Temperature Scale Converter

Physics Thermodynamics • Temperature and Zeroth Law

Written by STEM Calculators Team Published January 2, 2026 Updated February 24, 2026

1. Temperature Scale Converter

Convert between $^{\circ}\mathrm{C}$ , $\mathrm{K}$ , $^{\circ}\mathrm{F}$ , and $\,^{\circ}\mathrm{R}$ (Rankine), with absolute-zero checking, detailed steps, a particle-state animation, and a multi-scale temperature graph.

You can type in any scale field. Values below absolute zero are rejected. Slider updates in real time. Materials use known melting/boiling points to show solid/liquid/gas.

Inputs (bidirectional)

$T$ in $^{\circ}\mathrm{C}$: $T$ in $\mathrm{K}$: $T$ in $^{\circ}\mathrm{F}$: $T$ in $^{\circ}\mathrm{R}$:

Real-time slider (Celsius): 100 °C

Tip: Adjust the slider range in “Graph window” if you want higher/lower temperatures.

Absolute zero + quick facts

Absolute zero: $0\,\mathrm{K} = -273.15^{\circ}\mathrm{C} = -459.67^{\circ}\mathrm{F} = 0^{\circ}\mathrm{R}$.
Water reference: freezing $0^{\circ}\mathrm{C}$, boiling $100^{\circ}\mathrm{C}$ at 1 atm (approx.).
Triple point of water: $273.16\,\mathrm{K}$ (university extension; see theory).

Material (for particle-state animation)

Choose material: Melting/freezing point $T_m$ (°C): Boiling point $T_b$ (°C):

The animation switches: solid if $T<T_m$, liquid if $T_m\le T<T_b$, gas if $T\ge T_b$. (Near $T_m$ or $T_b$, you’ll see “phase change” behavior.)

Graph window (optional)

Graph min (°C): Graph max (°C): Tick density:

The scale-graph shows aligned rulers for $^{\circ}\mathrm{C}$, $\mathrm{K}$, $^{\circ}\mathrm{F}$, and $^{\circ}\mathrm{R}$, and marks the current temperature.

Ready

Steps

Enter a temperature in any scale, then click Convert.

Particle animation

State preview: —

Particles move faster at higher temperature; arrangement changes by state (solid/liquid/gas).

Multi-scale graph

Temperature rulers: $^{\circ}\mathrm{C}$, $\mathrm{K}$, $^{\circ}\mathrm{F}$, $^{\circ}\mathrm{R}$

Hover to read: $T_C$, $T_K$, $T_F$, $T_R$.

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1. Temperature Scale Converter — Theory

Temperature scales are linear mappings of the same physical quantity. This page explains how each scale is defined, why absolute zero matters, and how phase (solid/liquid/gas) relates to melting and boiling points.

1) Celsius, Kelvin, Fahrenheit, Rankine

The common conversion formulas can be derived from two facts: (i) the scales are linear, and (ii) they share reference points (like the freezing/boiling of water in basic contexts).

\[ T_K = T_C + 273.15 \] \[ T_F = T_C\frac{9}{5} + 32 \] \[ T_R = T_K\frac{9}{5} = (T_C + 273.15)\frac{9}{5} \] \[ T_C = (T_F - 32)\frac{5}{9}, \qquad T_C = T_R\frac{5}{9} - 273.15 \]

Kelvin ($\mathrm{K}$) and Rankine ($^{\circ}\mathrm{R}$) are absolute scales (their zero corresponds to absolute zero). Celsius and Fahrenheit are offset scales that place zero at a historical reference.

2) Absolute zero and physical validity

Absolute zero is the lowest possible temperature in classical thermodynamics (where thermal motion is minimal). Any computed temperature below absolute zero is physically invalid and should be rejected.

\[ 0\,\mathrm{K} = -273.15^{\circ}\mathrm{C} = -459.67^{\circ}\mathrm{F} = 0^{\circ}\mathrm{R}. \]

3) Phase (solid/liquid/gas) from melting and boiling points

For a chosen material, two characteristic temperatures are used: the melting/freezing point $T_m$ and the boiling point $T_b$ (usually quoted at 1 atm unless stated otherwise). A simple phase rule is:

\[ T < T_m \Rightarrow \text{solid}, \qquad T_m \le T < T_b \Rightarrow \text{liquid}, \qquad T \ge T_b \Rightarrow \text{gas}. \]

Near $T_m$ or $T_b$, real substances can undergo a phase change where both phases coexist. The calculator’s animation shows a transitional behavior in a small band around those points.

4) Graph interpretation: aligned rulers

The graph displays four aligned rulers for the same physical temperature window (in °C internally). A single vertical marker corresponds to the same physical temperature, while each row shows the numeric value in its own unit.

Absolute zero is marked when it lies inside the current window.
$T_m$ and $T_b$ are marked to show where the material changes phase.
You can pan/zoom the graph to focus on specific ranges.

5) Extensions (university notes)

Triple point: For water, the triple point is $273.16\,\mathrm{K}$, used historically as a calibration reference.
ITS-90: In precise thermometry, practical temperature scales (like ITS-90) define interpolation instruments and fixed points for high-accuracy measurements.
Pressure dependence: Melting/boiling points depend on pressure (phase diagrams). The “known” values in the presets are typical 1 atm values.

Steps

Particle animation

Multi-scale graph

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