Converting Temperatures

Converting Between Celsius and Fahrenheit

Some Common Temperatures and their Equivalents on both Scales.

Why the Conversion Works

The Fahrenheit and Celsius scales both measure the same thing, but their degrees have different sizes and they start at different places:

Because the two scales start at different numbers, we need to add or subtract \(32\) in our conversions.

The size of the degrees is different in each scale (the Celsius scale takes \(100^\circ\) to move from water freezing to water boiling, while the Fahrenheit scale takes \(180^\circ\) to move from water freezing to water boiling), so we need to multiply the Celsius degrees by \(\dfrac{180}{100} = \dfrac{9}{5}\) to convert them to Fahrenheit degrees.

Combining these two steps gives us our conversion formulas:

Let's try a few examples.

The temperature today was \(32^\circ \text{C}\). In Fahrenheit, that is \(32 \times \dfrac{9}{5} + 32 = 89.6^\circ \text{F}\).

When we visited our family in Canada, the temperature was \(-20^\circ \text{C}\). In Fahrenheit, that is \(-20 \times \dfrac{9}{5} + 32 = -4^\circ \text{F} \).

While we were in Canada, we saw weather reports from the US. They said the temperature was \(16^\circ \text{F}\). In Celsius, that is \( (16 - 32)\times \dfrac{5}{9} = -8.9^\circ\text{ C}\).

Our weather station sometimes has a glitch and reports the temperature in Fahrenheit. At the moment, it is reading \(73.4^\circ \text{ F}\). In Celsius, that is \((73.4 - 32) \times \dfrac{5}{9} = 23^\circ \text{ C}\).

A Third Temperature Scale Used by Scientists

Did you know that the SI unit for temperature is not degrees Celsius? It is Kelvin. The size of the Kelvin unit is exactly the same as one degree Celsius, but the two scales start at different points.

\(0^\circ \text{ C}\) is actually \(273.16 \text{ K}\). There are no "degrees" in the unit for the Kelvin scale.

The temperature of \(0 \text{ K}\) is called absolute zero, but it can never be reached. It represents the absence of all heat.

The temperature of an object measures how fast its particles are moving. Cool temperatures correspond to slowly moving particles, and warm temperatures correspond to more quickly moving particles.

Theoretically, a temperature of \(0 \text{ K}\) is the temperature at which the particles of the object stop moving altogether.

It is easy to convert from degrees Celsius to Kelvin: just add \(273.16\) to your Celsius temperature. To go back the other way, subtract \(273.16\) from your Kelvin temperature to give a temperature in degrees Celsius.