Saturation Pressure Calculator and Formula

This calculator estimates water’s saturation pressure at a chosen temperature using the Antoine equation. Enter temperature in °C and the equation returns pressure in mmHg; use it only within the stated temperature range for this set of constants.

Formula

The calculator uses the Antoine equation, an empirical relationship that estimates the equilibrium vapor pressure of a liquid at a given temperature:

log₁₀(P) = A − B / (C + T)

• P is saturation pressure in mmHg.
• T is temperature in °C.
• A = 8.07131, B = 1730.63, and C = 233.426 are Antoine constants for water in this unit system.

The second output converts the first result to kilopascals: 1 mmHg = 0.133322 kPa. These constants are commonly used for water over approximately 1–100°C. The calculator’s input limits match that practical range; do not extrapolate the equation beyond it. Other substances require their own constants, and some substances need different constant sets across different temperature ranges.

Worked Example

Using the default temperature, T = 25°C:

1. Substitute the value into the Antoine equation: log₁₀(P) = 8.07131 − 1730.63 / (233.426 + 25).
2. Add the denominator: 233.426 + 25 = 258.426.
3. Divide: 1730.63 / 258.426 ≈ 6.697.
4. Subtract: 8.07131 − 6.697 ≈ 1.374.
5. Undo the base-10 logarithm: P = 10^1.374 ≈ 23.76 mmHg.
6. Convert to kPa: 23.76 × 0.133322 ≈ 3.168 kPa.

The displayed outputs are rounded to the precision specified in the calculator: 23.76 mmHg and 3.168 kPa.

What You’ll Need

• The temperature of the water, measured or specified in °C.
• A calculator or spreadsheet if you want to check the calculation manually; use base-10 logarithms or the equivalent power operation.
• The correct Antoine constants and valid temperature interval if calculating for a liquid other than water.

Step-by-Step

1. Identify the substance. Saturation pressure depends on both temperature and the liquid. This calculator is configured for water, not a general-purpose fluid. For another substance, find a reliable source for its Antoine constants and their applicable temperature range.
2. Find the relevant temperature. Use the liquid’s temperature at the location and conditions of interest. The input must be between 1°C and 100°C for this calculator. A temperature outside that range is not accepted because these constants should not be used here beyond their stated interval.
3. Enter temperature in Celsius. Convert a Fahrenheit reading with T(°C) = [T(°F) − 32] × 5/9. For example, 77°F is 25°C. Do not enter a Fahrenheit number directly into a Celsius field.
4. Calculate the pressure. The calculator substitutes the temperature into the Antoine equation and returns the estimated water vapor pressure in mmHg. Its second result is the same pressure converted to kPa.
5. Check the pressure unit before using the result. mmHg and kPa are both pressure units, but their numerical values differ. For reference, 760 mmHg is approximately 101.325 kPa, or one standard atmosphere.
6. Interpret the result as an equilibrium value. Saturation pressure is the vapor pressure when liquid and vapor are in equilibrium at the stated temperature. It is not automatically the pressure in a closed vessel, a pipe, or a process; actual system pressure depends on its contents and conditions.
7. Record the conditions and precision. Note the temperature, substance, equation/constants, and pressure unit along with the result. Keep more digits during intermediate calculations, then round the final value to a precision appropriate for the temperature measurement and application.

Common Mistakes

• Mixing temperature scales: the constants here require °C. Entering Fahrenheit without conversion can produce a plausible-looking but incorrect result.
• Using constants with the wrong pressure unit: Antoine constants are tied to specific units and logarithm conventions. These constants give mmHg; they cannot be paired unchanged with a formula expecting kPa or bar.
• Applying water constants to another substance: each liquid has its own vapor-pressure behavior. Select constants specifically for the substance and temperature interval.
• Extrapolating beyond the valid range: an equation can still produce a number outside its fitted interval, but that does not make the number reliable. Use a suitable correlation or reference data for the needed range.
• Confusing saturation pressure with total pressure: in a gas mixture, water’s saturation pressure is not the mixture’s total pressure. It is the equilibrium vapor-pressure limit at that temperature.
• Rounding too early: rounding the denominator or logarithm before exponentiating can affect the final pressure. Carry several digits through the calculation.

Tips

• For a quick plausibility check, water’s saturation pressure rises as temperature rises. Near 25°C it is about 3.17 kPa; near 100°C it is approximately one atmosphere.
• If your source reports pressure in bar, convert from kPa by dividing by 100. To convert kPa to psi, multiply by approximately 0.145038. Use consistent units throughout.
• For temperatures given in kelvin, convert to Celsius first: T(°C) = T(K) − 273.15.
• Use a reference table or a more appropriate equation when high accuracy is important, especially close to the edge of a correlation’s range.
• Distinguish absolute pressure from gauge pressure. Saturation pressure is an absolute pressure; gauge pressure is measured relative to local atmospheric pressure.

Troubleshooting

• The input is rejected: check that it is a number in the range 1–100°C. Convert Fahrenheit or kelvin to Celsius first.
• Your answer differs from a table: verify the table’s temperature, pressure unit, and rounding. Check whether it lists absolute pressure and whether it uses a different correlation or constants.
• The result seems far too large or small: check the temperature scale and confirm that the Antoine equation uses base-10 logarithms. Also verify that the constants correspond to mmHg.
• You need a value outside 1–100°C: do not force an extrapolation. Find a water-vapor-pressure source or equation validated for that temperature and state the source and units.
• You need another fluid’s result: obtain that fluid’s Antoine constants, the pressure unit associated with them, and their valid temperature interval. Replace the constants and conversion as needed; do not reuse the water settings.

Frequently Asked Questions

What does saturation pressure mean?
It is the equilibrium vapor pressure of a substance at a specified temperature, when liquid and vapor can coexist.

Does saturation pressure depend on the amount of liquid?
For a pure substance at a fixed temperature in equilibrium, the saturation pressure is determined primarily by temperature, not by the amount of liquid, provided both phases are present.

Is saturation pressure the same as boiling pressure?
Boiling occurs when a liquid’s saturation pressure reaches the surrounding pressure. Thus, the boiling temperature depends on the external pressure.

Can I use this calculator for steam?
It estimates water’s saturation pressure, which is relevant to water and steam equilibrium in the listed range. For engineering or high-accuracy steam calculations, use validated steam tables or a suitable property formulation.

Why does water pressure rise so quickly with temperature?
Increasing temperature gives more molecules enough energy to enter the vapor phase, so the equilibrium vapor pressure rises nonlinearly.

Can saturation pressure be greater than atmospheric pressure?
Yes. At temperatures above water’s normal boiling point, its saturation pressure exceeds standard atmospheric pressure; the liquid can still exist if the surrounding pressure is high enough.

Related

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in t | Temperature | °C | 25 | 1 | 100
out p | Saturation pressure | mmHg | 10^(8.07131 - 1730.63 / (233.426 + t)) | 2
out k | Saturation pressure | kPa | p * 0.133322 | 3