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 at a given temperature. In plain terms: it is the force pushing outward from water molecules that have escaped into the air above a liquid surface. The higher the temperature, the more molecules escape, and the higher the vapor pressure becomes.
You encounter vapor pressure every day. It is why wet clothes dry faster on a hot day than a cold one, why a pot of water boils at lower temperatures at high altitude, and why humidity feels different depending on the air temperature. For cooking, chemistry, or engineering work, knowing the vapor pressure of water at a specific temperature lets you predict whether water will boil, how fast it will evaporate, and how much moisture the air can hold.
Key Takeaways
- The Antoine equation is the most practical method for home or kitchen use, requiring only the temperature in Celsius and three known constants for water.
- Vapor pressure increases sharply with temperature—doubling roughly every 10°C rise—so small temperature changes produce large pressure changes.
- At sea level, water boils when its vapor pressure reaches 760 mmHg (or 1 atmosphere); at higher altitudes, this happens at lower temperatures because atmospheric pressure is lower.
- Steam tables provide pre-calculated vapor pressure values for common temperatures and are faster than equations if your temperature is already listed.
- Common mistakes include forgetting to convert temperature to the correct scale, mixing up units (mmHg versus pascals), or using the wrong constants for the equation.
The Antoine Equation: The Practical Method
The Antoine equation is the standard tool for calculating vapor pressure in kitchens, labs, and engineering settings. It is accurate, fast, and requires only basic arithmetic. The equation is:
log₁₀(P) = A − B / (C + T)
Here, P is vapor pressure in mmHg (millimeters of mercury), T is temperature in degrees Celsius, and A, B, and C are constants specific to water. For water, these constants are: A = 8.07131, B = 1730.63, and C = 233.426.
To use this equation, substitute your temperature in Celsius into the formula, solve for log₁₀(P), then convert back from the logarithm to get P. For example, at 25°C (room temperature): log₁₀(P) = 8.07131 − 1730.63 / (233.426 + 25) = 8.07131 − 7.19 = 0.881. Then P = 10^0.881 = 7.6 mmHg. This means water at 25°C exerts a vapor pressure of about 7.6 mmHg.
The Antoine equation works best between 0°C and 100°C. Outside that range, the constants change, and you should use steam tables or a more advanced equation instead.
Using Steam Tables for Quick Lookup
If you need vapor pressure for a common temperature, steam tables are faster than any calculation. These tables list pre-computed vapor pressures (and other properties like density and enthalpy) for water at standard temperatures. You straightforward find your temperature in the left column and read the vapor pressure from the right.
Steam tables are available free online from engineering sites and textbooks. Most tables list temperatures in 1°C or 5°C increments. If your exact temperature is not listed, you can estimate by linear interpolation—drawing a straight line between the two nearest temperatures and reading the value in between.
For example, if a table shows 23°C at 21.1 mmHg and 24°C at 22.4 mmHg, the vapor pressure at 23.5°C would be roughly 21.75 mmHg (halfway between). This method is accurate enough for most cooking and practical purposes.
Converting Between Units of Pressure
Vapor pressure can be expressed in several units, and you may need to convert depending on what your recipe, equipment manual, or reference material asks for. The most common units are millimeters of mercury (mmHg), pascals (Pa), atmospheres (atm), and bar.
Here are the conversion factors you need:
| From | To | Multiply By |
|---|---|---|
| mmHg | Pa | 133.322 |
| mmHg | atm | 0.001316 |
| mmHg | bar | 0.001333 |
| Pa | mmHg | 0.00750 |
| atm | mmHg | 760 |
| bar | mmHg | 750.06 |
For instance, if the Antoine equation gives you 23.8 mmHg and you need the answer in pascals, multiply 23.8 × 133.322 = 3,173 Pa. If you need it in atmospheres, multiply 23.8 × 0.001316 = 0.0313 atm. Always check what unit your source material expects before you report your answer.
Why Temperature Matters So Much
Vapor pressure is extremely sensitive to temperature. A change of just 10°C can roughly double the vapor pressure, and this effect gets stronger at higher temperatures. This is why boiling happens so much faster at higher heat settings and why pressure cookers work—they trap steam, raising the pressure inside, which raises the boiling point and cooks food faster.
At sea level, water boils when its vapor pressure reaches 760 mmHg, which happens at 100°C. But at high altitude, where atmospheric pressure is lower, water boils at a lower temperature because it does not need to reach 760 mmHg to escape the liquid. In Denver (about 5,280 feet above sea level), atmospheric pressure is roughly 630 mmHg, so water boils at about 95°C instead. This is why cooking times are longer at altitude—the food is cooking in cooler water.
Conversely, in a pressure cooker at sea level, if you raise the internal pressure to 2 atmospheres (1,520 mmHg), water will not boil until about 121°C. This higher temperature cooks food much faster.
Common Mistakes to Avoid
The most frequent error is forgetting to convert temperature to Celsius before plugging it into the Antoine equation. The constants A, B, and C are calibrated for Celsius only. If you use Fahrenheit by mistake, your answer will be completely wrong. Always convert first: °C = (°F − 32) × 5/9.
A second common mistake is mixing up units. The Antoine equation produces pressure in mmHg, but your reference material might expect pascals or bar. Always convert at the end, and double-check which unit your source asks for before you report your result.
A third mistake is using the Antoine constants outside their valid range. The standard constants work well from 0°C to 100°C. If you need vapor pressure at 150°C or −10°C, you must either look up different constants (which vary by source) or use a steam table instead. Pushing the equation beyond its range produces increasingly inaccurate results.
Finally, do not round intermediate steps too early. Keep at least three decimal places through your calculation, then round only at the end. Rounding too early compounds errors and can throw off your final answer by several percent.
Frequently Asked Questions
What is the vapor pressure of water at body temperature (37°C)?
Using the Antoine equation: log₁₀(P) = 8.07131 − 1730.63 / (233.426 + 37) = 8.07131 − 6.925 = 1.146. Then P = 10^1.146 = 14.0 mmHg. At body temperature, water has a vapor pressure of about 14 mmHg, or roughly 1,867 Pa.
Why does water boil at a lower temperature on a mountain?
At high altitude, atmospheric pressure is lower. Water boils when its vapor pressure equals the atmospheric pressure pushing down on it. Since the atmosphere is pushing down with less force, water only needs to reach a lower vapor pressure to boil, which happens at a lower temperature. In Denver, for example, water boils at 95°C instead of 100°C because the atmospheric pressure there is about 630 mmHg instead of 760 mmHg.
Can I use the Antoine equation for temperatures below 0°C or above 100°C?
The standard Antoine constants for water work reliably between 0°C and 100°C. Outside this range, the equation becomes less accurate. For temperatures below 0°C or above 100°C, use a steam table or look up different Antoine constants published for that range. Engineering handbooks often provide extended constants for wider temperature ranges.
What is the difference between vapor pressure and partial pressure?
Vapor pressure is the pressure exerted by water vapor alone when it is in equilibrium with liquid water. Partial pressure is the pressure that one gas contributes to a mixture of gases. In humid air, the partial pressure of water vapor is always less than or equal to the vapor pressure at that temperature. When they are equal, the air is saturated (100% relative humidity).
Do I need to know vapor pressure for cooking, or is it just for chemistry?
Vapor pressure matters in cooking when you use a pressure cooker, when you cook at high altitude, or when you need to understand why food dries out or cooks at different rates. For everyday cooking at sea level without special equipment, you usually do not need to calculate it. But understanding vapor pressure helps explain why these things happen and how to adjust recipes when conditions change.