# Phase Rule Calculator (Gibbs Phase Rule)

URL: https://speedycalculator.com/calculators/chemistry/phase-rule/
Last updated: 2026-10-30

> The phase rule calculator applies Gibbs' phase rule F = C − P + 2 to find the degrees of freedom of a system in equilibrium from the number of components and phases, with options for fixed temperature or pressure and for counting components from species and reactions.

## Inputs

- How do you want to give the components?
- Number of components C
- Number of chemical species N
- Number of independent reactions R
- Extra constraints Z (fixed ratios, charge balance)
- Number of phases P
- Are temperature and pressure constant?

## Results

- Number of components C
- Degrees of freedom F
- Type of system
- Maximum number of coexisting phases (F = 0)
- Factor used in the rule

## Formula

```
F = C − P + 2 (T and P both free) · F = C − P + 1 (T or P fixed) · F = C − P (both fixed) · C = N − R − Z (species − independent reactions − extra constraints)
```

## Explanation

Gibbs' phase rule answers a simple question: how many intensive variables – temperature, pressure, concentrations – can you change independently without making a phase appear or disappear? That number is the degrees of freedom F. For pure water with liquid and vapour present (C = 1, P = 2), F = 1: choose the temperature and the pressure is fixed by the vapour-pressure curve. At the triple point, where ice, liquid and vapour coexist, F = 0 – there is exactly one temperature and pressure where this can happen.

The rule reads phase diagrams for you. Areas of a one-component diagram are bivariant (F = 2), lines are univariant (F = 1) and points are invariant (F = 0). It also caps the number of phases that can coexist: for one component at most three, for two components at most four.

Counting components is the tricky part. C is the smallest number of independent chemical species needed to describe every phase. Chemical equilibria and fixed ratios reduce it: in the decomposition NH₄Cl(s) ⇌ NH₃(g) + HCl(g) started from pure NH₄Cl, three species, one reaction and one stoichiometric constraint give C = 1.

### How to use the Phase Rule Calculator

- **How do you want to give the components?**
- **Number of components C**
- **Number of chemical species N**
- **Number of independent reactions R**
- **Extra constraints Z (fixed ratios, charge balance)**
- **Number of phases P**
- **Are temperature and pressure constant?**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the number of components (or the number of species, independent reactions and extra constraints, and let the calculator find C) and the number of phases. Choose whether temperature and pressure can vary: the "+2" becomes +1 if one of them is fixed and 0 if both are. The result is F; a negative value means that many phases cannot coexist at equilibrium.

### Worked example

Solid CaCO₃ heated in a closed vessel: CaCO₃(s) ⇌ CaO(s) + CO₂(g). Species N = 3, one independent reaction R = 1, no other constraint (the CO₂ and CaO are in different phases), so C = 2. Phases: two solids and one gas, P = 3. F = 2 − 3 + 2 = **1**: the system is univariant, so at each temperature there is only one equilibrium CO₂ pressure – the decomposition pressure of limestone.

The default inputs (C = 2, P = 2, both T and P free) give F = 2, for example a salt solution in equilibrium with its vapour: you can choose both temperature and concentration.

### Phase rule examples

SystemCPF (T, P free)Liquid water112Water + steam (boiling)121Ice + water + vapour (triple point)130Salt solution + vapour222Saturated salt solution + solid salt + vapour231NH₄Cl(s) ⇌ NH₃(g) + HCl(g)121

### Tips

- Use kelvin for every temperature in thermodynamic formulas – the unit menus convert for you.
- Watch the units: ΔH is usually in kJ/mol and ΔS in J/(mol·K).
- Tabulated values are for standard conditions (1 bar, usually 25 °C).
- Everything is calculated in your browser.

### Common mistakes to avoid

- Mixing kJ and J between ΔH and ΔS.
- Assuming ΔH and ΔS do not change with temperature over large ranges.
- Using Celsius in ln(T₂/T₁).

### Inputs explained

FieldWhat to enterHow do you want to give the components?Choose one: I know the number of components C, Count from species, reactions and constraintsNumber of components CA numberNumber of chemical species NA numberNumber of independent reactions RA numberExtra constraints Z (fixed ratios, charge balance)A numberNumber of phases PA numberAre temperature and pressure constant?Choose one: Neither is fixed (+2), One of them is fixed (+1), Both are fixed (+0)

### What each result means

- **Degrees of freedom F** = [Number of components C] - [Number of phases P] + [Are temperature and pressure constant?]
- **Maximum number of coexisting phases (F = 0)** = [Number of components C] + [Are temperature and pressure constant?]

## Worked example

Inputs — How do you want to give the components?: I know the number of components C; Number of components C: 2; Number of phases P: 2; Are temperature and pressure constant?: Neither is fixed (+2).

Results — Number of components C = 2; **Degrees of freedom F = 2**; Type of system = Bivariant – an area on the phase diagram; Maximum number of coexisting phases (F = 0) = 4; Factor used in the rule = 2.

## Key terms

- **Degrees of freedom (F)**: The number of intensive variables that can be changed independently without changing the number of phases.
- **Component**: An independently variable chemical constituent; the minimum number needed to define the composition of every phase.
- **Phase**: A homogeneous, physically distinct part of a system separated from others by boundaries.
- **Invariant point**: A state with F = 0, such as a triple point or a eutectic at fixed pressure.

## FAQ

**What is the phase rule formula?**
F = C − P + 2, where F is the degrees of freedom, C the number of components and P the number of phases. The 2 stands for temperature and pressure.

**How many degrees of freedom does the triple point of water have?**
None: C = 1 and P = 3, so F = 1 − 3 + 2 = 0. The triple point is at exactly 273.16 K and 611.66 Pa.

**How many phases can coexist in a one-component system?**
At most three, because F cannot be negative: 1 − P + 2 ≥ 0 gives P ≤ 3.

**When do I use F = C − P + 1?**
When either temperature or pressure is held constant, as in most binary phase diagrams drawn at 1 atm. This is the "condensed" phase rule.

**How do I count components with a chemical reaction?**
Subtract one for each independent equilibrium reaction and one for each extra restriction from the number of species. For CaCO₃(s) ⇌ CaO(s) + CO₂(g): 3 species − 1 reaction = 2 components.

**What is a phase?**
A region of uniform composition and physical state. Two immiscible liquids are two phases; a mixture of gases is always one phase.

**What does a negative F mean?**
That the chosen number of phases cannot be in equilibrium together – one of them must disappear.

**What formula does the Phase Rule Calculator use?**
F = C − P + 2 (T and P both free) · F = C − P + 1 (T or P fixed) · F = C − P (both fixed) · C = N − R − Z (species − independent reactions − extra constraints).


## Sources

- [IUPAC Compendium of Chemical Terminology (Gold Book)](https://goldbook.iupac.org/)
- [LibreTexts Chemistry](https://chem.libretexts.org/)
- [OpenStax – Chemistry 2e](https://openstax.org/details/books/chemistry-2e)