Kelvin equals Celsius plus 273.15. The two scales have identical degree sizes and differ only in where they put zero, which makes this the simplest temperature conversion — and the only one where a temperature difference converts one-for-one.
About the units
The kelvin is the SI base unit of temperature and the only one of the common scales with a physically meaningful zero: 0 K is absolute zero, the point at which a system has minimum thermal energy. Nothing can be colder, which is why kelvin values are never negative. Since the 2019 SI revision the kelvin has been defined by fixing the Boltzmann constant at exactly 1.380649 × 10⁻²³ joules per kelvin. Note the notation: it is written K, not °K, and spoken as "kelvin" rather than "degrees kelvin" — the degree sign was dropped in 1967 precisely because the scale is absolute rather than relative to an arbitrary reference.
The exact factor
The relationship is K = °C + 273.15, exactly. The offset is not a rounded figure: it was chosen so that the triple point of water sits at exactly 273.16 K, which under the pre-2019 definition was what defined the kelvin. Because the degree size is identical, a temperature interval converts without any offset at all: a rise of 5 °C is a rise of 5 K, and heat capacities are written per kelvin regardless of which scale the temperatures themselves are in. That is the practical reason scientists prefer kelvin — it removes a whole class of offset errors from thermodynamic arithmetic.
Where you meet this conversion
All of physics and chemistry, where gas laws, thermodynamic relations and radiation formulas require absolute temperature. A gas law calculation done in Celsius gives nonsense, because doubling 20 °C is not doubling the thermal energy while doubling 293.15 K is. Colour temperature of light sources is quoted in kelvin — 2,700 K for a warm bulb, 6,500 K for daylight — and cryogenics works entirely in kelvin, where liquid nitrogen boils at 77 K and liquid helium at 4.2 K.