Temperature

The forecast says 25 degrees today, but your friend's phone from abroad shows 77. Who is wrong? Neither — they are using different temperature scales. Temperature is not like length: the move-the-decimal-point tricks from metric units and conversions do not work here. The three rulers each have their own starting point and spacing, so each deserves a close look.

Three rulers for temperature

• Celsius (°C): freezing water is set at 0 and boiling water at 100, with 100 divisions between; most of the world uses it;
• Fahrenheit (°F): freezing water sits at 32 and boiling water at 212, with 180 divisions between; daily life in the US still runs on it;
• Kelvin (K): the scientific standard, starting not at freezing but at absolute zero — the lower limit of temperature, about $-273.15$ °C.

The same glass of ice water reads 0, 32 and 273.15 on the three rulers. Different numbers, one and the same temperature.

Celsius to Fahrenheit: times 1.8, then plus 32

Fahrenheit's divisions are denser (180 against 100), so multiply by $180 \div 100 = 1.8$ first; and its zero sits 32 degrees below Celsius zero, so add 32 afterwards:

$F = 1.8 \times C + 32$

A few clean examples: 0 °C → $1.8 \times 0 + 32 = 32$ °F; 25 °C → $25 \times 1.8 + 32 = 77$ °F; body temperature 37 °C ≈ 98.6 °F. To go backwards, subtract 32 first, then divide by 1.8: 77 °F → $(77 - 32) \div 1.8 = 25$ °C.

How to use

LengthMassTemperature

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Switch to the temperature tab and try it: enter 0, convert from °C to °F and get 32; then change the target to K and get 273.15 — all three scales lining up at the same point.

Kelvin: counted from absolute zero

Kelvin's conversion is actually the easiest — shift the starting point, leave the spacing alone:

$K = C + 273.15$

The freezing point, 0 °C, is 273.15 K, and a 20 °C room is 293.15 K. Why bother shifting to a point "too cold to get any colder"? Because many scientific formulas come out cleanest when counted from absolute zero — the floor of temperature becomes the true zero.

Temperature lives on a number line

Temperature runs positive and negative, so it settles naturally onto the number line from positive and negative numbers: above 0 °C is positive, below is negative. Five below zero is written $-5$ °C, and it sits 7 degrees below 2 °C — $2 - (-5) = 7$, the very same method as the distance between two points on the line.

There is also a fun meeting point: $-40$ °C converts to $1.8 \times (-40) + 32 = -72 + 32 = -40$ — the two scales read exactly alike at this temperature. As for what temperature really measures, the story of molecular motion continues in work and energy.

Check yourself

Quick quiz

Try again

0 / 3 correct0 / 3 correct

1. 1. Water freezes at 0 °C. What is that in Fahrenheit?

   0 °F32 °F100 °F

2. 2. Convert 25 °C to Fahrenheit.

   57 °F77 °F87 °F

3. 3. A 20 °C room is how many kelvin?

   20 K253.15 K293.15 K