Methodology & Verification
Correctness is the whole point of this site, so here is exactly how it is established — and the reference tables our automated tests assert against, published in full and recomputed at build below.
How every formula is checked
- Every constant is cross-checked against at least two primary sources before it is used.
- Each formula is computationally validated against its phase reference — IAPWS-95 over water, Murphy–Koop over ice — at reference check points within its documented range. The table below shows each one’s worst case across its full window.
- Those checks run as automated unit tests on every build. A failing verification test is a build blocker — the site cannot ship a formula that has drifted from the reference.
- The math is pure JavaScript with zero scientific dependencies — only
Math.expandMath.pow— so there is no opaque library between you and the equation, and the calculator formulas run in your browser.
IAPWS-95 reference check (over water)
Published IAPWS-95 saturation pressures versus the value this site computes, recomputed when this page was built. These are the exact figures the unit tests assert against.
| Temperature | IAPWS-95 reference (Pa) | This site (Pa) | Deviation |
|---|---|---|---|
| 0 °C | 611.21 | 611.213 | 0.000% |
| 10 °C | 1228.11 | 1228.11 | 0.000% |
| 20 °C | 2339.19 | 2339.19 | 0.000% |
| 25 °C | 3169.82 | 3169.82 | 0.000% |
| 50 °C | 12352.5 | 12352.5 | 0.000% |
| 100 °C | 101418 | 101418 | 0.000% |
| 150 °C | 476159 | 476159 | 0.000% |
| 200 °C | 1554940 | 1554940 | 0.000% |
Murphy–Koop reference check (over ice)
| Temperature | Murphy–Koop reference (Pa) | This site (Pa) | Deviation |
|---|---|---|---|
| -40 °C | 12.841 | 12.8443 | 0.026% |
| -20 °C | 103.24 | 103.252 | 0.012% |
| -10 °C | 259.87 | 259.892 | 0.009% |
Each formula versus IAPWS-95
The maximum deviation of each simple formula from IAPWS-95, sampled every 1 °C over the part of its range where IAPWS-95 is the solid reference (0 °C upward). Recomputed at build.
| Formula | Window | Max Δ vs IAPWS-95 |
|---|---|---|
| Buck (1996) | 0–100 °C | 0.11% |
| Magnus (Alduchov–Eskridge 1996) | 0–60 °C | 0.38% |
| Goff–Gratch | 0–102 °C | 0.15% |
| Antoine (NIST) | 0–300 °C | 19.16% |
| Tetens | 0–50 °C | 0.14% |
| Buck (1981) — legacy(legacy) | 0–50 °C | 0.14% |
Antoine’s larger figure comes entirely from its high-temperature NIST set; below about 90 °C it agrees with IAPWS-95 to within a few tenths of a percent. Each formula is evaluated over the full window shown, which is why the windows differ. See each formula’s equation and constants on its formula page, or compare them all at one temperature on the main calculator.
Specific errors we avoided
A handful of transcription traps recur across online vapor-pressure calculators. Each was checked explicitly:
The IAPWS-95 saturation equation multiplies the polynomial by Tc/T inside the exponential. Omitting it — a common transcription error — shifts the entire curve. It is present and tested here.
The widely copied 1981 Buck coefficients are superseded by the 1996 revision. We use 1996 as the default and expose 1981 only as a clearly labeled legacy option.
We use the optimized 17.625 / 243.04 °C coefficients, not the older intermediate sets, and the dew-point inversion uses the same constants so the two stay consistent.
NIST's Antoine constants for water give pressure in bar and are fitted piecewise. We convert bar → Pa and auto-select the correct sub-range set, never extrapolating the high-temperature set down to room temperature.
The 1988 WMO reprint of Goff–Gratch contains a sign typo. We implement the corrected Smithsonian (1984) form.
Below freezing the reference is Murphy–Koop 2005, the modern standard for vapor pressure over ice — not an OCR-garbled transcription of older tables.
Licensing note: equations and coefficients are facts and are free to use. Computed values on this site are our own; IAPWS material is used with attribution (see below). This site is not affiliated with IAPWS or NIST.
References
Every formula on this page is implemented from, and validated against, the following primary standards and papers.
- IAPWS R6-95(2018) / Wagner & Pruss 2002 — International Association for the Properties of Water and Steam — the reference standard
- Review of the vapour pressures of ice and supercooled water — Murphy & Koop 2005, QJRMS 131:1539
- Humidity Conversion Equations (rev. 7/96) — Buck Research CR-1A manual — the Buck 1996 coefficients
- Improved Magnus Form Approximation of Saturation Vapor Pressure — Alduchov & Eskridge 1996, J. Appl. Meteorol. 35:601
- NIST Chemistry WebBook (SRD 69) — Water — NIST — Antoine constants & validation reference
- Goff–Gratch equation (Smithsonian Met. Tables 1984) — Vömel (CIRES) tabulation — corrected form
- On the computation of saturation vapor pressure (Murray 1967) — Tetens 1930; Murray 1967, J. Appl. Meteorol. 6:203 — the Tetens form
Spotted an error? Let us know — reader corrections are the best review this site gets.