Vapor Pressure of Water Calculator
### Atmospheric Psychrometrics & Arden Buck Water Vapor Standards The **World Meteorological Organization (WMO)** and ASHRAE endorse the **Arden Buck Equation** as the gold standard.
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📐 Formula
💡 Practical Example
At standard room temperature of 20°C (68°F), air holds a maximum water vapor pressure of 23.38 hPa (17.54 mmHg); any moisture exceeding this threshold condenses into liquid water droplets.
📖 About Vapor Pressure of Water Calculator
Atmospheric Psychrometrics & Arden Buck Water Vapor Standards
The World Meteorological Organization (WMO) and ASHRAE endorse the Arden Buck Equation as the gold standard formulation for saturation vapor pressure over liquid water and ice.
Primary Water Vapor Equations
- Over Liquid Water (T in ^):
e_s(T) = 6.1121 × ((18.678 - (T) / (234.5)) × (T) / (257.14 + T)) [hPa]
- Over Ice (T < 0^):
e_s,ice(T) = 6.1115 × ((23.036 - (T) / (333.7)) × (T) / (279.82 + T)) [hPa]
- Relative Humidity (RH): RH (\%) = (e_actuale_s(T)) × 100\%
- Unit Conversions: 1 hPa = 0.1 kPa = 0.750062 mmHg = 0.0145038 psi
How to Use This Calculator
Enter your Water / Air Temperature (e.g. 20.0), Temperature Unit — choose from Degrees Celsius (°C), Degrees Fahrenheit (°F), Kelvin (K), and Phase Equilibrium — choose from Over Liquid Water (Standard Arden Buck), Over Ice (Sub-Zero Temperatures). Results update instantly as you type — adjust any value to compare scenarios.
The Formula
Formula Reference: Vapor Pressure of Water Calculator
Input variables:
waterTemperatureValue — Water / Air Temperature
temperatureScaleSelect — Temperature Unit
saturationPhaseSelect — Phase Equilibrium
Computed outputs:
vaporPressureHpa — Saturation Vapor Pressure (hPa / mbar)
vaporPressureKpa — Vapor Pressure (kPa)
vaporPressureMmHg — Vapor Pressure (mmHg / Torr)
vaporPressurePsi — Vapor Pressure (PSI)
vaporPressureAtm — Vapor Pressure (Atmospheres)
Mathematical relationships extracted from calculation logic:
tC = (tInput - 32) * (5 / 9)
expTerm = (23.036 - safeDiv(tC, 333.7)) * safeDiv(tC, 279.82 + tC)
esHpa = 6.1115 * Math.exp(expTerm)
esMmHg = esHpa * 0.7500616827
esPsi = esHpa * 0.014503773773
Standard: NIST / ISO mathematical definitions
Worked Example
At standard room temperature of 20°C (68°F), air holds a maximum water vapor pressure of 23.38 hPa (17.54 mmHg); any moisture exceeding this threshold condenses into liquid water droplets.
Understanding Your Result
Health calculations provide population-average estimates based on validated formulas. Individual variation exists — your actual physiology may differ from the calculated baseline. Compare your result to the relevant clinical reference range (WHO, CDC, NIH, or specialty guidelines). For values outside normal ranges or for clinical decisions, consult a qualified healthcare provider. A single measurement is less meaningful than a trend over time under consistent measurement conditions.
💡 Mathematical Rigor & Applied Context
- This calculator applies exact mathematical definitions following conventions established by NIST and international standards bodies.
- Rounding errors accumulate across multi-step calculations. For precision-critical work, maintain extra significant figures through all intermediate steps.
- Many mathematical concepts have multiple valid formulations — if a result seems unexpected, verify which convention or definition applies to your context.
- Dimensional analysis (unit tracking) is the fastest way to catch formula errors. Every term in an equation must have consistent, compatible units.
- Numerical methods used in digital calculators introduce floating-point precision limits (~15 significant digits for IEEE 754 double precision).
- For statistical and probabilistic calculations, always specify whether you are working with population parameters or sample statistics — formulas differ.
- Visualizing a problem geometrically or testing with known boundary values (zero, infinity, negative) reveals hidden errors faster than algebraic checking.
- When in doubt, validate your result against a simplified hand calculation or a published worked example from a textbook or standards document.
Results are for informational and educational purposes only. Always verify critical decisions with a qualified professional.