A reading is not a change
This is the one thing about temperature conversion that is genuinely easy to get wrong, and almost every converter gets it wrong by omission.
“It is 20 °C outside” converts to 68 °F. That is a reading: a point on the scale, and converting it applies both the size of the degree and the offset between the two zeros.
“It rose by 20 °C” converts to a rise of 36 °F — not 68 °F. That is a difference, and a difference has no zero point, so the offset must not be applied. Only the degree size matters, and a Fahrenheit degree is five ninths the size of a Celsius one, so 20 × 9⁄5 = 36.
The gap between 68 and 36 is not subtle, and yet it survives in practice because both look like plausible temperatures. It corrupts anything expressed as a change: a delta-T across a heat exchanger, a “10 degrees warmer than yesterday” in a forecast, a thermal expansion coefficient, a temperature rise limit on a motor winding, the tolerance band on a datasheet. The mode switch at the top of the tool exists so that the choice is made deliberately rather than defaulted.
One shortcut worth memorising, because it removes the arithmetic entirely: a difference in degrees Celsius and a difference in kelvin are the same number. A kelvin and a degree Celsius are exactly the same size; only their zeros differ. So a rise of 12 °C is a rise of 12 K, always.
Why the scales have an offset at all
Every other converter in this category multiplies by a constant, because the units share a zero: zero metres is zero feet, zero litres is zero gallons. Temperature scales do not share a zero, because they were built around different reference points before anyone knew where the bottom of the scale was.
Celsius set zero at the freezing point of water and 100 at its boiling point, which is why the degree is the size it is. Fahrenheit set zero at the coldest temperature its author could reproduce — a brine freezing mixture — and 96 at roughly body temperature, which is why its degree is smaller and its zero lands 32 degrees below freezing water.
Both were later redefined in terms of the kelvin, which starts at absolute zero and therefore needs no offset at all. That redefinition is why the conversions are now exact rather than approximate: a degree Celsius is defined to be exactly the same size as a kelvin, and the Celsius zero is defined to be exactly 273.15 K. Nothing here is measured, so nothing here carries uncertainty.
Absolute zero, and the two absolute scales
Absolute zero is the point at which a system has no thermal energy left to give up. It is −273.15 °C, −459.67 °F, and by definition 0 on both absolute scales. Nothing can be colder, which is why this tool refuses a reading below it rather than returning a number: an impossible temperature is an input error, not a result.
There are two absolute scales because there are two degree sizes. Kelvin is the SI base unit and uses Celsius-sized degrees; it takes no degree symbol, being written 300 K rather than 300 °K. Rankine uses Fahrenheit-sized degrees, and exists so that American thermodynamics and aerospace work can stay in Fahrenheit units while still having an absolute scale — gas laws, thermal efficiency and anything involving a ratio of temperatures require one, because a ratio of Celsius or Fahrenheit readings is meaningless.
That last point is worth stating plainly: 40 °C is not “twice as hot” as 20 °C. The ratio only means something on an absolute scale, where the same two readings are 313.15 K and 293.15 K — about 7% apart, not 100%.
Where −40 comes from
−40 °C is −40 °F. It is the one reading where the two everyday scales agree, and it is not a coincidence — it is the single solution to a linear equation. Setting F = C and substituting F = C × 9⁄5 + 32 gives C = C × 9⁄5 + 32, so −4⁄5 C = 32, and C = −40.
Two scales cross exactly once whenever their degrees are different sizes, and never when the degrees are the same size — Celsius and kelvin are parallel, so they never meet however far the scale is extended. The tool computes the crossing rather than storing it, so the same reasoning holds for any pair it offers.
It is genuinely useful as a sanity check. If a conversion sends a number the wrong side of −40, the sign or the direction is wrong: above −40 the Fahrenheit figure is always the larger of the two, and below it, always the smaller.
Doing it in a spreadsheet
CONVERT handles readings: =CONVERT(A1,"C","F"), with "K" and "Rank" for the absolute scales. Written by hand it is =A1*9/5+32 for Celsius to Fahrenheit and =(A1-32)*5/9 back.
For a difference, drop the offset: =A1*9/5 converts a change in Celsius to a change in Fahrenheit, and =A1*5/9 goes the other way. Using CONVERT on a delta is the spreadsheet version of the mistake this whole page is about — it will apply the offset and hand back a number that looks like a temperature.
A guard worth adding to any sheet holding readings: =IF(A1<-273.15,"below absolute zero",A1*9/5+32). A sensor fault often shows up as a large negative reading, and without the check it converts quietly into a plausible-looking Fahrenheit figure.
Sources and methodology
Nothing here is fetched and there is no data feed: every figure is computed from what you type. The conversions are definitional, and the one that most needs a citation is the distinction this page is built on — NIST’s own guide states plainly that a temperature difference in degrees Celsius equals the same number of kelvins while a temperature value does not.