Temperatura: Celsius<-->Fahrenheit

Converting Between Celsius and Fahrenheit

Most countries in the world use the Celsius temperature scale, but some countries, like the United States, use the Fahrenheit scale. Converting between these two temperature systems is a useful skill to have, and luckily all you need to remember are two formulas!

Converting Celsius to Fahrenheit

To convert a temperature from $^{\circ}\text{C}$ to $^{\circ}\text{F}$, we use the following formula:

For example, if we wanted to convert $80^{ \circ}\text{C}$ to degrees in Fahrenheit, we would simply plug in $80$ for $C$ in the formula above. $$\begin{align} F&=\dfrac{9}{5}C+32\\ &=\dfrac{9}{5}(80)+32\\ &=144+32\\ &=176 \end{align}$$ So, $80^{ \circ}\text{C}$ is equivalent to $176^{ \circ}\text{F}.$

To convert $15^{ \circ}\text{C}$ to degrees in Fahrenheit, we would simply plug in $15$ for $C$ in our formula. $$\begin{align} F&=\dfrac{9}{5}C+32\\ &=\dfrac{9}{5}(15)+32\\ &=27+32\\ &=59 \end{align}$$ So, $15^{ \circ}\text{C}$ is equivalent to $\boxed{59^{ \circ}\text{F}}$.

Converting Fahrenheit to Celsius

To convert a temperature from $^{\circ}\text{F}$ to $^{\circ}\text{C}$, we use the following formula:

For example, if we wanted to convert $4.46^{ \circ}\text{F}$ to degrees in Celsius, we would simply plug in $4.46$ for $F$ in the formula above. $$\begin{align} C&=\frac{5}{9}(F-32)\\ &=\frac{5}{9}(4.46-32)\\ &=\frac{5}{9}(-27.54)\\ &=-15.3 \end{align}$$ So, $4.46^{ \circ}\text{F}$ is equivalent to $-15.3^{ \circ}\text{C}.$

Try this next problem using the same technique.

To convert $77^{ \circ}\text{F}$ to degrees in Celsius, we would simply plug in $77$ for $F$ in our formula. $$\begin{align} C&=\frac{5}{9}(F-32)\\ &=\frac{5}{9}(77-32)\\ &=\frac{5}{9}(45)\\ &=25 \end{align}$$ So, $77^{ \circ}\text{F}$ is equivalent to $\boxed{25^{ \circ}\text{C}}$.

If you want more practice converting between Celsius and Fahrenheit, here's an easy way to get it. Pull up a weather forecast for your home town on your phone or computer. The temperatures will be listed in either Celsius or Fahrenheit. Using the formulas we discussed here, convert all the temperatures in the forecast to the other temperature system. Many apps will convert between Celsius and Fahrenheit for you, so you can check your work if you want to.

(Video) Converting Between Celsius and Fahrenheit

by mathtutordvd

This video by mathtutordvd shows how to convert from Celsius to Fahrenheit. Degrees Celsius is abbreviated $^{\circ}\text{C}$. Also, degrees Fahrenheit is abbreviated $^{\circ}\text{F}$.

$\large{\text{Summary}}$

Let's take a look at these two temperature systems. They are both used in different parts of the world.

Celsius (invented by Anders Celsius)

• $-273^{\circ}\text{C}\Rightarrow$ Absolute zero, the coldest temperature an object can be.
• $0^{\circ}\text{C}\Rightarrow$ Freezing point of water. Water freezes if it is set at any lower temperature.
• $37^{\circ}\text{C} \Rightarrow$ Average human body temperature.
• $100^{\circ}\text{C}\Rightarrow$ Boiling point of water. Water boils if it is set at any higher temperature.

Fahrenheit (invented by Daniel Fahrenheit)

• $-459^{\circ}\text{F}\Rightarrow$ Absolute zero, the coldest temperature an object can be.
• $32^{\circ}\text{F}\Rightarrow$ Freezing point of water. Water freezes if it is set at any lower temperature.
• $98.6^{\circ} \text{F} \Rightarrow$ Average human body temperature.
• $212^{\circ}\text{F}\Rightarrow$ Boiling point of water. Water boils if it is set at any higher temperature.

As you can see, Celsius is a way cleaner looking system.

Converting Celsius to Fahrenheit

To convert between these two systems, we have to use certain equations. There isn't a $1$-to-$1$ conversion factor so the equations are necessary. For an example of a $1$-to-$1$ conversion factor, look at feet and meters. The equation to turn Celsius into Fahrenheit is

$$\boxed{F=\frac95(C)+32}.$$

As the order of operations says, we want to multiply first and then add.

Example: Celsius to Fahrenheit

Suppose we want to convert $10^{\circ}\text{C}$ to $^{\circ}\text{F}$.

All we have to do is plug $10$ into the equation above and find $F$. This is sometimes called $\textit{direct substitution}$. $$\begin{align} F&=\frac95(C)+32\\ F&=\frac95({\color{#8925ae}{10}})+32\\ F&=18+32\\\ F&=\boxed{50^{\circ}} \end{align}$$

Converting Fahrenheit to Celsius

If we start with Fahrenheit we can also convert back to degrees Celsius. There is a different formula for doing this conversion:

$$C = \frac{5}{9}(F - 32)$$

Once again we can use the order of operations and plug in a value of $F$. However, this time the first step is to subtract everything in the parentheses. Take $F$ and subtract $32$, times $\frac59$.

Example: Fahrenheit to Celsius

We can also convert from the Fahrenheit scale to the Celsius scale. If we want to convert $86^{\circ}\text{F}$ to $^{\circ}\text{C}$, we plug $F = 86$ into the above equation

$$\begin{align} C&=\frac{5}{9}(F - 32) \\ C&=\frac{5}{9}({\color{#8925ae}{86}} - 32) \\ C&=\frac{5}{9}(54) \\ C&=\boxed{30^{\circ}} \end{align}$$

Another Solution

There is another way to do this problem that involves solving equations. If you want to practice solving equations with one variable, then keep reading.

Once more, let's convert $86^{\circ}\text{F}$ to $^{\circ}\text{C}$. This time we plug $86$ in our equation for $F$:

$$86 = \frac95(C) + 32$$

This is an equation we can solve for $C$, so we isolate the variable. Subtract $32$ from both sides of the equation:

$$54 = \frac95(C)$$

The reciprocal of $\frac95$ is $\frac59$. Therefore we multiply both sides of the equation by $\frac59$ to get rid of the $\frac 95$ on the right:

$$\begin{align} 54 \times \frac{5}{9} &= \frac{5}{9} \times \frac{9}{5}C \\ 30 &= \frac{\cancel{5}}{\cancel{9}} \times \frac{\cancel{9}}{\cancel{5}}C \\ \boxed{30^{\circ}} &= C \end{align}$$

This means $86^{\circ}\text{F}$ equals $30^{\circ}\text{C}$.

(Video) A Trick for Instant Temperature Conversions

by tecmath

This video by tecmath shows a way of approximating temperature conversions. If we know the temperature in degrees Fahrenheit, we can guess the temperature in degrees Celsius, and vice-versa.

$\large{\text{Summary}}$

Note that this method gives a quick approximation. It is an alternative to using equations to convert between Fahrenheit and Celsius.

Celsius to Fahrenheit

1. Multiply the degrees Celsius ($^{\circ}\text{C}$) by $2$.
2. Add $30$ to the answer you got in step $1$.

The bigger the Celsius is, the larger of an error you get.

Suppose your friend tells you its $12^{\circ}\text{C}$ outside. If you only know Fahrenheit, what would be a rough approximation of this?

First, we would multiply by $2$. $$12\times2=24$$ Then, add $30$. $$24+30=54$$

If we used the formula to convert these and get an exact answer, we find

$$\begin{align} F&=\frac95(C)+32\\ F&=\frac95({\color{#29a603}{12}})+32\\ F&=21.6+32\\ F&=53.6 \end{align}$$

As you can see, our guess isn't too far off!

Fahrenheit to Celsius

1. Subtract $30$ from your Fahrenheit.
2. Divide by $2$.

Suppose your friend tells you it's $78^{\circ}\text{F}$ outside. If you only know Celsius, what would be a rough guess of the temperature in Celsius?

First, we subtract $30$. $$78-30=48$$ Then, divide by $2$. $$48\div2=24$$

If we were to used the formula to convert these and get an exact answer, we find that: $$\begin{align} C&=\frac59(F-32)\\ C&=\frac59({\color{#29a603}{78}}-32)\\ C&=\frac59(44)\\ C&=24.4 \end{align}$$ As you can see, our guess isn't too far off! If you're in a day-to-day conversation with friends, this trick comes in handy.