Phase Rule Calculator — Gibbs Phase Rule F = C − P + 2
Enter the number of chemical components and phases in your system to compute the thermodynamic degrees of freedom using the Gibbs Phase Rule. Choose between the full rule (T and P variable) or the condensed form (constant pressure).
System type
3 degrees of freedom
Gibbs phase rule: F = C − P + 2
Substitute values
Degrees of freedom (F)
- 1
Components (C)
2 - 2
Phases (P)
1 - 3
Degrees of freedom F = C − P + 2
2 − 1 + 2 = 3
How does this calculator work?
F = C − P + 2 gives the number of independent intensive variables (temperature, pressure, composition) you can change without altering the number of phases. F = 0 (invariant): all variables fixed. F = 1 (univariant): one variable free. Use F = C − P + 1 for constant-pressure systems like phase diagrams.
Formula
How this is calculated
The Gibbs Phase Rule, derived by J. Willard Gibbs in 1875, states that at thermodynamic equilibrium: F = C − P + 2, where F is the variance (degrees of freedom — the number of intensive variables such as temperature or pressure that can be independently varied without changing the number of phases), C is the number of chemically independent components (the minimum number of species needed to describe the composition of all phases), and P is the number of phases present. The "+2" accounts for the two independent intensive variables temperature and pressure.
For systems at constant pressure (metallurgical phase diagrams, atmospheric-pressure experiments), pressure is fixed and is no longer a free variable, reducing the equation to the condensed form F = C − P + 1. The condensed rule is standard for binary and ternary alloy phase diagrams.
Key examples: pure water (C=1) with one phase (liquid) has F=2; it can exist as a single-phase liquid over a range of T and P. At the triple point (C=1, P=3), F=0 — T and P are completely fixed. For a two-component system (C=2) in a two-phase region (P=2), F=2, meaning both T and one composition can be freely varied. A negative F indicates a physically impossible combination — you cannot have more phases than C + 2 simultaneously at equilibrium.
Frequently asked questions
A component is the minimum number of chemically independent species needed to define the composition of every phase in the system. For pure water, C = 1 (just H₂O). For a salt dissolved in water, C = 2 (water + salt) — even though water contains H and O, the composition of all phases can be described with just two independent species.
At the triple point of a single-component system (C = 1, P = 3), F = 1 − 3 + 2 = 0. Zero degrees of freedom means neither temperature nor pressure can be varied without destroying one of the three phases. The triple point of water occurs at exactly 273.16 K and 611.66 Pa — it is used to define the kelvin.
Use the condensed form when pressure is fixed and is no longer a controllable variable — most commonly for metallurgical or ceramic phase diagrams where experiments and processes occur at atmospheric pressure. For example, a binary alloy (C = 2) in a two-phase region at constant pressure has F = 1, meaning only temperature (or equivalently composition) can be varied independently.
Also known as
TG we-Calculate Editorial Team. (2026). Phase Rule Calculator — Gibbs Phase Rule F = C − P + 2 [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/phase-rule-calculator
TG we-Calculate Editorial Team. "Phase Rule Calculator — Gibbs Phase Rule F = C − P + 2." TG we-Calculate. 2026. https://we-calculate.com/calculator/phase-rule-calculator.
TG we-Calculate Editorial Team, "Phase Rule Calculator — Gibbs Phase Rule F = C − P + 2," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/phase-rule-calculator
@misc{wecalculate_phase_rule_calculator, title = {Phase Rule Calculator — Gibbs Phase Rule F = C − P + 2}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/phase-rule-calculator}}, year = {2026}, note = {TG we-Calculate} }
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