What vapor pressure is and why it matters

Vapor pressure is the pressure exerted by water vapor when it is in equilibrium with liquid water (or ice) at a given temperature. In plain terms: it is the force pushing outward from water molecules that have turned into gas, held in balance with the liquid below. The higher the temperature, the higher the vapor pressure—more heat energy means more molecules escape from the liquid surface into the air.

You encounter vapor pressure in everyday life without thinking about it. It is why wet clothes dry faster on a hot day than a cold one, why a pot of water boils at sea level but takes longer at high altitude, and why a sealed container of hot water will eventually build up pressure inside. For homeowners, understanding vapor pressure matters when dealing with condensation in attics or crawl spaces, or when calculating whether moisture will condense on a cold pipe.

Key Takeaways

  • Vapor pressure increases with temperature, and you can estimate it using the Antoine equation or look it up in a reference table for common temperatures.
  • The Antoine equation requires three constants (A, B, C) that are specific to water and a temperature in degrees Celsius to produce pressure in millimeters of mercury.
  • For rough household estimates, the Magnus formula is simpler and gives results within a few percent of the Antoine equation for temperatures between 0°C and 50°C.
  • Reference tables published by the National Institute of Standards and Technology (NIST) provide exact vapor pressure values for water at any temperature without calculation.
  • Vapor pressure is always expressed relative to a reference pressure (usually atmospheres, bar, or millimeters of mercury), so you must know which unit your source uses.

The Antoine equation: the standard calculation method

The Antoine equation is the most widely used formula for calculating vapor pressure across a range of temperatures. It is an empirical equation—meaning it is based on observed data rather than pure physics—and it works well for water between roughly 0°C and 100°C. The equation is:

log₁₀(P) = A − B / (C + T)

In this formula, P is vapor pressure (in millimeters of mercury), T is temperature in degrees Celsius, and A, B, and C are constants specific to water. For water, the standard constants are: A = 8.07131, B = 1730.63, and C = 233.426. These numbers come from fitting the equation to experimental measurements of water vapor pressure.

To use the equation, plug in your temperature, subtract it from C, divide B by that result, subtract from A, and then raise 10 to the power of your answer. For example, at 25°C: log₁₀(P) = 8.07131 − 1730.63 / (233.426 + 25) = 8.07131 − 1730.63 / 258.426 = 8.07131 − 6.70 = 1.371. Then 10^1.371 = 23.5 millimeters of mercury. A scientific calculator or spreadsheet makes this much faster than doing it by hand.

The Magnus formula: a simpler alternative for household use

If you do not have a calculator handy or want a quicker mental estimate, the Magnus formula is simpler and accurate enough for most home purposes. It is:

VP = 6.1094 × exp[(17.625 × T) / (T + 243.04)]

Here, VP is vapor pressure in millibars (also called hectopascals), T is temperature in degrees Celsius, and "exp" means e (2.718) raised to the power of the fraction. The result is usually within 2 to 3 percent of the Antoine equation for temperatures between 0°C and 50°C, which is close enough for deciding whether condensation will form on a pipe or whether a basement will stay dry.

Again, a spreadsheet or scientific calculator is the practical way to compute this. Most online calculators that ask for temperature will use one of these two formulas behind the scenes and show you the result when ready.

Using reference tables instead of calculating

If you do not want to calculate at all, the National Institute of Standards and Technology (NIST) publishes detailed tables of water vapor pressure at every temperature from the freezing point to well above boiling. You straightforward find your temperature in the left column and read the pressure across. These tables are free and available on the NIST website under their thermophysical properties data.

Reference tables are the most accurate method because they are based on direct measurement, not a formula fitted to data. They also remove the risk of arithmetic error. For a homeowner trying to figure out whether a cold pipe will sweat, or whether a basement will stay dry at a certain temperature, a quick table lookup is faster and more reliable than any calculation.

Understanding vapor pressure units and conversions

Vapor pressure is reported in different units depending on the source, and you need to know which one you are looking at. The most common units are:

  • Millimeters of mercury (mmHg): the traditional unit, still used in many older tables and the Antoine equation as written above.
  • Millibars or hectopascals (mb or hPa): modern metric units, equivalent to each other, used in weather forecasting and the Magnus formula.
  • Atmospheres (atm): one atmosphere equals 760 mmHg or 1013.25 millibars; used when comparing vapor pressure to total air pressure.
  • Pascals or kilopascals (Pa or kPa): SI units, used in scientific and engineering contexts.

To convert between them: 1 mmHg = 1.333 millibars, 1 atmosphere = 760 mmHg = 1013.25 millibars. If you calculate vapor pressure using the Antoine equation (which gives mmHg) but your reference source uses millibars, multiply by 1.333 to convert. Most online calculators let you choose your output unit, so you can avoid the conversion step altogether.

Why vapor pressure changes with temperature

The reason vapor pressure rises steeply with temperature is that heat gives water molecules more energy to escape from the liquid surface into the air. At any temperature, some molecules at the surface have enough energy to break free and become vapor, while some vapor molecules collide with the surface and condense back into liquid. At equilibrium, these two rates are equal, and the pressure from the vapor molecules in balance with the liquid is the vapor pressure.

As temperature increases, more molecules have enough energy to escape, so the equilibrium pressure rises. This is not a linear relationship—vapor pressure roughly doubles for every 10°C increase in temperature in the range most homeowners care about. This is why a sealed container of hot water builds pressure quickly, and why condensation appears on a cold window on a warm, humid day: the air near the window cools below the dew point, and the vapor pressure of water at that lower temperature is lower than the actual amount of water vapor in the air, so some condenses out.

Practical examples: when you might need vapor pressure

A common household scenario: you have a cold water pipe running through an unconditioned space (a basement, crawl space, or attic), and you want to know whether it will sweat. To answer this, you need to know the vapor pressure of water at the pipe surface temperature, and compare it to the actual water vapor pressure in the air around it. If the actual vapor pressure is higher, condensation will form.

Another example: you are trying to understand why your basement feels damp in summer. The air temperature might be 25°C, and the vapor pressure of water at 25°C is about 23.5 mmHg. If the actual humidity in the basement is high (say, 80 percent relative humidity), the actual vapor pressure is 0.8 × 23.5 = 18.8 mmHg. When that air hits a cooler surface—say, a concrete wall that is 15°C—the vapor pressure of water at 15°C is only about 12.8 mmHg. Since the actual vapor pressure (18.8) exceeds the saturation pressure at the wall temperature (12.8), water condenses on the wall. Calculating vapor pressure at each temperature lets you predict where condensation will occur.

Frequently Asked Questions

What is the difference between vapor pressure and relative humidity?

Vapor pressure is the actual pressure exerted by water vapor in the air, measured in millimeters of mercury or millibars. Relative humidity is the ratio of actual vapor pressure to the saturation vapor pressure at that temperature, expressed as a percentage. At 25°C, if the vapor pressure is 18.8 mmHg and saturation is 23.5 mmHg, the relative humidity is 80 percent. Vapor pressure tells you how much water is in the air; relative humidity tells you how close the air is to being saturated.

Can I calculate vapor pressure for temperatures above 100°C?

The Antoine equation constants given here are fitted for temperatures up to about 100°C and become less accurate above that. For higher temperatures, you need different Antoine constants or a more complex equation. For household purposes, you will rarely need vapor pressure above 100°C. If you do, the NIST tables extend to much higher temperatures, or you can search for steam tables, which list vapor pressure for water and steam at any temperature up to the critical point.

Why do I need to know vapor pressure if I can just measure humidity with a meter?

A humidity meter tells you relative humidity, not absolute vapor pressure. To predict whether condensation will form on a surface, you need to know the actual vapor pressure in the air and compare it to the saturation vapor pressure at the surface temperature. Calculating vapor pressure at different temperatures lets you do this comparison. A meter alone cannot tell you whether a cold pipe will sweat or a basement wall will stay dry.

What happens to vapor pressure in a sealed container?

In a sealed container, vapor pressure rises until it reaches equilibrium—the point where as many molecules are condensing back into liquid as are escaping into vapor. This equilibrium pressure is the saturation vapor pressure at that temperature. If you heat the container, the equilibrium pressure rises. If you cool it, the pressure falls and some vapor condenses. This is why a sealed hot water bottle will eventually cool down and develop a partial vacuum inside.