Why temperature needs a formula, not a factor
Most unit conversions are a single multiplication because both units start from the same zero: zero kilograms is zero pounds. Temperature scales do not share a zero. Celsius puts 0 at the freezing point of water, Fahrenheit puts 32 there, and the kelvin starts at absolute zero, the coldest temperature possible. So a conversion has two parts: rescale the size of the degree, then shift the zero.
- A Celsius degree and a kelvin are the same size. Only the zero differs: 0 °C is 273.15 K.
- A Fahrenheit degree is 5/9 of a Celsius degree, so a span of 100 °C covers 180 °F.
- Rankine is to Fahrenheit what kelvin is to Celsius: Fahrenheit-sized degrees counted from absolute zero, which is 0 °R and −459.67 °F. It survives mainly in some US engineering fields.
Celsius is the everyday scale in nearly every country. The United States uses Fahrenheit for weather, cooking and body temperature, and scientists everywhere use kelvin.
The conversion formulas
These formulas are exact by definition. Results such as 176.666… °C for 350 °F are repeating decimals, not rounding errors, and the Result shows up to ten significant digits of them.
The two scales meet at −40: plugging −40 into either formula returns −40. Above that point the Fahrenheit number is always the larger one, and below it the Celsius number is.
A shortcut you can do in your head
Double the Celsius figure and add 30. It gives 70 °F for 20 °C, against the exact 68 °F. The shortcut’s error is 0.2 × °C − 2 degrees Fahrenheit, so it is exact at 10 °C, about 2 °F low at freezing, 4 °F high at 30 °C and 5.4 °F high at body temperature. It suits weather, not a fever reading or an oven dial. Reverse it for Fahrenheit: subtract 30 and halve.
Worked examples
- Multiply by 9/5: 180 × 9/5 = 324.
- Add 32: 324 + 32 = 356 °F.
- US recipes usually give oven settings in steps of 25 °F, so 350 °F is the usual equivalent.
- Subtract 32: 350 − 32 = 318.
- Multiply by 5/9: 318 × 5/9 = 176.67 °C.
- Add 273.15: 25 + 273.15 = 298.15 K.
- Kelvin is written without a degree sign.
- A difference has no zero point to shift, so skip the 32.
- Multiply by 9/5 only: 5 × 9/5 = 9 Fahrenheit degrees.
- Putting 5 into the converter returns 41 °F, which is the temperature 5 °C, not the size of the change.
Celsius to Fahrenheit table
| Celsius (°C) | Fahrenheit (°F) | Kelvin (K) |
|---|---|---|
| -40 | -40 | 233.15 |
| -20 | -4 | 253.15 |
| -18 | -0.4 | 255.15 |
| -10 | 14 | 263.15 |
| 0 | 32 | 273.15 |
| 4 | 39.2 | 277.15 |
| 10 | 50 | 283.15 |
| 15 | 59 | 288.15 |
| 20 | 68 | 293.15 |
| 25 | 77 | 298.15 |
| 30 | 86 | 303.15 |
| 37 | 98.6 | 310.15 |
| 40 | 104 | 313.15 |
| 100 | 212 | 373.15 |
| 180 | 356 | 453.15 |
| 200 | 392 | 473.15 |
| 220 | 428 | 493.15 |
Ways to get a temperature wrong
- Treating the conversion as a ratio. Multiplying 20 °C by 1.8 gives 36, not 68. The +32 offset is not optional for a reading.
- Applying the offset to a difference. Forecast changes, oven tolerances and climate anomalies are intervals. A 2 °C warming is 3.6 °F of warming, not 35.6 °F.
- Adding 273 and calling it exact. The offset is 273.15; dropping the 0.15 is fine for most purposes but not for lab work.
- Typing a value below absolute zero. Anything colder than −273.15 °C or −459.67 °F does not exist, and the converter says so instead of returning a number.
Water boils at 100 °C only at standard sea-level pressure. At higher altitudes the boiling point is lower, which is why cooking times and some baking instructions change in the mountains.
Questions people ask
Is 37 °C exactly 98.6 °F?
Yes, the arithmetic is exact: 37 × 9/5 + 32 = 98.6. Normal body temperature varies from person to person and through the day, so neither figure is a precise medical threshold.
What is 0 °F in Celsius?
About −17.8 °C. A common freezer setting of −18 °C is very close to 0 °F (−0.4 °F).
Why is kelvin written without a degree sign?
The kelvin is a unit in its own right, like the meter, so it is written “300 K” and read “300 kelvins”. Celsius, Fahrenheit and Rankine keep the degree sign.
Can a temperature in kelvin be negative?
No. The scale starts at absolute zero, so 0 K is the lowest possible value, and the converter rejects anything below it in any of the four units.
Sources
- SI Units - Temperature, National Institute of Standards and Technology.
- The International System of Units (SI Brochure), 9th edition, Bureau International des Poids et Mesures.
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811, National Institute of Standards and Technology.