Kelvin
The kelvin is the SI unit of temperature on an absolute scale that starts at absolute zero; K equals degrees Celsius plus 273.15.
Formula
K = ^\circ C + 273.15
Definition
The kelvin is the SI base unit of temperature, built on an absolute scale whose zero, absolute zero, is the coldest anything can possibly be, so there are no negative kelvin readings. A kelvin step is the same size as a Celsius degree; the scales just start counting from different places, and converting between them means adding $273.15$ to a Celsius reading: $K = ^\circ\text{C} + 273.15$. Since 2019 the kelvin has been defined by fixing Boltzmann's constant at exactly $k = 1.380649 \times 10^{-23}\ \text{J/K}$, tying temperature directly to energy per particle, with the triple point of water at $273.16\ \text{K}$ and the ice point at $273.15\ \text{K}$. Absolute temperature is what appears in every fundamental thermodynamic relation, including the ideal gas law $PV = nRT$, the Carnot efficiency $1 - T_c/T_h$, the Boltzmann factor $e^{-E/kT}$, and blackbody radiation $P \propto T^4$.
Example
Water freezes at $273\ \text{K}$ and boils at $373\ \text{K}$, and room temperature is about $293\ \text{K}$; converting $-40^\circ\text{C}$ gives $-40 + 273.15 = 233.15\ \text{K}$, and converting $310\ \text{K}$ (body temperature) back gives $310 - 273.15 = 36.85^\circ\text{C}$. A sealed rigid container of gas at $27^\circ\text{C}$ ($300\ \text{K}$) and $150\ \text{kPa}$ heated to $127^\circ\text{C}$ ($400\ \text{K}$) reaches $P_2 = 150 \times 400/300 = 200\ \text{kPa}$, since pressure scales with absolute temperature; using Celsius directly would have predicted a nonsensical $150 \times 127/27 \approx 706\ \text{kPa}$.
Key Insight
Gas laws only work with kelvin: saying a gas at $20^\circ\text{C}$ has twice the pressure of the same gas at $10^\circ\text{C}$ is wrong, since the real ratio is $293/283$, about $1.04$. The Kelvin scale exists because temperature is fundamentally energy per degree of freedom, and only a scale whose zero means zero thermal energy can make ratios of temperatures physically meaningful.