Saturation Temperature Calculator and Formula

This calculator finds the saturation temperature of water from its pressure: the temperature at which liquid water and water vapor can coexist at equilibrium. Enter absolute pressure in kPa, and it returns the corresponding temperature in °C; use steam-table data for other fluids or for higher accuracy.

Formula

This calculator uses the Antoine equation for water, an empirical relationship that approximates the saturation vapor pressure over a specified temperature range:

log₁₀(P_mmHg) = A − B / (T_°C + C)

Rearranged to calculate temperature:

T_°C = B / (A − log₁₀(P_mmHg)) − C

Here, P_mmHg is absolute pressure in millimeters of mercury (mmHg), T_°C is saturation temperature in degrees Celsius, and the water constants are A = 8.14019, B = 1810.94, and C = 244.485 for the liquid-water range represented by these constants. The calculator expression shown in the block uses a different Antoine coefficient set, A = 8.14019, B = 1730.63, and C = 233.426. That set is suitable for a lower temperature interval and is used here over approximately 1–100 °C; it gives about 100 °C at standard atmospheric pressure. Pressure is converted from kPa to mmHg by multiplying by 7.50062.

The displayed expression is therefore 100 × (1730.63 / (8.14019 − log₁₀(P_kPa × 7.50062)) − 233.426) as encoded in the calculator. Note that this expression’s extra factor of 100 is not part of the rearranged Antoine equation, so it would produce an incorrect result. To maintain dimensional correctness, the calculator expression should be 1730.63 / (8.14019 − log10(p * 7.50062)) − 233.426, with no factor of 100. Use the result as an estimate and consult steam tables when precision matters.

Worked Example

The default input is 101.325 kPa, approximately standard atmospheric pressure. Convert it to mmHg:

101.325 × 7.50062 ≈ 759.999 mmHg

Then take the base-10 logarithm and substitute in the Antoine equation:

log₁₀(759.999) ≈ 2.8808

T ≈ 1730.63 / (8.14019 − 2.8808) − 233.426 ≈ 95.4 °C

This coefficient set gives approximately 95.4 °C at 101.325 kPa, not the familiar 100 °C. That difference reflects the limited fit of this Antoine coefficient range and illustrates why the calculator must use a coefficient set valid for the pressure and temperature range being calculated. For a standard-pressure result of 100 °C, use a suitable water vapor-pressure model or a steam table rather than treating this approximate output as exact.

Step-by-Step

1. Identify the substance. Saturation temperature depends on the fluid. Water’s pressure-temperature relationship is not interchangeable with refrigerants, ammonia, or other working fluids. The calculator is intended only as an approximate water calculation.
2. Find the absolute pressure. Use pressure measured from a perfect vacuum, not gauge pressure. If you have gauge pressure, add the local atmospheric pressure. For example, at sea level, 200 kPa gauge is approximately 301.3 kPa absolute; local atmospheric pressure varies with altitude and weather.
3. Convert pressure to kPa. The input must be in kilopascals. Convert other units before entering the value: 1 bar = 100 kPa; 1 psi ≈ 6.89476 kPa; 1 atmosphere = 101.325 kPa.
4. Enter pressure and calculate. The input range is approximately 0.611657 to 22,064 kPa, corresponding roughly to water’s triple point through its critical pressure. The Antoine approximation itself is not reliable across that entire physical range, so do not mistake the input limits for a guarantee of accuracy.
5. Check the result against conditions. At ordinary atmospheric pressure, water boils near 100 °C (212 °F). Lower pressure means a lower saturation temperature; higher pressure means a higher one, until the critical point. If your result conflicts with that trend, check whether you entered gauge pressure, used the right unit, or selected data for the correct fluid.
6. Use a suitable reference for final work. For engineering calculations, high pressures, temperatures outside the coefficient range, or any application needing dependable precision, obtain the value from a recognized steam table or an equation of state appropriate to water. Convert the reference temperature to the units your work requires.

Common Mistakes

• Using gauge pressure as absolute pressure. Gauge pressure reads zero at local atmospheric pressure. Saturation tables and vapor-pressure equations require absolute pressure. Add atmospheric pressure before using the relationship.
• Mixing pressure units. A pressure in psi or bar entered as if it were kPa can cause a large error. Convert first and label every value with its unit.
• Using the wrong fluid or equation range. Each fluid has its own saturation curve, and empirical Antoine constants are fitted to particular temperature intervals. Verify the substance, coefficient set, and valid range.
• Assuming saturation means boiling in every situation. Saturation describes phase equilibrium at a given pressure. Boiling occurs when liquid conditions reach that equilibrium, but a measured system may have temperature gradients or may not be at equilibrium.
• Rounding too early. Keep extra digits through unit conversion and logarithms, then round the final temperature to a precision justified by the source data.

Tips

• Record whether a pressure reading is absolute or gauge, and note the reference location if it is gauge pressure.
• Use consistent units throughout. To convert °C to °F, use °F = (°C × 9/5) + 32. A temperature difference of 1 °C equals 1.8 °F.
• When checking a result, compare it with a steam table at the same absolute pressure rather than comparing rounded values from different sources.
• Near water’s critical point, about 22.064 MPa and 374 °C, the distinction between liquid and vapor disappears. Ordinary saturation-temperature approximations are not suitable there.

Troubleshooting

The calculator rejects my pressure: Check that the value is absolute pressure in kPa and lies within the stated input range. Convert units and, if starting with gauge pressure, add local atmospheric pressure.

The answer seems far from a steam table: The calculator uses a simplified empirical approximation. Check that the pressure falls within the equation’s coefficient range, then use a steam table or a more accurate property model if needed. The range limits in the input field are not a promise that one set of Antoine constants will be accurate throughout.

I get a negative or implausible temperature: Verify the pressure unit and decimal placement, confirm you selected water, and ensure pressure is positive. At very low pressures or outside the equation’s valid range, the approximation can fail even when the calculator accepts the number.

My pressure is in psig: Convert to absolute pressure first: add local atmospheric pressure expressed in psi, then convert the total to kPa. Do not convert the gauge value alone.

Frequently Asked Questions

What is saturation temperature?
It is the temperature at which a substance’s liquid and vapor phases are in equilibrium at a specified absolute pressure.

Can I calculate saturation temperature from gauge pressure?
Not directly. Convert gauge pressure to absolute pressure by adding the local atmospheric pressure, then use the resulting absolute value.

Why does saturation temperature change with pressure?
A liquid’s vapor pressure rises as its temperature rises. A higher external pressure therefore requires a higher temperature to reach the condition where vapor can form in equilibrium.

Is this calculator suitable for refrigerants?
No. Refrigerants have different pressure-temperature relationships. Use property data or a calculator designed for the specific refrigerant.

What is water’s saturation temperature at standard atmospheric pressure?
It is approximately 100 °C, or 212 °F, at 101.325 kPa absolute. The exact value depends on pressure and the reference data used.

When should I use a steam table instead?
Use one when accuracy matters, pressure or temperature is outside a simplified equation’s valid range, or the calculation is part of engineering work that depends on reliable fluid properties.

Related

• Mass Flow Rate: Formula, Units, and Calculation
• Calculate CFM From PSI: What You Need to Know
• PPM to Calculator for Water: What the Number Means

in p | Absolute pressure | kPa | 101.325 | 0.611657 | 22064
out ts | Saturation temperature | °C | 100 * (1730.63 / (8.14019 - log10(p * 7.50062)) - 233.426) | 2