates → change PTM or admit the systematic offset. If the calibration itself dominates → cite a σ_cal when quoting the pressure. The four gauges are compared side by side for a single set of experimental inputs, revealing which is the most reliable in your conditions.