Temperature Converter

What this calculates

Enter a temperature in Celsius, Fahrenheit or Kelvin, and this shows it on all three scales at once, with the formula worked through for each conversion. It also places the reading on an everyday scale from −40 °C to 120 °C, marked where water freezes, at 37 °C — a commonly used reference value for body temperature — and where water boils at sea level.

Anything below absolute zero is refused rather than converted, because no such temperature exists.

The formulas

Every conversion runs through Celsius. To and from Fahrenheit, the scale changes size as well as starting point, so there is a multiplication as well as an addition.

Kelvin uses the same size of step as Celsius and simply starts from absolute zero, so the conversion is a single addition or subtraction.

Between Fahrenheit and Kelvin there is no shortcut worth learning: convert to Celsius first, then out again. That is what the calculator does, and it shows both steps.

Worked examples

Going the other way, 98.6 °F — a commonly used reference value for body temperature — becomes (98.6 − 32) × 5/9 = 37 °C, and from there 37 + 273.15 = 310.15 K. Note the order: take 32 away first, then multiply.

At −40 the two everyday scales meet. −40 × 9/5 + 32 = −40 °F, and (−40 − 32) × 5/9 = −40 °C: the only temperature that reads the same on both. On the Kelvin scale it is 233.15 K.

At the bottom of every scale is 0 K, absolute zero. That is 0 − 273.15 = −273.15 °C, and −273.15 × 9/5 + 32 = −459.67 °F. Nothing can be colder, which is why the calculator refuses a reading such as −273.16 °C rather than converting it.

When to use it, and the mistakes to avoid

Use it when a recipe, a weather forecast or a set of instructions uses a scale you do not think in, when checking a thermostat or oven setting, and when working with Kelvin in a science or engineering context.

The mistakes that cost the most:

• Doing the steps in the wrong order. Celsius to Fahrenheit is multiply first, then add 32. Adding 32 first turns 100 °C into (100 + 32) × 9/5 = 237.6 °F instead of 212 °F. The reverse trips people up too: multiplying 98.6 °F by 5/9 before taking away 32 gives 22.78 °C instead of 37 °C.
• Using 273 instead of 273.15. It looks like a rounding choice, but it moves every answer. 20 °C becomes 293 K instead of 293.15 K, and absolute zero would come out as −273 °C instead of −273.15 °C. The 0.15 is part of the definition, not decimal dust.
• Writing "degrees Kelvin". Kelvin is not measured in degrees. The unit is the kelvin, the symbol is K, and there is no degree sign: 293.15 K, never 293.15 °K.
• Trusting "double it and add 30". It is a quick approximation for Celsius to Fahrenheit, and it is exact only at 10 °C, where both give 50 °F. Away from there it drifts: 20 °C gives 70 °F against the true 68 °F, 30 °C gives 90 °F against 86 °F, and 100 °C gives 230 °F against 212 °F. Below 10 °C it runs low instead: 0 °C gives 30 °F against 32 °F. Fine for deciding on a coat; not for an oven or a measurement.
• Converting a difference as if it were a reading. A rise of 10 Celsius degrees is a rise of 18 Fahrenheit degrees — 20 °C to 30 °C is 68 °F to 86 °F — not 50. Adding 32 only belongs to a reading on the scale, never to the gap between two.
• Entering a reading below absolute zero. −273.16 °C, −459.68 °F and −0.01 K are not temperatures at all. The calculator refuses them with a message rather than converting something impossible.

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