Equilibrium Constant Calculator
Calculate the equilibrium constant Kc from the equilibrium concentrations of reactants and products. Enter the stoichiometric coefficients and concentrations from your balanced equation to get Kc, 1/Kc, and whether the reaction is product- or reactant-favoured.
Find Kc from Equilibrium Concentrations
Equilibrium Constant Formula
Where:
- \(K_c\) — concentration equilibrium constant (dimensionless)
- \([A]\), \([B]\) — equilibrium concentrations of the reactants (mol/L)
- \([C]\), \([D]\) — equilibrium concentrations of the products (mol/L)
- \(a\), \(b\), \(c\), \(d\) — stoichiometric coefficients from the balanced equation \(aA + bB \rightleftharpoons cC + dD\)
The formula states that for a reversible reaction at equilibrium, the product of the product concentrations (each raised to its coefficient) divided by the product of the reactant concentrations (each raised to its coefficient) is a constant at a given temperature. If a species is absent, its term simply drops out of the expression.
Equilibrium Constant – Calculation Example
Example: for the reaction \(A + B \rightleftharpoons C + D\) (all coefficients equal to 1), the equilibrium concentrations are \([A] = 0.5\ \text{mol/L}\), \([B] = 0.3\ \text{mol/L}\), \([C] = 0.4\ \text{mol/L}\) and \([D] = 0.2\ \text{mol/L}\).
\[ K_c = \frac{[C]^1[D]^1}{[A]^1[B]^1} = \frac{0.4 \times 0.2}{0.5 \times 0.3} = \frac{0.08}{0.15} \approx 0.5333 \]
\[ \frac{1}{K_c} = \frac{1}{0.5333} \approx 1.875 \]
Result: \(K_c \approx 0.5333\); since \(K_c < 1\), the equilibrium mixture is dominated by reactants. The reverse reaction has \(K_c \approx 1.875\).
How to Use the Calculator
- Start with a balanced chemical equation. If you need help balancing one, use the Chemical Equation Balancer first.
- In Number of Reactants, select "1 reactant" or "2 reactants" depending on how many species appear on the left side of your equation. Do the same for Number of Products.
- Enter the Coefficient of A (a) and the Concentration of A [A] with its unit (mol/L or mmol/L) for the first reactant. If you selected 2 reactants, fill in Coefficient of B (b) and Concentration of B [B] as well.
- Enter the coefficients and equilibrium concentrations of the products: Coefficient of C (c), Concentration of C [C], and, if applicable, Coefficient of D (d) and Concentration of D [D].
- Read the results: the Concentration Equilibrium Constant \(K_c\), the Equilibrium Constant of the Reverse Reaction \(1/K_c\), and the Position of Equilibrium, which tells you whether products or reactants dominate.
What Is the Equilibrium Constant?
A reversible reaction does not stop when reactants and products reach equal amounts — it stops changing when the forward and reverse rates become equal. At that point, the equilibrium composition is fixed, and the ratio defined by the equilibrium expression is a constant characteristic of the reaction at that temperature. This constant, \(K_c\), tells you how far a reaction proceeds toward products before the net change ceases.
The value of \(K_c\) is a measure of the position of equilibrium. A large \(K_c\) (roughly above \(10^3\)) means the reaction goes almost to completion: at equilibrium, almost everything has been converted to products. A small \(K_c\) (roughly below \(10^{-3}\)) means very little product forms. Values in between indicate a genuine mixture of reactants and products at equilibrium. Note that \(K_c\) says nothing about how fast equilibrium is reached — that is a question of reaction rate, covered by the Arrhenius Equation.
Every reaction has a matching reverse reaction whose equilibrium constant is the reciprocal: \(K_{reverse} = 1/K_{forward}\). This is why the calculator also reports \(1/K_c\) — useful when you are asked about the reverse direction or want to check consistency between tabulated values.
\(K_c\) is temperature-dependent. Changing concentration, pressure or volume shifts the equilibrium position (Le Chatelier's principle) but never changes \(K_c\); only a change in temperature does. When comparing values from different sources, always check they refer to the same temperature.
Assumptions, Limitations and Practical Tips
- Use equilibrium concentrations, not starting ones. The calculator expects the concentrations that exist at equilibrium. If you are given initial concentrations and one equilibrium value, set up an ICE table (Initial, Change, Equilibrium) first to work out the remaining equilibrium concentrations.
- The equation must be balanced. The coefficients you enter are used as exponents, so an unbalanced equation gives a wrong \(K_c\).
- Pure solids and liquids are excluded. Only dissolved species (and gases, for \(K_p\)) appear in the equilibrium expression. If your reaction involves a solid or pure liquid, omit it from the count of reactants or products.
- The calculator handles up to 2 reactants and 2 products. For reactions with more species, apply the same pattern by hand: every product concentration to its coefficient power in the numerator, every reactant concentration to its coefficient power in the denominator.
- Units are converted automatically. Concentrations entered in mmol/L are converted to mol/L before the calculation, so all terms must simply be in the same unit system for the result to be meaningful.
- \(K_c\) is formally dimensionless. Although the underlying concentrations carry units, thermodynamic equilibrium constants are defined in terms of activities, so the result is treated as a pure number.
- Equilibrium problems often involve solutions prepared from molar masses. To convert between mass and concentration, the Molarity and Molality calculators can help.
Frequently Asked Questions
How do I calculate Kc step by step by hand?
First, write the balanced equation, e.g. \(N_2 + 3H_2 \rightleftharpoons 2NH_3\). Second, build the expression with each concentration raised to its coefficient: \(K_c = \frac{[NH_3]^2}{[N_2][H_2]^3}\). Third, substitute the equilibrium concentrations in mol/L and compute. For example, with \([N_2] = 0.5\), \([H_2] = 1.0\), \([NH_3] = 0.2\): \(K_c = \frac{0.2^2}{0.5 \times 1.0^3} = 0.08\).
What is the difference between Kc and Kp, and how do I convert between them?
\(K_c\) is written in terms of molar concentrations, while \(K_p\) uses partial pressures of gases. They are related by \(K_p = K_c(RT)^{\Delta n}\), where \(R = 0.0821\ \text{L·atm/(mol·K)}\), \(T\) is the temperature in kelvin, and \(\Delta n\) is the change in moles of gas (products minus reactants). If \(\Delta n = 0\), then \(K_p = K_c\).
How is Kc related to Gibbs free energy?
The standard Gibbs free energy change and the equilibrium constant are linked by \(\Delta G^\circ = -RT\ln K\), with \(R = 8.314\ \text{J/(mol·K)}\) and \(T\) in kelvin. A negative \(\Delta G^\circ\) corresponds to \(K > 1\) (product-favoured), while a positive \(\Delta G^\circ\) corresponds to \(K < 1\). When \(\Delta G^\circ = 0\), the equilibrium constant equals exactly 1.
If I already know Kc, how do I find the equilibrium concentrations?
This is the reverse problem. Set up an ICE table: write initial concentrations, express changes in terms of an unknown \(x\) using the stoichiometric coefficients, and write equilibrium concentrations as algebraic expressions. Substitute these into the \(K_c\) expression and solve for \(x\). This often produces a quadratic equation; if \(K_c\) is very large or very small, a simplifying approximation (dropping \(x\) added to or subtracted from a big number) is usually valid.
What is the difference between Kc and the reaction quotient Q?
They use the same mathematical expression, but \(K_c\) is built from equilibrium concentrations while \(Q\) is built from concentrations at any moment. Comparing them predicts the direction of change: if \(Q K_c\), it shifts backward toward reactants; if \(Q = K_c\), the system is already at equilibrium.
Does a catalyst or a change in concentration affect Kc?
No. A catalyst speeds up both the forward and reverse reactions equally, so it changes how quickly equilibrium is reached but never the value of \(K_c\). Similarly, changing concentrations, pressure, or volume shifts the position of equilibrium (Le Chatelier's principle) without altering \(K_c\). Only a change in temperature changes \(K_c\) itself, so always record the temperature with any tabulated value.
What happens to Kc if I multiply or reverse the equation?
Reversing a reaction inverts the constant: \(K_{reverse} = 1/K_{forward}\) — that is why the calculator reports \(1/K_c\). Multiplying all coefficients by a factor \(n\) raises the constant to that power: \(K' = K_c^n\). For example, doubling every coefficient squares \(K_c\). This is also why fractional coefficients (common in thermodynamics tables) must be handled carefully when comparing values from different sources.