Gibbs' Phase Rule Calculator

Created by Filip Derma
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Sep 21, 2023

Gibbs' phase rule calculator assists you in calculating the number of anova degrees of freedom calculator degrees of freedom for the phase rule. In the article below, you can find the explanation of Gibbs' phase rule, Gibb's equation, and some information about how to use the calculator correctly. Scroll down to find out more!

💡 For more about calculating the degrees of freedom of a system, check out our degrees of freedom calculator.

What is Gibbs' phase rule?

Gibbs' phase rule is based on the laws of thermodynamics and provides the theoretical principle for characterizing the chemical state of a system. It predicts the equilibrium relations of phases and is present as a function of physical conditions such as pressure and temperature. Moreover, the phase rule allows the creation of phase diagrams to represent and interpret phase equilibria in heterogeneous systems.

The phase rule equation proposed by Josiah Willard Gibbs in 1875 (American theoretical physicist, a professor at Yale University) is expressed by the formula:

F = C - P + factor


  • F – Number of degrees of freedom;
  • C – Number of components;
  • P – Number of phases in the system; and
  • factor (by default = 2) – An integer value in the equation that depends on the temperature and pressure of the system (see the pressure calculator). If one of these variables is constant, you have to change its value to "1". If both are constant, change the value to "0".

This equation allows computing the number of degrees of freedom (F) from the number of components (C) and the number of phases in the system (P).

Phase rule details

Number of phases (P)

A phase is a form of matter which is homogeneous in the chemical composition and physical properties throughout its volume. It is also a physically separable material in the system. We can distinguish:

  • Solid;
  • Liquid;
  • Gas; and
  • Plasma.

Number of components (C)

C means the minimum number of chemical components required to constitute all the phases in the system. The compound cannot be a product of the chemical reaction between other components of the system.

Number of degrees of freedom (F)

F refers to the number of variables (e.g., temperature, pressure, the concentration of the component) that can be changed independently (with certain limits) without altering the state of the system (e.g., the number of phases and compounds).

The number of degrees of freedom increases with the increasing number of components and with the decreasing number of phases in balance.

Gibb's equation

Let's see the application of Gibbs' equation in the example below:

NH₄HCO₃(s) <-> NH₃(g) + CO₂(g) + H₂0(g)

In this system, there are 4 compounds, 1 equation, and 2 conditions (the third condition results from the previous two):

I. [NH₃] = [CO₂]
II. [CO₂] = [H₂0]
III. [NH₃] = [H₂0]

That gives:

C = 4 - 1 - 2 = 1

P = 2

And the number of degrees of freedom equals:

F = 2 + 1 - 2 = 1

How to use Gibbs' phase rule calculator

  1. Choose the chemical system for calculations. Let's assume that it consists of 1 component, which is present in 2 phases.

  2. In that system, both pressure and temperature can change.

  3. Type in the relevant numbers into the calculator: the number of compounds and number of phases; the factor is equal 2 for this example.

  4. Check the result in the last calculator field 😀

    F = 1 - 2 + 2 - 0 = 1

Now you can do your calculations with Gibbs' phase rule calculator.

💡 You might be interested in our Gibbs free energy calculator, which tells you whether a chemical reaction will be spontaneous or not.

Filip Derma
Number of:
Pressure and temperature variability
Degrees of freedom
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