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Temperature converter

Convert between Celsius, Fahrenheit and kelvin, with all three shown together, the formulas spelled out, and readings below absolute zero refused rather than converted.

The temperature you have

Negative readings are fine. Nothing below absolute zero is.

This converts a reading. A change converts differently: a rise of 10°C is a rise of 18°F, not 50°F, because the offset cancels out.

Converted

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Enter a temperature and pick the two scales.

Temperatures worth knowing

Reference temperatures on all three scales
Reference point°C°FK
Absolute zeroExact. Nothing can be colder.-273.15-459.670
Water freezesAt sea level pressure, and pure water.032273.15
A cool roomA common comfort figure rather than a fixed one.1864.4291.15
Body temperatureThe traditional figure. Healthy readings vary by about a degree.3798.6310.15
Water boilsAt sea level. It falls by roughly a degree every 300 m of altitude.100212373.15
A moderate ovenRecipes pair this with 350°F, which is really 176.7°C.180356453.15

Three scales that start counting in different places

Converting metres to feet is one multiplication, because both start at nothing. Temperature is not like that. Celsius starts at water freezing, Fahrenheit starts about 32 degrees below that, and kelvin starts at absolute zero, the coldest anything can be. Each scale needs its own formula.

The formulas, in full:

  • Celsius to Fahrenheit: multiply by 9, divide by 5, add 32
  • Fahrenheit to Celsius: subtract 32, multiply by 5, divide by 9
  • Celsius to kelvin: add 273.15

The order matters in the first two. Subtracting 32 after dividing rather than before is the mistake that produces an answer roughly 18 degrees out.

A reading and a change are different questions

This is the trap worth knowing about, and the reason this page shows both figures.

A reading of 10°C is 50°F. A rise of 10°C is a rise of 18°F. The offset of 32 is a starting position, so it cancels out the moment you subtract one reading from another, leaving only the nine fifths. Anyone reporting that a temperature climbed ten degrees, or that a fever went up by one, is talking about the second kind of number.

Doing it in your head

Double and add 30 gets you close for ordinary weather. 20°C becomes 70 against a true 68. 25°C becomes 80 against a true 77. It holds to within a couple of degrees roughly between 5°C and 25°C and falls apart outside that.

A few anchors are more useful than a formula: 0°C is 32°F, 10°C is 50°F, 20°C is 68°F, 30°C is 86°F, and -40 is the same on both. Getting from one anchor to the next is 18 Fahrenheit degrees for every 10 Celsius ones.

Why kelvin has no degree sign

Because it is not measuring degrees above anything. Celsius and Fahrenheit give a position on a scale whose zero was chosen, so a reading is written 20°C. Kelvin counts from absolute zero, so a reading is an amount of temperature rather than a position, and is written 300 K.

One kelvin is exactly the size of one degree Celsius, which is why converting between the two is only ever adding or subtracting 273.15. It also means the tool can say something about kelvin it cannot say about Fahrenheit: doubling a kelvin figure really does mean twice as hot, because the scale starts at the bottom.

Questions

How do I convert Celsius to Fahrenheit?
Multiply by 9, divide by 5, then add 32. So 20°C is 20 × 1.8 = 36, plus 32, which is 68°F. Going the other way, subtract 32 first and then divide by 1.8: 68°F is 36, divided by 1.8, which is 20°C. The order matters, and subtracting after dividing is the most common mistake.
Is there a quick way to do it in my head?
Double the Celsius figure and add 30. That gives 70 for 20°C against a true 68, and 50 for 10°C against a true 50. It is within a couple of degrees between about 5°C and 25°C, which covers most weather, and it drifts badly outside that range.
What is minus 40?
The one temperature where the two scales agree: -40°C is exactly -40°F. It happens because Fahrenheit readings climb 1.8 degrees for every one degree Celsius while starting 32 lower, and the two effects cancel at -40. It is a useful thing to remember, because it tells you which direction each scale runs.
Why is a rise of 10°C not a rise of 50°F?
Because a change is not a reading. Converting a reading uses both the scaling and the offset, but an offset cancels when you take the difference between two readings, so only the 1.8 remains. A rise of 10°C is a rise of 18°F. This matters for a fever, a weather forecast and a thermostat, where the number being discussed is usually a change.
What is absolute zero?
The coldest anything can be: -273.15°C, -459.67°F, or 0 K. It is a floor rather than a convention, so there is no such thing as a temperature below it. This tool refuses a figure below absolute zero instead of converting it, because at that point what you have is a typo rather than a reading.
Why is kelvin written without a degree sign?
Because it is not a degree scale. Celsius and Fahrenheit measure degrees above an arbitrary zero, so a reading is written 20°C. Kelvin counts from absolute zero, so a reading is an amount rather than a position, and it is written 300 K. One kelvin is exactly the same size as one degree Celsius, which is why converting between those two is only ever adding or subtracting 273.15.
What is a normal body temperature?
37°C, or 98.6°F, is the figure everyone learned, and it comes from a study published in 1868. Healthy readings vary by around a degree with the person, the time of day and where the reading is taken, and several modern studies put the average slightly lower. Treat 37°C as a reference point rather than a target, and follow your doctor's guidance on what counts as a fever.
Why does water boil below 100°C on a mountain?
Because boiling depends on air pressure, and there is less of it higher up. Water boils at 100°C at sea level and falls by roughly a degree every 300 metres of altitude, so at 2,000 m it boils near 93°C. The reference table on this page gives the sea level figures.

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