Vapour Pressure of Water Calculator

Calculate the vapour pressure of water at any temperature using five different approximation formulas. Works for the full range from below freezing to above 100°C.

What is Vapour Pressure?

Vapour pressure is the pressure exerted by a vapour in thermodynamic equilibrium with its liquid (or solid) phase at a given temperature. When water sits in a closed container, some molecules at the surface gain enough kinetic energy to escape into the gas phase. Simultaneously, some gas-phase molecules lose energy and return to the liquid. When the rate of evaporation equals the rate of condensation, the system reaches a state called dynamic equilibrium. The pressure exerted by the water vapour at this equilibrium is the vapour pressure.

At the molecular level, vapour pressure depends on how strongly molecules attract one another. Water molecules form hydrogen bonds, which are relatively strong intermolecular forces. This means water has a lower vapour pressure compared to many organic solvents at the same temperature, because more energy is needed to break those hydrogen bonds and allow molecules to escape into the gas phase.

Vapour pressure is a fundamental physical property that plays a crucial role in evaporation, boiling, humidity calculations, and many industrial processes. It is measured in various units including kilopascals (kPa), millimetres of mercury (mmHg), atmospheres (atm), and bars.

Does Vapour Pressure Increase with Temperature?

Yes, vapour pressure increases exponentially with temperature. This is one of the most important relationships in thermodynamics and physical chemistry. As temperature rises, a greater fraction of molecules at the liquid surface possess enough kinetic energy to overcome intermolecular attractions and escape into the gas phase.

The relationship is not linear but exponential. For example, the vapour pressure of water at 20°C is about 2.34 kPa, but at 100°C it jumps to 101.325 kPa, a roughly 43-fold increase for a five-fold increase in temperature (on the absolute scale). This exponential behaviour is described mathematically by the Clausius-Clapeyron equation:

ln(P2/P1) = (ΔH_vap / R) × (1/T1 - 1/T2)

Where ΔH_vap is the enthalpy of vaporisation, R is the universal gas constant, and T1 and T2 are absolute temperatures. The various formulas implemented in this calculator (Antoine, Magnus, Tetens, Buck, and the empirical formula) are all approximations of this fundamental exponential relationship, each optimised for different temperature ranges and applications.

Vapour Pressure of Water Table

The reference table above provides experimentally determined vapour pressure values for water at temperatures from 0°C to 100°C in 5°C increments. These values are widely used in chemistry, meteorology, and engineering. At 0°C, the vapour pressure is approximately 0.611 kPa (4.585 mmHg), representing the triple point pressure of water. At 100°C, the vapour pressure equals standard atmospheric pressure (101.325 kPa or 760 mmHg), which is precisely why water boils at 100°C at sea level.

Key reference points to remember:

0°C: 0.611 kPa (triple point of water)
20°C: 2.338 kPa (approximately room temperature)
25°C: 3.169 kPa (standard laboratory temperature)
37°C: 6.275 kPa (human body temperature)
100°C: 101.325 kPa (normal boiling point)

Antoine Equation for Water

The Antoine equation is one of the most widely used empirical correlations for vapour pressure. It was developed by French engineer Louis Charles Antoine in 1888 and relates vapour pressure to temperature using three empirically determined constants:

log₁₀(P) = A - B / (C + T)

For water in the temperature range of 1°C to 100°C, the standard Antoine constants are:

A = 8.07131
B = 1730.63
C = 233.426

With these constants, temperature is entered in degrees Celsius and the resulting pressure is in millimetres of mercury (mmHg). The Antoine equation is valued for its simplicity and reasonable accuracy over moderate temperature ranges. However, it becomes less accurate at temperatures far from the range for which the constants were fitted. For temperatures above 100°C, a different set of Antoine constants should be used (A = 8.14019, B = 1810.94, C = 244.485).

This calculator uses the first set of constants, which gives excellent results for temperatures commonly encountered in laboratory and environmental conditions.

Magnus and Tetens Formulas

The Magnus formula (also called the Magnus-Tetens or August-Roche-Magnus formula) is especially popular in meteorology for calculating saturation vapour pressure. It takes the form:

P = 0.61094 × exp(17.625 × T / (T + 243.04))

Where T is in degrees Celsius and P is in kilopascals. The constants 17.625 and 243.04 have been refined over the years by various researchers, and slightly different versions exist in the literature. The version used here follows the Alduchov and Eskridge (1996) improvement, which provides accuracy better than 0.4% over the range -40°C to 50°C.

The closely related Tetens formula was published by O. Tetens in 1930:

P = 0.61078 × 10^{(7.5 × T / (T + 237.3))}

Both formulas are derived from fitting experimental data to an exponential form and differ mainly in their constants. They are widely used in atmospheric science, weather forecasting models, and agricultural applications because they provide a good balance between simplicity and accuracy across the temperature range typically encountered in Earth's atmosphere.

Buck Equation

The Buck equation (1981) represents an improvement over the Magnus and Tetens formulas, offering better accuracy over a wider temperature range. Developed by Arden L. Buck, the formula is:

P = 0.61121 × exp((18.678 - T/234.5) × T / (T + 257.14))

Where T is in degrees Celsius and P is in kilopascals. The key innovation of the Buck equation is the inclusion of the T/234.5 correction term, which improves accuracy at extreme temperatures. According to Buck's original publication, the equation achieves accuracy better than 0.05% over the range -80°C to 50°C, making it one of the most accurate simple formulas available.

The Buck equation is particularly favoured in precision meteorological instruments and calibration standards. If you need a single formula that offers the best accuracy for temperatures found in Earth's atmosphere, the Buck equation is generally the recommended choice.

Factors Affecting Vapour Pressure

Several factors influence the vapour pressure of a substance:

Temperature: The most significant factor. Higher temperatures provide more kinetic energy, allowing more molecules to escape into the gas phase. The relationship is exponential, not linear.
Intermolecular forces: Stronger intermolecular forces (such as hydrogen bonding in water) result in lower vapour pressure because more energy is needed to overcome these attractions. This is why ethanol (fewer hydrogen bonds) has a higher vapour pressure than water at the same temperature.
Molecular weight: In general, lighter molecules have higher vapour pressures than heavier ones with similar intermolecular forces, because lighter molecules move faster at the same temperature.
Dissolved solutes: According to Raoult's Law, dissolving a non-volatile solute in water lowers its vapour pressure. This is a colligative property and is proportional to the mole fraction of the solute. For example, seawater has a slightly lower vapour pressure than pure water.
Surface curvature: The Kelvin effect describes how vapour pressure increases over a curved surface (small droplets) compared to a flat surface. This is important for cloud formation and aerosol science.

Why Vapour Pressure Matters

Vapour pressure is not just an abstract physical chemistry concept; it has critical practical applications in many fields:

Weather and humidity: Relative humidity is defined as the ratio of actual water vapour pressure to the saturation vapour pressure at the same temperature. Understanding vapour pressure is essential for weather forecasting, dew point calculations, and predicting condensation and fog.
Boiling and cooking: A liquid boils when its vapour pressure equals the external atmospheric pressure. At high altitudes where atmospheric pressure is lower, water boils at temperatures below 100°C, affecting cooking times. Pressure cookers increase the boiling point by raising the pressure.
Industrial drying: In processes like spray drying, freeze drying, and paint curing, vapour pressure determines the rate of evaporation and the effectiveness of the drying process.
Distillation: Separation of liquid mixtures by distillation relies on differences in vapour pressure between components. A component with higher vapour pressure evaporates preferentially.
Environmental science: Vapour pressure determines how quickly pollutants evaporate from water surfaces and soil, affecting air quality and exposure assessments.

Can Vapour Pressure Be Zero?

In theory, vapour pressure can only reach exactly zero at absolute zero (0 Kelvin, or -273.15°C). At absolute zero, all molecular motion ceases, and no molecules have the kinetic energy to escape from the liquid or solid phase into the gas phase. However, absolute zero has never been achieved and, according to the Third Law of Thermodynamics, cannot be reached in a finite number of steps.

In practice, at very low temperatures, the vapour pressure of water becomes extraordinarily small but never truly zero. For example, at -40°C, the vapour pressure of ice is approximately 0.013 kPa (0.1 mmHg). Even in the deep cold of interstellar space, ice still sublimes at an immeasurably slow rate. This is why comets, which are largely made of ice, slowly develop tails as they approach the Sun: the increasing temperature raises the vapour pressure enough for significant sublimation to occur.

Vapour Pressure and Boiling Point

The boiling point of a liquid is the temperature at which its vapour pressure equals the external (atmospheric) pressure. At sea level, where atmospheric pressure is 101.325 kPa (760 mmHg), water boils at 100°C because that is the temperature at which water's vapour pressure reaches 101.325 kPa.

This relationship explains several everyday observations:

High altitude cooking: In Denver, Colorado (elevation ~1600 m), atmospheric pressure is about 83 kPa. Water boils at approximately 95°C, meaning food takes longer to cook.
Pressure cookers: By sealing the vessel and allowing pressure to build to about 200 kPa, the boiling point of water rises to approximately 120°C, allowing food to cook faster.
Vacuum distillation: Reducing the pressure above a liquid lowers its boiling point. This technique is used in chemistry to distil heat-sensitive compounds that would decompose at their normal boiling points.

You can use this calculator to find the boiling point at any pressure by finding the temperature at which the vapour pressure equals the ambient pressure. Simply adjust the temperature until the calculator output matches your target pressure.

Applications

Vapour pressure calculations find use in a remarkably diverse range of fields:

HVAC Engineering: Designing heating, ventilation, and air conditioning systems requires accurate vapour pressure data to calculate humidity ratios, dew points, and energy requirements for humidification or dehumidification.
Meteorology: Weather models rely on vapour pressure calculations for predicting cloud formation, precipitation, fog, and frost. The Magnus and Tetens formulas are standard in operational meteorology.
Food Science: Water activity (aw), which determines microbial growth and food shelf life, is directly related to vapour pressure. It is defined as the ratio of vapour pressure of water in food to the vapour pressure of pure water at the same temperature.
Chemical Engineering: Process design for reactors, distillation columns, evaporators, and dryers all require accurate vapour pressure data. The Antoine equation is commonly used in chemical engineering handbooks and process simulation software.
Pharmaceutical Manufacturing: Controlling humidity in pharmaceutical production facilities prevents degradation of moisture-sensitive drugs and ensures consistent tablet coating processes.
Environmental Monitoring: Vapour pressure is used in models that predict the fate and transport of chemicals in the environment, including evaporation from water bodies and soil.
Aerospace: Understanding vapour pressure at low pressures is crucial for designing life support systems for spacecraft and high-altitude aircraft, where water can boil at near body temperature.

Frequently Asked Questions

What is the vapour pressure of water at room temperature (25°C)?

At 25°C (77°F), the vapour pressure of water is approximately 3.169 kPa, which is equivalent to 23.77 mmHg, 0.03127 atm, or 0.03169 bar. This means that at room temperature, about 3.1% of standard atmospheric pressure is due to water vapour at saturation. You can verify this value using any of the five formulas in the calculator above.

Which formula is the most accurate?

For temperatures between -40°C and 50°C (the most common atmospheric range), the Buck equation provides the best accuracy, with errors less than 0.05%. The Magnus formula with updated constants (Alduchov and Eskridge) is also excellent for meteorological use. For general laboratory use between 1°C and 100°C, the Antoine equation with appropriate constants is very reliable. Use the "Compare all formulas" feature to see how results differ at your temperature of interest.

Can I use these formulas for temperatures below 0°C?

Yes, but with some caveats. Below 0°C, the vapour pressure over ice differs from the vapour pressure over supercooled liquid water. The formulas in this calculator technically compute vapour pressure over liquid water (or supercooled water below 0°C). For vapour pressure over ice, slightly different constants should be used. The difference becomes significant below about -20°C. For most practical purposes above -10°C, the formulas give acceptable results.

Why do the five formulas give slightly different results?

Each formula uses different mathematical forms and empirically fitted constants, optimised for different temperature ranges and applications. The Antoine equation uses a logarithmic form; the Magnus and Buck equations use an exponential form with different correction terms. The constants in each formula were determined by fitting to experimental data, and different researchers used different datasets and fitting criteria. For most practical temperatures (0-100°C), the differences between formulas are typically less than 1%, which is within the uncertainty of most measurements.

How do I calculate relative humidity from vapour pressure?

Relative humidity (RH) is defined as the ratio of the actual partial pressure of water vapour in air to the saturation vapour pressure at the same temperature, expressed as a percentage: RH = (e / e_s) × 100%, where e is the actual vapour pressure and e_s is the saturation vapour pressure. Use this calculator to find e_s at your temperature, then divide your measured actual vapour pressure by e_s and multiply by 100 to get relative humidity.

What is the difference between vapour pressure and partial pressure?

Vapour pressure specifically refers to the equilibrium pressure of a vapour above its own liquid (or solid) in a closed system. Partial pressure refers to the pressure contribution of any single gas in a mixture. In an unsaturated atmosphere, the partial pressure of water vapour is less than the saturation vapour pressure. When the partial pressure equals the saturation vapour pressure, the air is at 100% relative humidity and is said to be saturated.

Why does water boil at a lower temperature at high altitude?

Boiling occurs when a liquid's vapour pressure equals the surrounding atmospheric pressure. At high altitudes, atmospheric pressure is lower. Since water's vapour pressure at 100°C is exactly 101.325 kPa (sea-level pressure), a lower atmospheric pressure means the vapour pressure reaches the ambient pressure at a lower temperature. For example, on Mount Everest (atmospheric pressure about 34 kPa), water boils at approximately 71°C.