Antoine Equation Calculator
Calculate the vapor pressure of a pure liquid at a given temperature, or the boiling temperature at a given pressure, using Antoine coefficients A, B and C. Works with mmHg, kPa, bar and other pressure units.
Find Vapor Pressure or Boiling Temperature from Antoine Coefficients
Antoine Equation Formula
Where:
- \(P\) — vapor pressure of the pure compound, in the unit that matches the coefficient set (often mmHg)
- \(T\) — temperature, almost always in \(^\circ\text{C}\) for tabulated coefficients
- \(A\), \(B\), \(C\) — empirical Antoine coefficients specific to each substance, pressure unit and temperature range
The Antoine equation is an empirical correlation for the saturation vapor pressure of a pure liquid. The second form is the inverted equation, which gives the temperature at which the liquid boils at a chosen pressure.
Antoine Equation – Calculation Example
Example: water at 100 °C, using the standard coefficient set for water with P in mmHg and T in °C: A = 8.07131, B = 1730.63, C = 233.426.
\[ \log_{10} P = 8.07131 - \frac{1730.63}{233.426 + 100} = 8.07131 - 5.1906 = 2.8807 \]
\[ P = 10^{2.8807} \approx 760.1 \ \text{mmHg} \approx 101.34 \ \text{kPa} \]
Result: the vapor pressure of water at 100 °C is about 760 mmHg — exactly 1 atmosphere, which is why water boils at 100 °C at sea level.
Inverting the equation with P = 760 mmHg confirms this:
\[ T = \frac{1730.63}{8.07131 - \log_{10}(760)} - 233.426 = \frac{1730.63}{5.1905} - 233.426 \approx 100.0\ ^\circ\text{C} \]
Result: water boils at approximately 100.0 °C when the surrounding pressure is 760 mmHg.
How to use the calculator
- Choose Solve for: "Vapor pressure (from temperature)" or "Temperature (from pressure)". The relevant input field appears automatically.
- Enter the Temperature (T) and its unit (°C or K), or the Vapor Pressure (P) if you are solving for the boiling temperature. A value in kelvin is converted to °C automatically.
- Select the Pressure Unit of the Coefficients — this is the unit for which your A, B, C values were tabulated (e.g. mmHg for most water tables), not the unit you want the answer in. The result is also converted to kPa, atm, bar and psi.
- Enter the coefficients A, B and C from a reliable source such as the NIST Chemistry WebBook.
- Optionally fill in the Lower and Upper Validity Limit of the coefficient set. The calculator warns you if the temperature falls outside this range, where the equation becomes an unreliable extrapolation.
- Read the Vapor Pressure or Saturation Temperature result together with the detailed step-by-step calculation.
What is the Antoine equation?
The Antoine equation is the most widely used simple correlation for the vapor pressure of pure liquids. It relates the saturation vapor pressure to temperature through three empirical coefficients fitted to experimental data. Because vapor pressure rises steeply and non-linearly with temperature, the equation uses the reciprocal of \(C + T\) to capture the characteristic curvature of the vapor pressure curve — a much better fit than a straight line, while remaining easy to invert by hand.
Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid at a given temperature. It matters whenever a liquid evaporates into a closed space: a liquid boils when its vapor pressure equals the surrounding pressure, and vapor pressure also governs evaporation rates, distillation, drying and the behavior of fuel vapors. This is why the Antoine equation appears throughout chemical engineering, thermodynamics and laboratory work.
The inverted form is just as useful. Setting \(P\) equal to the external pressure gives the boiling temperature at that pressure — for example the boiling point of water on a mountain, or the reflux temperature of a solvent under reduced pressure in a rotary evaporator. Chemists also use vapor pressures to predict how volatile components partition between liquid and vapor phases, a foundation of Raoult's Law for mixtures and of distillation design.
Note that the coefficients are not universal constants. Each substance has its own A, B and C, and they are valid only for the specific pressure unit, temperature unit and temperature range stated in the source. Mixing units — for instance using coefficients tabulated for mmHg with a pressure in kPa — is the most common mistake and can shift the result by orders of magnitude.
Assumptions, limitations and practical tips
- Pure compounds only. The equation describes a single substance at vapor–liquid equilibrium. For mixtures, combine pure-component vapor pressures with an activity-coefficient model such as Raoult's Law.
- Limited temperature range. Antoine coefficients are fitted typically over a span of a few tens of degrees (the water set used here is valid from 1 °C to 100 °C). Outside that range the equation is an extrapolation and can be badly wrong, especially near the critical point, where vapor pressure behavior follows different physics. Always enter the validity limits if you know them.
- Unit consistency is critical. A is not dimensionless in a physical sense — it absorbs the pressure unit. A set tabulated for mmHg cannot be used with kPa pressures without refitting. Typical A values are 8–9 for mmHg and 5–7 for kPa or bar sets.
- Temperature is almost always in °C. The coefficient C (typically 230–280) already contains the offset from absolute zero for Celsius tables. If your source tabulates T in kelvin, its C will be near zero — check before entering values.
- Accuracy. Within its valid range, the Antoine equation usually reproduces experimental vapor pressures to within a few percent, which is sufficient for most engineering and laboratory estimates. For higher precision or wide temperature spans, use the Wagner or Cox equations, or the integrated van 't Hoff equation when you have enthalpy-of-vaporization data.
- Related gas-phase calculations. Once you know the vapor pressure, you can estimate properties of the resulting vapor — for example its density under given conditions with the Gas Density Calculator or typical molecular speeds with the Molecular Speed of a Gas Calculator.
Frequently Asked Questions
How do I calculate vapor pressure by hand with the Antoine equation?
Take the base-10 logarithm form \( \log_{10} P = A - \frac{B}{C + T} \), plug in the temperature in the unit the coefficients were fitted for (almost always °C), and evaluate the right side. Then raise 10 to that power: \( P = 10^{A - B/(C+T)} \). For water at 25 °C with the standard mmHg set, you get \( \log_{10} P \approx 1.75 \), so \( P \approx 23.8 \) mmHg.
Why does my answer come out wrong by orders of magnitude?
Almost always a unit mismatch. Antoine coefficients are fitted for one specific pressure unit: a set tabulated for mmHg has \( A \approx 8\text{–}9 \), while kPa or bar sets have \( A \approx 5\text{–}7 \). If you use mmHg coefficients but interpret the result as kPa, you are off by a factor of about 7.5. Check the source of A, B, C and select the matching pressure unit in the calculator.
Where can I find reliable Antoine coefficients for a substance?
The NIST Chemistry WebBook is the most trustworthy free source — search your compound, open its phase-change data, and the Antoine coefficients are listed together with their pressure unit and valid temperature range. Other options include the CRC Handbook of Chemistry and Physics and Perrys Chemical Engineers Handbook. Always copy the stated validity range along with A, B and C; using coefficients outside it is an unreliable extrapolation.
My coefficient table uses ln P (natural log) instead of log₁₀. Can I still use this calculator?
No, not directly — this calculator uses the base-10 form. If your source tabulates \( \ln P = A - B/(C+T) \), convert the coefficients: multiply A and B by \( \log_{10} e \approx 0.434294 \), keeping C unchanged. Then the set works with \( \log_{10} P \). Alternatively use a tool that accepts the natural-log form, but never mix the two conventions — the difference is a factor of 2.303 in the exponent.
What counts as a normal or good vapor pressure value?
It depends entirely on the substance and temperature. Volatile solvents like acetone or ethanol have vapor pressures of hundreds of mmHg at room temperature, while water is about 23.8 mmHg (3.2 kPa) at 25 °C and heavy oils can be a tiny fraction of a mmHg. A useful sanity check: the vapor pressure equals 760 mmHg exactly at the normal boiling point, so if your result at the boiling temperature is far from 1 atm, something is wrong.
Can I use the Antoine equation below 0 °C or for solids?
It depends on the coefficient set, not on the phase alone. Some tabulated sets cover subcooled liquids or even solids (ice has published Antoine coefficients), and within their fitted range they work fine. But most common sets for liquid water stop around 1 °C. Above the melting point the supercooled-liquid extrapolation is usually acceptable for estimates; near or beyond the critical point the equation fails badly because the underlying physics changes.
How is the Antoine equation related to the Clausius–Clapeyron equation?
The Antoine equation is an empirical refinement of Clausius–Clapeyron, which predicts that \( \ln P \) should vary linearly with \( -1/T \) if the enthalpy of vaporization were constant. In reality it is not, so Antoine adds the empirical offset C, replacing \( 1/T \) with \( 1/(C+T) \) to capture the true curvature. This keeps the fit accurate over tens of degrees while remaining easy to invert algebraically.