Temperature Converter
Temperature is the one common conversion that is not a simple multiplication, because two of the three scales put zero in an arbitrary place. That single fact is behind the mistake people make most often here: converting a temperature difference as though it were a temperature.
How to use it
- Enter a value and pick its scale.
- Pick the target scale.
- Read the converted value.
Why an offset is needed
Length, mass, and volume are ratio scales: zero means none of the quantity, so converting is a single multiplication. Celsius and Fahrenheit are interval scales, where zero was chosen for convenience rather than corresponding to an absence of thermal energy.
So conversion needs both a scale factor and an offset. Celsius to Fahrenheit is multiply by 9/5 and add 32. Fahrenheit to Celsius is subtract 32 and multiply by 5/9. The 9/5 accounts for the Fahrenheit degree being smaller — 180 Fahrenheit degrees span what 100 Celsius degrees span — and the 32 accounts for the different zero point.
Kelvin is a ratio scale: zero kelvin is absolute zero, the point at which there is no thermal energy to remove. Converting Celsius to Kelvin therefore needs only the offset of 273.15, since the degree size is identical. This is why Kelvin is used in physics, where ratios of temperature appear in equations and would be meaningless on an interval scale. Doubling the Kelvin temperature of a gas genuinely doubles the average kinetic energy of its molecules; doubling the Celsius figure means nothing physical.
Converting a difference is not the same as converting a temperature
This is the error worth internalising. When you convert a temperature change, a tolerance, or a gradient, you apply the scale factor and not the offset.
A rise of 10 degrees Celsius is a rise of 18 degrees Fahrenheit — 10 times 9/5. It is not 50 degrees Fahrenheit, which is what you get by converting 10 °C as an absolute temperature. Both calculations use the same numbers and only one answers the question asked.
This appears constantly in engineering and specifications. A material with a thermal expansion coefficient per degree Celsius converts to per degree Fahrenheit by dividing by 1.8. A thermostat differential of 2 °C is 3.6 °F. A stated accuracy of plus or minus 0.5 °C is plus or minus 0.9 °F. Applying the 32-degree offset to any of these produces an answer that is wrong by an enormous margin, and because the resulting number still looks like a temperature it can survive review.
A useful mental check: a difference in Celsius and the same difference in Kelvin are numerically identical, because both scales use the same degree size. If your converted difference is not consistent with that, you have applied an offset you should not have.
Reference points worth knowing
Having a handful of anchors makes it possible to sanity-check a conversion without doing the arithmetic.
- Minus 40 is the point where the two scales cross: −40 °C equals −40 °F exactly. It is the only such point, and it makes a good check on any conversion routine.
- 0 °C is 32 °F, water freezing at standard pressure.
- 20 °C is 68 °F, ordinary room temperature.
- 37 °C is 98.6 °F, normal human body temperature.
- 100 °C is 212 °F, water boiling at sea level.
- 180 °C is 356 °F, a common baking temperature.
- 0 K is −273.15 °C or −459.67 °F, absolute zero.
The quick mental approximation
Doubling the Celsius figure and adding 30 gives a usable estimate of Fahrenheit. At 20 °C that gives 70 against the true 68. At 30 °C it gives 90 against 86.
The error grows as you move away from ordinary ambient temperatures, because doubling overstates the 1.8 factor. At 100 °C the shortcut gives 230 against the true 212, so it is fine for judging whether to wear a coat and not for anything else.
The reverse approximation is to subtract 30 and halve. At 70 °F that gives 20 against the true 21.1. Both are good to a couple of degrees across the range humans actually experience, which is the only range they are for.
At a glance
| C to F | Multiply by 9/5, then add 32 |
|---|---|
| C to K | Add 273.15 |
| Differences | Apply the factor only, never the offset |
| Crossover | −40 °C equals −40 °F |
Frequently asked questions
Why does temperature conversion need an offset?
Because Celsius and Fahrenheit put zero at arbitrary points rather than at an absence of thermal energy. Kelvin does not, so Celsius to Kelvin needs only the offset.
How do I convert a temperature difference?
Apply the factor only. A 10 °C rise is an 18 °F rise, not 50 °F. Adding the offset to a difference is a large error that still looks like a temperature.
Where do Celsius and Fahrenheit meet?
At −40, the only point where the two scales give the same number. It makes a good check on any conversion.
Is there a quick mental conversion?
Double and add 30 for Celsius to Fahrenheit. At 20 °C that gives 70 against 68. The error grows away from ambient temperatures.
Read more
Unit conversion done properly — Most conversions are exact multiplications. The ones that are not cause the expensive mistakes.