Free Vapour Pressure of Water Calculator

Overview of Water Vapor Pressure and the Calculator

The Water Vapor Pressure Calculator is an online tool designed to compute the saturation vapor pressure of water (or ice) at any specified temperature. It implements five widely used empirical models, including the Antoine equation, Buck formula, Magnus (August–Roche–Magnus) formula, Tetens formula, and a simple exponential correlation. This tool is ideal for researchers, engineers, and students who need a quick and accurate vapor pressure of water at temperature without manual table lookup. It also provides a built‑in water vapor pressure table for instant reference across a range of conditions. Pressures can be displayed in units such as kilopascals (kPa), millimeters of mercury (mmHg), torr, atmospheres (atm), or pascals (Pa).

What Is Vapor Pressure? Definition and Key Factors

Vapor pressure is the equilibrium pressure exerted by a vapor above its condensed phase (liquid or solid) in a closed system at a fixed temperature. At equilibrium, the rate of evaporation from the liquid (or sublimation from the solid) equals the rate of condensation of the vapor — the system is in a dynamic steady state.

Two primary factors influence the vapor pressure of a substance:

• Temperature: As temperature rises, the average kinetic energy of molecules increases, enabling more molecules to overcome intermolecular forces and enter the gas phase. Consequently, vapor pressure increases with temperature. At low temperatures, fewer molecules have sufficient energy, so the vapor pressure is lower.
• Nature of the molecules: Stronger intermolecular forces (e.g., hydrogen bonding, dipole–dipole interactions) make it harder for molecules to escape into the vapor, resulting in a lower vapor pressure. Conversely, substances with weak forces exhibit higher vapor pressures.

Importantly, the surface area of the liquid or solid in contact with the gas does not affect the equilibrium vapor pressure — a wide dish and a narrow tube containing the same liquid at the same temperature will show identical vapor pressure.

Five Empirical Formulas for Water Vapor Pressure

The calculator uses the following equations, each with its own range of applicability and unit conventions:

1. Simple exponential formula (T in Kelvin, P in mmHg):

$$P_{\text{simple}} = \exp\!\left(20.386 - \frac{5132}{T}\right)$$

2. Antoine equation (T in °C, P in mmHg):

$$\log_{10} P_{\text{Antoine}} = 8.14019 - \frac{1810.94}{244.485 + T}, \qquad\text{or equivalently}\qquad P_{\text{Antoine}} = 10^{\,8.14019 - \frac{1810.94}{244.485 + T}}.$$

3. Magnus (August–Roche–Magnus) formula (T in °C, P in kPa):

$$P_{\text{Magnus}} = 0.61094\;\exp\!\left(\frac{17.625\,T}{T + 243.04}\right)$$

4. Tetens formula (T in °C, P in kPa):

$$P_{\text{Tetens}} = 0.61078\;\exp\!\left(\frac{17.27\,T}{T + 237.3}\right)$$

5. Buck equation (T in °C, P in kPa):

$$P_{\text{Buck}} = 0.61121\;\exp\!\left(\frac{18.678 - T/234.5}{T + 257.14}\right)$$

Accuracy Comparison of the Models

To help users select the most appropriate formula for their application, the table below compares the outputs of each model against the reference data from Lide’s table of water vapor pressures over the temperature range 0 °C to 100 °C (32 °F–212 °F). All pressures are in kPa, and the percentage deviation from the reference is shown in parentheses.

Temp (°C)	Temp (°F)	Reference (kPa)	Simple (kPa)	Antoine (kPa)	Magnus (kPa)	Tetens (kPa)	Buck (kPa)
0	32	0.6113	0.6593 (+7.85%)	0.6056 (−0.93%)	0.6109 (−0.06%)	0.6108 (−0.09%)	0.6112 (−0.01%)
20	68	2.3388	2.3755 (+1.57%)	2.3296 (−0.39%)	2.3334 (−0.23%)	2.3382 (+0.05%)	2.3383 (−0.02%)
35	95	5.6267	5.5696 (−1.01%)	5.6090 (−0.31%)	5.6176 (−0.16%)	5.6225 (+0.04%)	5.6268 (+0.00%)
50	122	12.344	12.065 (−2.26%)	12.306 (−0.31%)	12.361 (+0.13%)	12.336 (+0.08%)	12.349 (+0.04%)
75	167	38.563	37.738 (−2.14%)	38.463 (−0.26%)	39.000 (+1.13%)	38.646 (+0.40%)	38.595 (+0.08%)
100	212	101.32	101.31 (−0.01%)	101.34 (+0.02%)	104.08 (+2.72%)	102.21 (+1.10%)	101.31 (−0.01%)

The Lide reference values are taken from standard thermophysical tables.

Key observations:

• The Buck formula consistently produces the smallest absolute error across the entire 0–100 °C window, making it the most reliable single‑choice for general‑purpose calculations.
• The Antoine equation performs well at elevated temperatures but exhibits a noticeable negative bias near 0 °C (−0.93%). Its error, however, remains below ±1% throughout the range, and above 100 °C the Antoine model often becomes the most accurate option.
• The simple exponential yields substantial positive errors at low temperatures (+7.85% at 0 °C) and is therefore recommended only for rough estimations.
• The Magnus and Tetens formulas offer good accuracy in the 0–50 °C interval, but the Magnus error grows rapidly above 75 °C (reaching +2.72% at 100 °C).

The Antoine Equation in Depth

The Antoine equation is derived from the Clausius–Clapeyron relation and is one of the most widely used semi‑empirical correlations for vapor pressure. For water, two sets of Antoine constants are commonly employed:

• Below the normal boiling point (0 °C to 100 °C / 32 °F–212 °F):
  $A = 8.14019,\; B = 1810.94,\; C = 244.485$ (when P is in mmHg and T in °C).
• From the boiling point to the critical point (100 °C to 374 °C / 212 °F–705 °F):
  A second set of constants is used to maintain accuracy in this higher‑temperature regime. The calculator applies the appropriate constants automatically.

The general form is:

$$\log_{10} P = A - \frac{B}{C + T}$$

Sometimes the C coefficient is omitted, producing a simpler two‑parameter version, or additional terms are added to increase flexibility.

Quick‑Reference Vapor Pressure Table for Water

For rapid manual lookup, the following table lists saturated water vapor pressures at regular temperature intervals from the freezing point to the boiling point. Values are provided in kPa, torr, and atm.

Temp (°C)	Temp (°F)	Pressure (kPa)	Pressure (torr)	Pressure (atm)
0	32	0.6113	4.5851	0.0060
5	41	0.8726	6.5450	0.0086
10	50	1.2281	9.2115	0.0121
15	59	1.7056	12.7931	0.0168
20	68	2.3388	17.5424	0.0231
25	77	3.1690	23.7695	0.0313
30	86	4.2455	31.8439	0.0419
35	95	5.6267	42.2037	0.0555
40	104	7.3814	55.3651	0.0728
45	113	9.5898	71.9294	0.0946
50	122	12.3440	92.5876	0.1218
55	131	15.7520	118.1497	0.1555
60	140	19.9320	149.5023	0.1967
65	149	25.0220	187.6804	0.2469
70	158	31.1760	233.8392	0.3077
75	167	38.5630	289.2463	0.3806
80	176	47.3730	355.3267	0.4675
85	185	57.8150	433.6482	0.5706
90	194	70.1170	525.9208	0.6920
95	203	84.5290	634.0196	0.8342
100	212	101.3200	759.9625	1.0000

These numbers are consistent with the Lide reference and can be used for quick verification of calculations or for educational purposes.

How to Use the Calculator

Operating this tool is extremely simple:

1. Enter the temperature in the input field (in °C, °F, or K — the calculator accepts all common units).
2. The tool instantly computes the saturation vapor pressure using each of the five formulas.
3. The results are displayed side‑by‑side, allowing you to compare the outputs. By default, the Antoine and Buck values are highlighted because they represent the most accurate options for most applications.
4. To change the output unit, click on the current unit label and select a different unit from the dropdown (Pa, hPa, kPa, mmHg, torr, atm, etc.).

If a negative temperature (below 0 °C) is entered, the calculator automatically applies the Buck and Tetens models, which are validated for supercooled water and ice. This feature is useful for cold‑region meteorology and frost‑point studies.

Why Water Vapor Pressure Matters

The vapor pressure of water is a critical parameter in many natural and industrial processes. It governs evaporation and condensation rates, influences weather and climate (humidity, cloud formation), and is essential in engineering fields such as air‑conditioning, distillation, and drying. On Earth, the fact that water’s vapor pressure is high enough to permit evaporation but low enough to maintain liquid and solid phases is fundamental to the existence of life as we know it.

By combining multiple empirical models and providing both instant calculation and a reference table, this Water Vapor Pressure Calculator offers a versatile resource for anyone working with water‑vapor‑related data.