Temperature Converter
Celsius, Fahrenheit, Kelvin and Rankine. Temperature is the one conversion on this site that is not a factor — the scales disagree about where zero is, so every answer needs an offset as well as a multiplier, and this page shows you both.
Convert a temperature
The reading you have, on the scale chosen below. Negative values are fine down to absolute zero.
The scale the reading is already on.
The scale you want the answer on. All four are listed underneath the result anyway.
Not a factor — an offset and a scale. Everything routes through the kelvin: 20 °C is 293.15 K.
- The conversion
- °F = °C × 1.8 + 32
- In kelvin
- 293.15 K
- Absolute zero on this scale
- -459.67 °F
- Definition
- Water freezes at 32 and boils at 212 — 180 degrees between the two, which is why a Fahrenheit degree is five ninths of a Celsius one.
| Scale | Symbol | Reading |
|---|---|---|
| Celsius | °C | 20 |
| Fahrenheit | °F | 68 |
| Kelvin | K | 293.15 |
| Rankine | °R | 527.67 |
An offset and a scale, routed through the kelvin
Converting metres to feet is a multiplication, because zero metres is zero feet. Converting Celsius to Fahrenheit is not, because 0 °C is 32 °F. Each scale here is stored as two numbers — how many kelvins are in one of its degrees, and what its zero reads in kelvin — and every conversion composes those two maps.
K = value × step(from) + zero(from) • result = (K − zero(to)) ÷ step(to)- step(u)
- Kelvins in one degree of scale u — exactly 5/9 for °F
- zero(u)
- What the zero of scale u reads in kelvin — 273.15 for °C
- K
- The reading in kelvin, the SI base unit
Compose the two and any pair of scales collapses to one line, result = value × scale + offset — which is what the calculator prints above, because seeing °F = °C × 1.8 + 32 is more use than seeing 68.
- Kelvin is the base. Since 20 May 2019 it has been defined by fixing the Boltzmann constant at 1.380649 × 10⁻²³ joules per kelvin. Before that it was defined by the triple point of water, which was exactly 273.16 K by decree and is now a measured quantity that happens to sit there.
- Celsius is kelvin shifted by exactly 273.15. The degree Celsius and the kelvin are the same size, which is why a temperature difference can be quoted in either without conversion.
- Fahrenheit degrees are exactly 5/9 of a kelvin, with its zero at 459.67 °F below absolute zero. Anders Celsius put 100 degrees between the freezing and boiling points of water; Daniel Fahrenheit had already put 180 between the same two.
- Rankine is Fahrenheit with the offset removed — absolute zero at 0 °R, and the same degree size. Water freezes at 491.67 °R.
Results are rounded to four decimal places. A fixed number of decimals would be wrong for the length or mass converters, which span twelve orders of magnitude, but temperature has a hard floor at absolute zero and a practical ceiling, and no thermometer anyone owns resolves ten-thousandths of a degree.
Why 20 °C is not twice as warm as 10 °C
Celsius and Fahrenheit are interval scales. The spacing between their marks is meaningful — the gap from 10 °C to 20 °C really is the same as the gap from 30 °C to 40 °C — but their zeros are conventions. Zero Celsius is where water freezes; zero Fahrenheit is roughly where a brine of ice and ammonium chloride does. Neither is the absence of heat.
An arbitrary zero is exactly what makes a ratio meaningless. Take the same physical pair of temperatures and ask how many times warmer one is:
- In Celsius, 20 and 10 — twice.
- In Fahrenheit, 68 and 50 — 1.36 times.
- In kelvin, 293.15 and 283.15 — 1.04 times.
Three answers for one pair of afternoons. The physics did not change, so the question was broken. Kelvin is the one that can be trusted, because it is a ratio scale: its zero is the real floor, and 600 K genuinely carries twice the mean molecular kinetic energy of 300 K. If you catch yourself dividing two temperatures, convert them to kelvin first or do not divide them at all.
The same trap catches percentages. A day that goes from 10 °C to 20 °C did not get 100% hotter; it got 10 kelvins hotter, which is a 3.5% increase in absolute temperature.
20 °C in Fahrenheit, both ways
Through kelvin, which is what the engine does: 20 + 273.15 = 293.15 K. Then 293.15 × 9/5 = 527.67, and 527.67 − 459.67 = 68 °F. The intermediate 527.67 is not a wasted step — it is the Rankine reading, which is why that column of the table costs nothing to produce.
Directly, using the composed map the calculator prints: °F = 20 × 1.8 + 32 = 36 + 32 = 68. Same answer, one line, and the 1.8 and the 32 are the whole of what separates the two scales.
A kitchen one: a recipe calling for 180 °C is 356 °F, which is why American recipes say 350 °F and British ones say 180 °C for what is nearly the same oven. The 6-degree gap is smaller than the swing of a domestic thermostat.
And the crossover: set the two scales equal and solve. C = 1.8C + 32 gives −0.8C = 32, so C = −40. Minus forty is the single reading where a Celsius and a Fahrenheit thermometer, side by side, show the same number.
What this converter assumes
- Every value is a reading, not an interval. To convert a rise or a fall, multiply by the scale and ignore the offset: a 5 °C change is a 9 °F change and a 5 K change.
- Readings below absolute zero are refused rather than converted. The arithmetic would happily return a number; the number would not describe anything.
- The familiar landmarks — water freezing at 0 °C and boiling at 100 °C — hold at standard atmospheric pressure, 101.325 kPa. Water boils at about 71 °C on the summit of Everest, and the conversion arithmetic is unaffected either way.
- Results are rounded to four decimal places, which is finer than any thermometer in domestic or clinical use and far finer than the ±0.5 °C a typical weather station reports.
- Nothing here models how a temperature feels. Wind chill, heat index and dew point need wind speed or humidity as well, and they are models rather than conversions.
Temperature conversion FAQ
What is 20 °C in Fahrenheit?
68 °F. The arithmetic is 20 × 9/5 = 36, then 36 + 32 = 68. Going through kelvin, which is how this tool does it: 20 + 273.15 = 293.15 K, and 293.15 × 9/5 − 459.67 = 68 °F.
What is the formula for Celsius to Fahrenheit?
°F = °C × 9/5 + 32, and back the other way °C = (°F − 32) × 5/9. The 9/5 is there because there are 180 Fahrenheit degrees between the freezing and boiling points of water where there are 100 Celsius degrees, and the 32 is there because the two scales put their zeros in different places.
At what temperature are Celsius and Fahrenheit the same?
−40. Set the two equal and solve: C = 1.8C + 32 gives −0.8C = 32, so C = −40. It is the only reading the two scales share, which is why −40 needs no unit — the weather report can just say forty below.
Is 20 °C twice as warm as 10 °C?
No, and the question has no answer on that scale. Celsius is an interval scale: its zero is the freezing point of water, a convention, not the absence of heat. In kelvin the same two readings are 293.15 and 283.15, a ratio of 1.04. In Fahrenheit they are 68 and 50, a ratio of 1.36. Three scales, three different answers to 'how many times warmer', which is how you know the question is malformed. Kelvin is the exception: it has a true zero, so 600 K really does carry twice the mean molecular kinetic energy of 300 K.
Why does kelvin have no degree sign?
Because it is not a degree of anything — it is an absolute unit, like the metre. The 13th General Conference on Weights and Measures dropped 'degree Kelvin' and '°K' in 1967 in favour of 'kelvin' and 'K'. The unit name is lowercase even though it honours William Thomson, Lord Kelvin; only the symbol is capitalised. Rankine keeps its degree sign by convention in US engineering practice, despite being absolute too.
Can anything be colder than absolute zero?
No, which is why this converter refuses readings below it rather than quietly converting them. Absolute zero is 0 K, −273.15 °C, −459.67 °F and 0 °R: the point at which a system has no thermal energy left to give up. The third law of thermodynamics says it can be approached but never reached, and laboratories have got within a billionth of a kelvin. Physicists do write about 'negative absolute temperature' in population-inverted spin systems, but those states are hotter than any positive temperature, not colder — the scale wraps around through infinity rather than continuing downwards.
How do I convert a temperature difference, like a 5-degree rise?
Use the scale and drop the offset. A 5 °C rise is a 9 °F rise, not 41 °F — you multiply by 9/5 and stop, because the two thermometers disagree about where zero is but agree on how far apart the marks are. This tool converts readings, not intervals, so a 5 typed into it means the temperature 5 °C.
What is Rankine, and who still uses it?
Rankine is absolute temperature with Fahrenheit-sized degrees: 0 °R is absolute zero and water freezes at 491.67 °R. It was proposed by the Scottish engineer William Rankine in 1859 and survives in US combustion, gas turbine and thermodynamics work, where the equations need an absolute temperature but the rest of the drawing is in Fahrenheit.
Sources and review notes
- BIPM — The International System of Units (SI) Brochure, for the definition of the kelvin and the degree Celsius
- NIST Special Publication 811 — Guide for the Use of the International System of Units (SI), including the conversion relations and the rule that a space goes between the number and °C
- NIST — the 2019 redefinition of the kelvin in terms of the Boltzmann constant
The relations on this page are exact by definition and do not go stale: the degree Celsius has been kelvin minus 273.15 since 1954, and the Fahrenheit degree exactly 5/9 of a kelvin for as long as both have been defined from the same fixed points. The 2019 redefinition changed what a kelvin is and was deliberately chosen to leave every number here unaltered.