Who needs this?
Most temperature conversions happen because two people grew up with different thermometers. A few groups run into it all the time:
- Home cooksA recipe from a British or Australian site says 180 °C, and the oven dial only shows Fahrenheit.
- TravelersThe forecast in Lisbon says 31. Is that a jacket day or a beach day?
- Students and lab workGas-law and thermodynamics problems only work in kelvins.
- Parents and caregiversA thermometer bought overseas reads 38.4. Is that a fever?
- TradesHVAC, refrigeration and auto techs read specs written in one system and gauges built in the other.
- Photography and lightingColor temperature (a "5600 K" daylight bulb) is in kelvins, too.
How the three scales line up
All three scales measure the same thing. They disagree about two details: where zero sits and how big one degree is.
Picture two rulers side by side, one marked in centimeters and one in inches, with the second ruler slid 32 marks along. To read one against the other you have to account for both the size of the marks and the starting point. That's why the Celsius–Fahrenheit formula has two parts: a multiply (size) and an add (starting point).
- Celsius puts water's freezing point at 0 and its boiling point at sea level at about 100. There are 100 degrees between them.
- Fahrenheit puts the same two points at 32 and 212, so there are 180 degrees between them. 180 ÷ 100 = 1.8, which is where the 1.8 (or 9/5) comes from.
- Kelvin uses degrees the same size as Celsius but starts at absolute zero, the coldest anything can get. It's the SI unit scientists use, and it never goes negative.
Converting, step by step
Celsius to Fahrenheit
Multiply by 1.8, then add 32. The order matters: scale the degree size first, then shift the starting point.
- Multiply by 1.8
37 × 1.8 = 66.6 - Add 32
66.6 + 32 = 98.6 °F
Fahrenheit to Celsius
Undo the same two steps in reverse order: take away 32 first, then divide by 1.8.
- Subtract 32
350 − 32 = 318 - Divide by 1.8
318 ÷ 1.8 = 176.67 °C
Kelvin
Kelvin is the easy one. A kelvin is the same size as a Celsius degree, so you only shift: add 273.15 to go from °C to K, and subtract it to go back. For Fahrenheit, go through Celsius first.
Real situations, worked out
180 × 1.8 + 32 = 356 °F. American oven dials step in 25 degrees, so set it to 350 °F. The "fan" figure is for convection ovens: 160 °C works out to 320 °F, so use 325 °F if you bake on the convection setting.
180 °C ≈ 350 °F · 160 °C ≈ 325 °F38.4 × 1.8 + 32 = 101.12 °F. Many doctors use 100.4 °F (38 °C) as the line for a fever, so this one is just over it. RocketCalc isn't medical advice; when in doubt, call a doctor or a nurse line.
38.4 °C = 101.12 °F31 × 1.8 + 32 = 87.8 °F, so it's shorts weather. The mental shortcut in the next section gets you to 92, which is close enough to pack the same bag.
31 °C ≈ 88 °FThe ideal gas law (PV = nRT) needs T in kelvins: 25 + 273.15 = 298.15 K. Plugging in 25 instead gives an answer that's off by a factor of about twelve.
25 °C = 298.15 KDoing it in your head
For weather and everyday use, double it and add 30 gets you close enough. Going the other way, subtract 30 and halve it. It's most accurate around 10 °C (50 °F) and drifts as you move away from there, so don't use it for cooking or medicine.
| °C | Exact °F | Double + 30 | Off by |
|---|---|---|---|
| 0 | 32 | 30 | 2 |
| 10 | 50 | 50 | 0 |
| 20 | 68 | 70 | 2 |
| 30 | 86 | 90 | 4 |
| 40 | 104 | 110 | 6 |
| 100 | 212 | 230 | 18 |
Memory pegs. 16 °C is about 61 °F and 28 °C is about 82 °F, so the digits swap. Add 0 = 32, 10 = 50, 20 = 68 and 30 = 86, and you can place most forecasts without doing any math.
Common mistakes
Adding 32 to a temperature change. If the weather warms up by 10 °C, that's a rise of 18 °F, not 50 °F. A change only needs the size step (× 1.8), because the starting points cancel out. The same goes for "this oven runs 10 degrees hot" or a ±0.5 °C sensor spec.
Doing the steps in the wrong order. (100 + 32) × 1.8 = 237.6, not 212. Multiply first when going to Fahrenheit; subtract first when coming back.
Writing "degrees Kelvin" or "°K". The unit has been just "kelvin" (symbol K, no degree sign) since 1967. Write 300 K.
Rounding 273.15 to 273 too early. That's fine for a weather report, but in a chain of lab calculations the error builds up. Keep the .15 until the last step. The rounding guide explains when it matters.
A bit of history
The odd numbers in the Fahrenheit scale make more sense once you know where they came from.
- 1724Daniel Gabriel Fahrenheit, an instrument maker born in Danzig (now Gdańsk) and working in Amsterdam, publishes his scale. Its zero came from a freezing mix of ice, water and salt, the coldest thing he could make reliably in his workshop.
- 1742Swedish astronomer Anders Celsius proposes a 100-step scale, but upside down: 0 for boiling water and 100 for freezing. It was flipped to the version we use within a few years of his death.
- 1848William Thomson, later Lord Kelvin, argues for an "absolute" scale that starts at the coldest possible temperature.
- 1948An international conference renames "centigrade" to "degree Celsius".
- 2019The kelvin is redefined from a fixed constant of nature (the Boltzmann constant) instead of the properties of water, so it no longer depends on any physical sample.
Today the United States is the main country still using Fahrenheit for everyday weather and cooking, which is why so many of these conversions start or end with an American recipe or forecast.
Reference table
| What | °C | °F | K |
|---|---|---|---|
| Absolute zero | −273.15 | −459.67 | 0 |
| Celsius and Fahrenheit agree | −40 | −40 | 233.15 |
| Home freezer | −18 | 0 | 255.15 |
| Water freezes | 0 | 32 | 273.15 |
| Fridge | 4 | 39 | 277.15 |
| Mild room | 20 | 68 | 293.15 |
| Body temperature | 37 | 98.6 | 310.15 |
| Water boils (sea level) | 100 | 212 | 373.15 |
| Moderate oven | 180 | 356 (set 350) | 453.15 |
| Hot oven | 220 | 428 (set 425) | 493.15 |
Questions people ask
Why is it 1.8 and not 2?
Between freezing and boiling water there are 100 Celsius degrees and 180 Fahrenheit degrees. 180 ÷ 100 = 1.8. It's also written as 9/5, which is the same number.
At what temperature are Celsius and Fahrenheit the same?
At −40. Set °F equal to °C in the formula (x = 1.8x + 32) and solve: x = −40. It's the one number you never need to convert.
Can a temperature be below 0 K?
Not in the everyday sense. 0 K is absolute zero, where particles have the least motion physics allows. That's why our Kelvin converters reject negative values.
Is 100 °C always the boiling point of water?
Only at sea-level pressure. In Denver, about a mile up, water boils near 95 °C (203 °F), which is why some recipes have high-altitude adjustments. The pressure guide covers why.
What's the Rankine scale?
It's Fahrenheit's version of Kelvin: Fahrenheit-sized degrees starting at absolute zero (°R = °F + 459.67). You'll mostly see it in older American engineering tables.