Temperature Converter Explained: Celsius, Fahrenheit, Kelvin, Rankine and Réaumur

Why temperature conversion is trickier than length or weight

Convert 1 metre to feet and you multiply by a single number (3.2808). Convert 1 kilogram to pounds and you do the same (multiply by 2.2046). Temperature does not work that way, and the difference catches almost everyone the first time they meet it. The reason is that the temperature scales we use are affine, not linear — they have different zero points as well as different step sizes — so converting between them needs a stretch and a shift, never just one or the other. Doubling 10 °C does not give you 20 °C’s worth of Fahrenheit; you have to multiply 10 by 9/5 first and then add 32, which gives 50 °F, not the 100 °F that a naive doubling would suggest. The temperature converter handles this automatically for every pair of scales, but the formulas underneath are worth understanding once.

This guide walks through the five scales the calculator supports — Celsius, Fahrenheit, Kelvin, Rankine and Réaumur — how each is defined under the SI, the exact conversion formulas, the historical reasons Fahrenheit looks so awkward compared to Celsius, and the absolute-zero floor that no temperature can go below. After reading it you should be able to do every conversion the temperature converter does by hand, and to spot when an online answer somewhere has been rounded too aggressively.

What a temperature scale actually is

A temperature scale is two choices: a zero point and a step size. Celsius chooses the freezing point of water at 1 atmosphere as its zero and divides the gap to the boiling point into 100 equal degrees. Fahrenheit historically chose the freezing point of a cold brine as its zero and divided the gap to human body temperature into 96 (later 180, after the scale was redefined against water). Kelvin chooses absolute zero — the temperature at which thermal motion stops — as its zero and uses Celsius-sized degrees. Rankine chooses absolute zero too but uses Fahrenheit-sized degrees. Réaumur chooses the freezing point of water and divides the gap to boiling into 80 degrees.

Every pairwise conversion is therefore an affine transformation — one multiplication for the step-size ratio and one addition for the zero-point offset. The temperature converter stores Celsius as the canonical intermediate and converts everything via it, which keeps the implementation small and avoids the rounding drift that would show up if it converted directly between, say, Fahrenheit and Rankine. The next sections cover each scale in turn before bringing them together with the worked example.

Celsius: the everyday metric scale

Celsius was proposed by Anders Celsius in 1742 and originally ran backwards — 0 °C was the boiling point of water and 100 °C was the freezing point. Carl Linnaeus flipped it the following year to the orientation we use today. Since 2019 it has been defined by the SI as 0 °C = 273.15 K exactly, with the kelvin itself defined via the Boltzmann constant. That makes the freezing point of water at 1 atm approximately 0 °C and the boiling point approximately 100 °C — the “approximately” matters at the millikelvin level but never matters for everyday life.

Celsius is the working scale in almost every country and almost every science. Weather forecasts, thermostats, ovens, refrigerators, lab equipment, medicine, engineering specifications outside the US — all use Celsius. The big exceptions are the United States (Fahrenheit for weather, cooking and body temperature) and physics and chemistry calculations involving ratios (which use Kelvin). The temperature converter uses Celsius as its default “From” scale because most users start there.

Fahrenheit: the awkward one, explained

Daniel Fahrenheit proposed his scale in 1724 and built precision mercury thermometers to support it. He picked 0 °F as the freezing point of a mixture of ice, water and ammonium chloride — the coldest stable mix he could reliably produce in his Amsterdam lab — and 96 °F as human body temperature, with 32 °F as the freezing point of pure water. The choice of 96 looks bizarre now but was deliberate: 96 = 2⁵ × 3, so the scale could be divided in half repeatedly without fractions, which mattered for marking the brass scales on his thermometers. The 32 was probably an accident of the brine mix.

In 1859 the scale was redefined against the freezing and boiling points of water at 32 °F and 212 °F exactly, which fixed the awkward 98.6 °F for body temperature (originally 96, drifted up after recalibration). The 180-degree span from freezing to boiling is what produces the 9/5 ratio with Celsius: 180 / 100 = 9/5. So the conversion is:

F = C × 9/5 + 32

and the inverse:

C = (F − 32) × 5/9

Fahrenheit survives in the United States and in a handful of Caribbean countries. It has a real ergonomic argument for weather use — the 0–100 °F range covers roughly the temperatures a human will experience in everyday life in temperate climates, whereas Celsius wastes half its 0–100 range on temperatures you would never live in. For anything technical, Celsius and Kelvin are the standards. The temperature converter handles Fahrenheit alongside the rest with no special case.

Kelvin: the SI base unit

Kelvin is the SI base unit for temperature. It uses Celsius-sized degrees but counts from absolute zero, so the conversion from Celsius is just an offset:

K = C + 273.15

with the inverse C = K − 273.15. Note the missing degree sign — Kelvin is written as “300 K”, not “300 °K”, because it is a unit of thermodynamic temperature rather than a position on a scale that needs a degree symbol. The same convention applies to differences: a 10 K change is the same size as a 10 °C change but is written without the degree symbol.

Use Kelvin for any calculation that depends on absolute temperature: the ideal gas law (PV = nRT), the Stefan–Boltzmann radiation law (P = σAT⁴), the Arrhenius equation, thermal-expansion coefficients, the Carnot efficiency of a heat engine (1 − T_cold/T_hot). The reason is that ratios of temperatures only make physical sense on an absolute scale. 300 K is genuinely twice as hot as 150 K in the sense that a black body at 300 K radiates 2⁴ = 16 times as much power per unit area as one at 150 K; 30 °C is not twice as hot as 15 °C in any meaningful sense.

Since the 2019 SI redefinition, the kelvin is defined via the Boltzmann constant k = 1.380649 × 10⁻²³ J/K exactly, rather than against the triple point of water as it used to be. The change does not affect any conversion at the precision you will ever care about, but it does mean Kelvin is now defined in terms of fundamental physical constants rather than a property of a substance.

Rankine: Kelvin with Fahrenheit-sized degrees

Rankine is the absolute scale you get if you keep the Fahrenheit degree but move the zero to absolute zero. The conversion from Kelvin is:

°R = K × 9/5

which makes 0 °R = absolute zero, 491.67 °R = the freezing point of water, and 671.67 °R = the boiling point. From Fahrenheit the conversion is the offset:

°R = F + 459.67

Rankine is used in US thermodynamics, HVAC and combustion engineering — places where Fahrenheit is the working scale but ratios or gas-law calculations need an absolute reference. The temperature converter includes it for that audience; outside that niche you will rarely see it.

Réaumur: the historical scale you still meet in cookbooks

René-Antoine Ferchault de Réaumur proposed his scale in 1730 and chose to divide the gap between freezing and boiling water into 80 degrees rather than 100. So 1 °Ré is 1.25 °C, and the conversion is:

°Ré = C × 4/5

Réaumur was widely used in continental Europe — France, Germany, Italy, Russia — until Celsius replaced it through the 19th century. You will still meet it in historical chemistry texts, in 18th- and 19th-century French and German cooking literature (cheese making, sugar boiling, syrup work in particular), and on antique thermometers. The temperature converter supports it because anyone reading those sources will occasionally need to translate a number into something modern.

Absolute zero and why the converter refuses to go below it

Absolute zero is the temperature at which classical thermal motion stops. On every scale it has a fixed value: 0 K = −273.15 °C = −459.67 °F = 0 °R = −218.52 °Ré. The third law of thermodynamics rules out reaching it exactly — you can only get arbitrarily close — but the value itself is exact under the SI definitions.

The temperature converter refuses to accept inputs below absolute zero on the chosen scale. If you ask it to convert −300 °C to Fahrenheit it returns an “Below absolute zero” message rather than a numerical answer, because no temperature can be colder. That guard exists because typos — an extra digit, a missing minus sign — can otherwise produce nonsense answers that look plausible. The same check applies whichever scale you start from: −500 °F, −1 K and −300 °Ré are all rejected, because all five scales agree on the floor.

Real laboratories have cooled small atomic samples to within a few nanokelvin of absolute zero using laser cooling and magnetic-trap evaporation, producing Bose–Einstein condensates and Fermi-degenerate gases. The current record is below 100 picokelvin in a controlled atom-interferometry experiment. No system has reached zero exactly, and the third law says none ever will.

Worked example: converting 100 °C to every other scale

Take 100 °C — the boiling point of water at 1 atmosphere — and convert it to every other scale by hand, the way the temperature converter does internally.

To Fahrenheit: F = 100 × 9/5 + 32 = 180 + 32 = 212 °F. The famous 212.

To Kelvin: K = 100 + 273.15 = 373.15 K. Add the offset and you are done.

To Rankine: °R = 373.15 × 9/5 = 671.67 °R. Or equivalently °R = 212 + 459.67 = 671.67 °R, which is a good cross-check.

To Réaumur: °Ré = 100 × 4/5 = 80 °Ré. By construction — Réaumur was defined so that 100 °C lands at 80 °Ré.

Now try the well-known crossover at −40. F = −40 × 9/5 + 32 = −72 + 32 = −40 °F. The two scales agree at exactly this one point, and the equality is the standard sanity check for any conversion tool.

Common mistakes

Forgetting the offset. By far the most common slip is multiplying by 9/5 without adding 32 (or subtracting 32 without dividing by 9/5). The offset is what makes temperature conversion affine rather than linear, and dropping it produces an answer that is consistently wrong by 32 degrees. The temperature converter applies the offset automatically; if you are doing the arithmetic by hand, write the formula out before plugging in numbers.

Confusing differences and absolute values. A temperature difference of 10 °C equals 18 °F (multiply by 9/5, no offset). A temperature of 10 °C equals 50 °F (multiply and add). Both are correct in their context — the difference between 50 °F and 32 °F is 18 °F = 10 °C, and 10 °C as an absolute temperature is 50 °F. The mistake is using the wrong formula for the wrong question.

Using Celsius in gas-law calculations. The ideal gas law PV = nRT uses absolute temperature. Plug a Celsius value in and the answer is meaningless — sometimes catastrophically so, if the temperature is near zero where the proportional error blows up. Always convert to Kelvin first.

Writing “°K” instead of “K”. The SI dropped the degree symbol for Kelvin in 1967. Modern usage is “300 K”, not “300 °K”. The degree symbol survives for Celsius, Fahrenheit, Rankine and Réaumur because those are scales with arbitrary zeros, whereas Kelvin is the unit of thermodynamic temperature.

Sources and further reading

The exact SI definitions of the kelvin and the other base units are in the BIPM’s SI Brochure. NIST publishes SP 811, the official US guide for the use of the SI, which includes the exact conversion factors for every base and derived unit. Both sources agree to the precision shown in the temperature converter, and both are the right place to look if you need a number to more decimal places than this article shows.

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