Kₚ equilibrium constant calculator
Convert between concentration-based Kc and pressure-based Kp for an ideal-gas reaction using temperature, pressure units, and the change in gaseous stoichiometric moles.
Example workbook is ready.
Reaction inputs
Live result
Gas constants used by pressure basis
| Pressure unit | R value | R unit | Current selection |
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The numerical value of R must match the pressure unit used for Kp. Torr and mmHg use the same conventional numerical value here.
How to use the Kₚ equilibrium constant calculator
What this calculator does. This tool converts between Kc, an equilibrium constant written from molar concentrations, and Kp, an equilibrium constant written from gaseous partial pressures. It applies the ideal-gas relationship Kp = Kc(RT)Δn, where Δn is the total stoichiometric moles of gaseous products minus the total stoichiometric moles of gaseous reactants. It does not balance a chemical equation, identify phases, or determine whether an experimental mixture has reached equilibrium; those tasks must be completed before entering values. For a broader explanation of gas-phase equilibrium expressions, see the Chemistry LibreTexts guide to gas equilibrium constants.
When to use it. Use the calculator when a textbook, laboratory report, or thermodynamics problem gives Kc but requests Kp; when a pressure-based constant must be converted back to a concentration-based constant; when checking the effect of reaction stoichiometry on the conversion; or when comparing answers expressed with atm, kPa, bar, Torr, or mmHg conventions.
How to calculate. The calculator opens with a complete demonstration for N2(g) + 3H2(g) ⇌ 2NH3(g): Kc = 0.0227, T = 298 K, two gaseous product moles, and four gaseous reactant moles. The example result and a validated Excel workbook are available immediately.
- Select Conversion direction to state whether the known value is Kc or Kp.
- Replace Equilibrium constant (Kc/Kp) with the positive known constant. Plain decimals and scientific notation such as 2.27e-2 are accepted.
- Choose the Pressure unit for Kp, then enter Temperature (T) in kelvin.
- Enter the summed stoichiometric coefficients in Gaseous product moles and Gaseous reactant moles. Include gases only; omit pure solids and liquids.
- Read the primary constant, Δn, R, RT, conversion factor, and substituted formula. Select Download Excel to export the current validated state. Reset clears the demonstration values, results, and workbook state; Download Excel remains unavailable until a complete valid state is entered again.
Input guide. Conversion direction is required and changes which constant is treated as the input and which is solved. Equilibrium constant (Kc/Kp) is a required positive finite number; for example, 0.0227. Zero or negative values are rejected because an equilibrium constant for a valid equilibrium expression is positive. Pressure unit for Kp is required and selects a matching gas constant; changing it changes the numerical Kp convention whenever Δn is not zero. Temperature (T) is required in kelvin and must exceed zero; 298 is a typical room-temperature example, while entering Celsius directly is a common mistake. Gaseous product moles and Gaseous reactant moles are required nonnegative totals of balanced gaseous coefficients. Fractions are accepted when the balanced equation uses them. Do not count solids or pure liquids, and do not enter measured sample moles unless they happen to equal the stoichiometric totals.
Output guide. The primary Equilibrium constant (Kp/Kc) is the converted constant and is shown as a decimal or scientific notation. Change in gaseous moles (Δn) is products minus reactants; zero means Kp and Kc are numerically equal. Gas constant (R) is the pressure-compatible numerical constant. R × T is the ideal-gas conversion base, and Conversion factor (R × T)Δn is the multiplier used for Kc → Kp; for the reverse direction the calculator divides by that factor. The formula line is an exact identity based on the entered values, not a prediction of reaction yield or direction. A very large or small result can be chemically reasonable and should be interpreted in the context of the balanced reaction and temperature.
Worked example. For the startup reaction, Δn = 2 – 4 = – 2. On an atm basis R = 0.08205746 L·atm·mol – 1·K – 1, so RT = 0.08205746 × 298 = 24.4531. The factor is 24.4531 – 2 = 0.00167234. Multiplying Kc = 0.0227 by that factor gives Kp = 0.000037962, displayed as 3.7962 × 10 – 5. The workbook stores the unrounded numeric values and applies spreadsheet number formats for readability.
Learn more. The numerical gas constants are consistent with the exact SI molar gas constant documented in the NIST fundamental physical constants collection. For general equilibrium notation and interpretation, consult the IUPAC definition of equilibrium constant.
Formula, assumptions, and interpretation
For a balanced gas-phase reaction, Δn is calculated from stoichiometric coefficients, not from transient measured amounts. The relationship follows by substituting the ideal-gas expression for partial pressure into the concentration-based equilibrium expression. Because the exponent can be positive, zero, or negative, the same temperature and Kc can yield very different Kp values for reactions with different gas stoichiometry.
When Δn is positive, increasing temperature increases the numerical factor (RT)Δn. When Δn is negative, the factor decreases as temperature rises. This is a mathematical conversion effect and should not be confused with the physical temperature dependence of the equilibrium constant itself, which is governed by thermodynamics. The calculator converts constants specified at the same temperature; it does not use the van 't Hoff equation to predict K at another temperature.
Common mistakes
- Entering Celsius instead of kelvin. Convert with T(K) = T(°C) + 273.15.
- Counting solids or pure liquids in Δn. Only gaseous species contribute to this conversion exponent.
- Using unbalanced reaction coefficients or forgetting that reversing a reaction also inverts its equilibrium constant.
- Mixing an R value in kPa with a Kp intended for atm, bar, Torr, or mmHg.
- Interpreting Kp as a reaction rate. Equilibrium constants describe equilibrium composition tendencies, not how quickly equilibrium is reached.