Antoine Equation Vapor Pressure Calculator
Solve the Antoine equation log₁₀(P) = A − B / (C + T) for vapor pressure or temperature using substance-specific constants — with unit conversion, a substance preset library, and a full step-by-step solution.
It is a three-parameter fit of the Clapeyron equation
The Antoine equation is a compact empirical approximation to the exact Clausius–Clapeyron relation d(ln P)/dT = ΔHvap/(RT²). The exact integration would give ln P = −ΔHvap/(RT) + const, which is linear in 1/T. Antoine replaces 1/T with 1/(C+T), a small empirical correction that widens the useful temperature range from a few degrees to tens of degrees. The three constants A, B and C are fitted to experimental vapor-pressure data for each substance.
Pressure rises exponentially with temperature
Because T sits inside the denominator of the exponent, vapor pressure grows very fast with temperature — roughly exponentially over modest ranges. Water at 20 °C has P ≈ 17.5 mmHg; at 50 °C it is 92.5 mmHg; at 100 °C it reaches 760 mmHg and boils. This steepness is why a small temperature rise can dramatically change evaporation rate, why distillation is so temperature-sensitive, and why food and pharmaceuticals are dried under vacuum at low temperature.
B controls the slope, C the curvature
The constant B is proportional to the enthalpy of vaporization divided by R, so it sets how steeply the curve climbs. C is a small temperature offset that improves the fit over a wide range; for most substances C is close to −18 °C when T is in °C (equivalently ≈230 K when T is in K). A is a vertical offset that sets where the curve sits. Getting B right matters most for the slope; getting A right shifts the whole curve.
It is only valid over its fitted range
Antoine constants are regressed over a specific temperature window — often 1–100 °C for water, or a narrower range for specialty chemicals. Extrapolating far outside that window produces errors that grow rapidly, because the true ln P vs. 1/T curve is only approximately linear. For cryogenic or near-critical applications, use a Wagner equation, a corresponding-states correlation, or tabulated data instead. The boiling point predicted by extrapolating water's low-range constants to 200 °C is off by tens of degrees.
How to Use This Calculator
The Antoine equation links vapor pressure P to temperature T through three substance-specific constants A, B and C. Give the tool the constants and one of P or T, and it will find the other.
1. Pick a substance from the library
Click any substance card — water, ethanol, benzene, ammonia, mercury and more — to load its A, B and C constants automatically. The library uses the standard fit with P in mmHg and T in °C; the tool converts internally if you choose other units.
2. Choose what to solve for
Pick P to get vapor pressure from a known temperature, or T to get the temperature at which a given vapor pressure is reached. The calculator rearranges log₁₀(P) = A − B/(C+T) for whichever you choose.
3. Set your preferred units
The constants are native to mmHg and °C, but you can display pressure in kPa, bar, Pa, psi or atm, and temperature in °C, K or °F. The tool converts on the fly and shows the result in both your chosen unit and the native units.
4. Enter the remaining inputs
Type or drag the temperature (or pressure, depending on what you are solving for) plus the A, B and C constants. Each field has presets and a hint showing the current value's role in the calculation.
5. Read the result and verdict
The result card shows the solved value in your chosen unit plus the native mmHg / °C equivalent. A colour-coded verdict classifies the state — sub-atmospheric liquid, ambient liquid, near-boiling, superheated vapor, etc. — so you can see at a glance what regime you are in.
6. Switch to Advanced for depth
Advanced mode adds the linearised Antoine plot (log₁₀P vs 1/(C+T)), a +1% sensitivity check on each constant, and companion metrics including the Clausius–Clapeyron enthalpy of vaporization, the normal boiling point, dP/dT, and a Trouton's-rule consistency check.
What This Tool Offers
Built around the Antoine relation log₁₀(P) = A − B/(C+T), the standard engineering fit for vapor pressure as a function of temperature.
Two-way solving
Solve for vapor pressure from temperature, or for temperature from vapor pressure. The calculator rearranges the Antoine equation automatically for whichever you choose.
Substance preset library
Twelve common substances — water (two ranges), ethanol, methanol, benzene, acetone, ammonia, toluene, chloroform, hexane, heptane, diethyl ether, acetic acid, carbon tetrachloride and mercury — each with its standard Antoine constants.
Full unit conversion
Display pressure in mmHg, kPa, bar, Pa, psi or atm, and temperature in °C, K or °F. Internally everything is converted to the native units of the Antoine constants so the maths is always correct.
Live VLE schematic
A sealed vessel showing the liquid pool, the vapor headspace, the pressure gauge, the thermometer, and the Antoine relation acting as the link between them — all scaled to the current inputs.
Dual charts
The main chart plots P vs T for the current constants and two nearby perturbations. The Advanced chart plots log₁₀P vs 1/(C+T), exposing the linearity that makes the Antoine equation work.
Reference tables
A pressure unit converter, a vapor-pressure lookup grid across temperatures and substances, a full substance library with A/B/C values and validity ranges, and a variable reference table.
Reference Tables & Conversions
A pressure unit converter, a vapor-pressure lookup grid, the full substance library, and the variable reference.
Pressure unit converter
Vapor Pressure of Water Lookup (Antoine, 1–100 °C)
Computed from P = 10^(A − B/(C+T)) with A = 8.07131, B = 1730.63, C = 233.426 (P in mmHg, T in °C). Values shown in mmHg and kPa.
| T (°C) | P (mmHg) | P (kPa) | P (bar) | P (psi) | P (atm) |
|---|
Substance Library — Antoine Constants
Standard Antoine constants with P in mmHg and T in °C. Valid over the stated temperature range; extrapolation outside is unreliable.
| Substance | Formula | A | B | C | Valid range (°C) |
|---|
Variable Reference
| Symbol | Meaning | Typical range | Units |
|---|---|---|---|
| P | Vapor pressure | 10⁻³ – 10⁴ | mmHg (native) |
| T | Temperature | −50 – 400 | °C (native) |
| A | Antoine constant (entropy term) | 6.5 – 9.5 | – |
| B | Antoine constant (enthalpy/R) | 900 – 3,500 | K |
| C | Antoine constant (temperature offset) | 200 – 260 | K |
| ΔHvap | Molar enthalpy of vaporization ≈ 2.303·R·B | 20 – 80 | kJ/mol |
| Tb | Normal boiling point (P = 760 mmHg) | −50 – 400 | °C |
What Does log₁₀(P) = A − B/(C+T) Measure?
The Antoine equation is the standard engineering correlation for the vapor pressure of a pure liquid as a function of temperature. It says that the base-10 logarithm of the vapor pressure is a linear function of 1/(C+T), where A, B and C are fitted constants that are specific to each substance. It is a three-parameter empirical approximation to the exact Clausius–Clapeyron relation, and it is accurate to a fraction of a percent over the temperature window for which the constants were regressed.
The Antoine Equation
The defining relationship, written with P in mmHg and T in °C, is:
Rearranged to solve for the other two unknowns:
T = B / ( A − log₁₀(P) ) − C
The equation is often written with P in kPa, bar or Pa and T in K. In that case the constants A, B and C take different values. This calculator accepts either convention — choose the units you want and the tool converts to the native mmHg / °C form internally.
Antoine Variables
| Symbol | Meaning | Notes |
|---|---|---|
| P | Vapor pressure of the pure substance | Pressure at which liquid and vapor coexist at equilibrium |
| T | Temperature | The independent variable in the P-from-T form |
| A | Antoine constant | Vertical offset; related to the entropy of vaporization |
| B | Antoine constant | Slope; proportional to ΔHvap/R |
| C | Antoine constant | Small temperature offset that improves the fit at low T |
How Each Constant Affects the Curve
The three constants play distinct roles. A shifts the curve vertically — increasing A by 1 multiplies the vapor pressure by 10 at every temperature. B controls the slope in the log₁₀P versus 1/(C+T) plane — increasing B makes the curve steeper, which corresponds to a larger enthalpy of vaporization. C controls the subtle curvature at low temperatures: a larger C makes the 1/(C+T) term vary more slowly with T, flattening the low-temperature end of the curve.
The single most important sanity check is the relationship between B and the enthalpy of vaporization: ΔHvap ≈ 2.303·R·B, with R = 8.314 J/(mol·K). For water with B ≈ 1,731 K, this gives ΔHvap ≈ 33 kJ/mol at the mid-range temperature, which is close to the tabulated value of 40.7 kJ/mol at 100 °C — the difference is the temperature dependence of ΔHvap itself, which the three-parameter form partially absorbs. For mercury with B ≈ 3,296 K, the estimate is ≈ 63 kJ/mol, again in the right range.
Antoine Calculation Examples
log₁₀ P = 8.07131 − 1730.63/(233.426 + 25) = 8.07131 − 6.69678 = 1.37453
P = 101.37453 = 23.68 mmHg ≈ 3.16 kPa
T = 1730.63 / (8.07131 − log₁₀ 760) − 233.426 = 1730.63 / (8.07131 − 2.88081) − 233.426
T = 1730.63 / 5.19050 − 233.426 = 100.0 °C (the normal boiling point)
log₁₀ P = 8.20417 − 1642.89/(230.300 + 78.3) = 8.20417 − 5.32252 = 2.88165
P = 102.88165 = 761 mmHg ≈ 1 atm (the boiling point)
ΔHvap ≈ 2.303 × 8.314 × 1211.033 = 23.2 kJ/mol (tabulated ≈ 30.7 kJ/mol at 80 °C)
Frequently Asked Questions
The constants have units that depend on the units chosen for P and T. In the most common convention — P in mmHg and T in °C — A is dimensionless, B has units of temperature (often written as °C or K, but strictly the same numerical scale as C + T), and C also has units of temperature. When P is in kPa or bar, both A and B change value. The NIST Chemistry WebBook and most handbooks state the convention explicitly. This calculator uses the mmHg / °C convention by default, but converts internally if you select other units — so the constants you enter are always interpreted as mmHg / °C.
Because the Antoine equation is an empirical fit, and a single set of three constants cannot reproduce the vapor-pressure curve accurately over the entire range from the triple point to the critical point. Water is commonly fitted in three overlapping ranges: 1–100 °C (A = 8.07131, B = 1730.63, C = 233.426), 99–374 °C (A = 8.14019, B = 1810.94, C = 244.485), and 0–60 °C (A = 8.10765, B = 1750.286, C = 235.0). Outside its fitted range a given set produces errors that grow rapidly. Always check the stated validity range before using a set of constants.
The Clausius–Clapeyron equation is the exact thermodynamic relation d(ln P)/dT = ΔHvap/(RT²). Integrating it with a constant ΔHvap gives ln P = −ΔHvap/(RT) + const, which is linear in 1/T and accurate over only a narrow temperature range. The Antoine equation replaces 1/T with 1/(C+T), a small empirical correction that dramatically widens the useful range. In effect, C absorbs the temperature dependence of ΔHvap that the two-parameter Clausius–Clapeyron form cannot capture. The Antoine equation is thus a three-parameter fit, and the extra parameter is what buys the accuracy over tens of degrees.
No. The Antoine equation describes liquid–vapor equilibrium, which ceases to exist above the critical temperature — there is no liquid phase there. Even approaching the critical point, the Antoine form loses accuracy because the vapor pressure curve flattens and its curvature becomes incompatible with the 1/(C+T) functional form. For near-critical or supercritical work, use the Wagner equation, a corresponding-states correlation such as the Lee–Kesler method, or direct tabulated experimental data. As a rough rule, do not use Antoine constants more than about 20–30 K beyond their stated upper validity limit.
The Clausius–Clapeyron relation connects the slope of the vapor-pressure curve to ΔHvap. In the Antoine form, the effective slope is B/(C+T)², so the temperature-dependent enthalpy of vaporization is approximately ΔHvap(T) = 2.303 · R · B · (T/(C+T))². At moderate temperatures T/(C+T) ≈ 0.5 for most organic liquids, giving the simple estimate ΔHvap ≈ 2.303 · R · B / 4 = 0.576 · R · B, or roughly 4.79 · B J/mol. The Advanced panel of this calculator uses the more careful temperature-dependent form and reports both the estimate and a Trouton's-rule check (ΔHvap/Tb ≈ 88 J/(mol·K) for most non-associated liquids).
Trouton's rule states that for most non-associated liquids, the entropy of vaporization at the normal boiling point is approximately constant: ΔSvap = ΔHvap/Tb ≈ 85–90 J/(mol·K). Because the Antoine constants give you both ΔHvap (from B) and Tb (from solving for the temperature at P = 760 mmHg), you can compute the ratio and check it against Trouton's rule. Liquids that hydrogen-bond strongly — water, alcohols, acetic acid — deviate upwards because their vapor phase is much more disordered than the liquid, giving ΔSvap of 100–110 J/(mol·K). This calculator reports the ratio as a consistency check on the constants you entered.
The Antoine equation is a fit to experimental data and is accurate to a fraction of a percent over its stated range, but steam tables are based on a much more detailed multi-parameter equation of state (IAPWS-95 for water) that reproduces the true vapor pressure to within experimental uncertainty. For most engineering work the Antoine result is more than adequate, but for thermodynamic-cycle calculations, steam-turbine design, or any application where sub-percent accuracy matters, use the steam tables or the IAPWS formulation. Other sources of discrepancy include using the wrong constant set for the temperature range and unit-conversion slips — check both first.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| P | Vapor pressure | mmHg |
| T | Temperature | °C |
| A, B, C | Antoine constants (component-specific) |
What it means
The Antoine equation is a semi‑empirical correlation used to estimate the vapour pressure of pure substances over a range of temperatures. It is written as log₁₀(P) = A − B/(C + T), where P is vapour pressure (often in mmHg or kPa), T is temperature in °C, and A, B, C are substance‑specific constants. This equation is widely used in distillation, condensation, and drying calculations because vapour pressure is critical for phase equilibrium. It is more accurate than the simpler Clausius‑Clapeyron equation over a limited temperature range. The constants are available for many compounds in databases like the DIPPR or NIST. The equation is used to calculate boiling points, to design condensers and evaporators, and to model atmospheric and environmental transport of volatile chemicals. It is also applied in the petroleum industry for crude oil fractions. The Antoine equation is a standard tool for chemical engineers and is essential for process simulation and design.
Worked example
Antoine Equation – Two Examples
Real‑World| Parameter | Value |
|---|---|
| A | 8.07131 |
| B | 1730.63 |
| C | 233.426 |
| T | 25 °C |
| Parameter | Value |
|---|---|
| A | 8.20417 |
| B | 1642.89 |
| C | 230.3 |
| T | 25 °C |
Common mistakes
- Constants A, B, C: These are substance‑specific and depend on temperature range; use the correct set for your compound and temperature units.
- Temperature T: Usually in °C for the given constants; check the reference. If using Kelvin, adjust constants accordingly.
- Pressure unit: The equation gives pressure in the same unit as the constants (e.g., mmHg, kPa).
- Log base: Usually log₁₀; some variants use natural log – verify.
- Valid range: The Antoine equation is empirical and valid only within a specified temperature range; extrapolation is unreliable.
Applications
The Antoine equation, log₁₀(P) = A − B/(C+T), provides a practical correlation for the vapour pressure of pure substances as a function of temperature. It is widely used in distillation, evaporation, and drying calculations, as well as in the design of vacuum systems and safety relief devices. Engineers use it to determine boiling points, to calculate relative volatility for distillation, and to estimate evaporation rates. The equation constants are empirically derived for each compound, making it applicable over limited temperature ranges. In process simulation software, the Antoine equation is a standard method for vapour‑liquid equilibrium (VLE) calculations. By applying this correlation, engineers can design separation processes, size condensers, and assess the flammability of solvents.
- Distillation column design and simulation
- Evaporation and drying process design
- Design of vacuum and pressure relief systems
- Vapour‑liquid equilibrium (VLE) predictions
- Safety analysis for flammable or volatile materials
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