What water vapour pressure is and why you need it

Water vapour pressure is the pressure exerted by water molecules that have evaporated into the air above a liquid surface. It tells you how much water is trying to escape from a liquid into the gas phase at a given temperature. The higher the temperature, the higher the vapour pressure — which is why wet clothes dry faster on a hot day than a cold one.

You need to calculate it when you're working with humidity, designing equipment that handles water, predicting when condensation will form, or understanding how fast water will evaporate under specific conditions. In food science, HVAC design, and chemistry labs, knowing the exact vapour pressure at your working temperature prevents equipment failure and helps you predict what will happen to moisture in your system.

Key Takeaways

  • The Antoine equation is the most practical method for calculating water vapour pressure at temperatures between 0°C and 100°C, using three known constants and your temperature value.
  • The Magnus formula is faster to calculate by hand and gives results within 1% accuracy for temperatures between 0°C and 50°C.
  • Temperature must be in the correct unit (Celsius or Kelvin, depending on the equation) or your result will be completely wrong.
  • Vapour pressure increases exponentially with temperature, so a 10-degree change produces a much larger pressure change at high temperatures than at low ones.
  • You can verify your calculation by checking published steam tables, which list exact vapour pressures at standard temperatures.

The Antoine equation: the standard method

The Antoine equation is the most widely used formula for calculating water vapour pressure. It works across a wide temperature range and is accurate enough for most practical applications. The equation is:

log₁₀(P) = A − B / (C + T)

In this formula, P is the vapour pressure in millimetres of mercury (mmHg), T is the 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 it, plug in your temperature in Celsius, subtract it from C, divide B by that result, subtract that from A, and then find the antilog (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 − 6.69897 = 1.37234. Then P = 10^1.37234 = 23.56 mmHg. This matches published steam tables for water at 25°C.

The Magnus formula: faster calculation

If you need a result quickly and don't have a calculator, the Magnus formula is simpler and still accurate for most kitchen and workshop conditions. The formula is:

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

Here, P is vapour pressure in hectopascals (hPa), T is temperature in Celsius, and exp means e (2.71828) raised to the power shown in the brackets. At 25°C: P = 6.1094 × exp[(17.625 × 25) / (25 + 243.04)] = 6.1094 × exp[440.625 / 268.04] = 6.1094 × exp[1.6438] = 6.1094 × 5.1768 = 31.64 hPa.

The Magnus formula gives results within 1% of the Antoine equation between 0°C and 50°C, which covers most everyday situations. Above 50°C, accuracy drops, so use Antoine for higher temperatures. Note that this formula gives pressure in hectopascals, not millimetres of mercury — if you need mmHg, multiply by 0.75006.

Converting between pressure units

Different fields use different units for vapour pressure, so you may need to convert your result. The most common units are millimetres of mercury (mmHg), hectopascals (hPa), kilopascals (kPa), and atmospheres (atm).

To convert from mmHg to other units: multiply by 133.322 to get pascals, then divide by 1000 for kilopascals. One atmosphere equals 760 mmHg. One hectopascal equals 100 pascals. At 25°C, water vapour pressure is 23.56 mmHg, which equals 3.169 kPa or 0.0310 atm. Most scientific work uses kilopascals or hectopascals, while older tables and some industrial equipment still reference mmHg.

Common mistakes that throw off your calculation

The most frequent error is using the wrong temperature unit. The Antoine equation requires Celsius; if you plug in Fahrenheit or Kelvin, your answer will be nonsense. Convert first: Celsius = (Fahrenheit − 32) × 5/9, and Kelvin = Celsius + 273.15. Double-check which unit your equation expects before you start.

A second mistake is rounding intermediate steps too early. If you round 1730.63 / 258.426 to 6.7 instead of keeping 6.69897, your final answer shifts noticeably. Keep at least four decimal places through all steps, then round only at the end.

The third common error is forgetting that vapour pressure is temperature-dependent in a non-linear way. A change from 20°C to 30°C does not double the vapour pressure — it increases it by roughly 50%. This means small temperature errors create larger pressure errors at higher temperatures. If your thermometer is off by 2 degrees at 80°C, your vapour pressure calculation will be off by several percent.

Checking your answer against steam tables

Once you've calculated a vapour pressure, verify it using a steam table — a published reference that lists exact vapour pressures at standard temperatures. Steam tables are available free online from engineering sites and in most chemistry textbooks. They list pressure at every degree Celsius from 0°C to 100°C, and at higher temperatures in larger increments.

If your calculated value matches the table value within 1%, your calculation is correct. If it's off by more than 2%, check your arithmetic and your temperature unit. Steam tables are the standard check because they're based on experimental measurements, not equations, so they're your ground truth. For temperatures between table values, you can interpolate — if 24°C gives 22.38 mmHg and 26°C gives 25.21 mmHg, then 25°C is roughly 23.80 mmHg, which matches the Antoine result of 23.56 mmHg closely enough.

When temperature changes during your process

In real situations, temperature often changes — water cools as it evaporates, or a system heats up over time. If you need to know vapour pressure at multiple points, calculate it at each temperature separately rather than trying to average. Vapour pressure does not change linearly with temperature, so averaging temperatures and then calculating gives the wrong answer.

If you're tracking a process where temperature changes continuously, calculate vapour pressure at the start, middle, and end temperatures. This shows you how much the driving force for evaporation changes across your process. In food drying, for example, the product starts cool and ends hot — the vapour pressure at the end is much higher, which is why drying accelerates as the product warms up.

Frequently Asked Questions

What's the difference between vapour pressure and humidity?

Vapour pressure is the actual pressure of water molecules in the air at a given temperature. Humidity is how much water is in the air compared to the maximum amount it can hold at that temperature. At 25°C, the maximum vapour pressure is 23.56 mmHg — if the air contains water at 11.78 mmHg, the relative humidity is 50%. Vapour pressure is an absolute measurement; humidity is relative.

Do I need to use Celsius or can I use Fahrenheit?

The Antoine equation requires Celsius. If you have Fahrenheit, convert it first: Celsius = (Fahrenheit − 32) × 5/9. The Magnus formula also requires Celsius. Using the wrong temperature unit will give you a completely incorrect answer, so always check which unit your equation expects before you calculate.

Why does vapour pressure matter for cooking or food storage?

Higher vapour pressure means water evaporates faster. In a dehydrator, you want high vapour pressure to pull moisture out quickly. In food storage, you want low vapour pressure — a cool, dry place — to slow spoilage. Understanding vapour pressure at your storage temperature tells you how fast your food will lose or gain moisture, which affects shelf life and texture.

Can I calculate vapour pressure above 100°C?

The Antoine equation works up to about 100°C with good accuracy. Above that, the constants change and the equation becomes less reliable. For temperatures above 100°C, use steam tables or more complex equations designed for high-temperature water. Most kitchen and workshop situations stay below 100°C, so Antoine is sufficient.

What if I only have a rough temperature estimate?

Calculate at your best estimate, then calculate again at 2 or 3 degrees higher and lower. This shows you the range of possible vapour pressures. If your temperature is uncertain by ±3°C, your vapour pressure is uncertain by roughly ±10–15% at room temperature, more at higher temperatures. Document your temperature uncertainty so anyone using your result knows its limits.