In this explainer, we will learn how to convert between the Celsius and Fahrenheit scales and the Kelvin scale and define absolute zero.

The Celsius and Fahrenheit temperature scales are the ones used most in daily life. On a thermometer, the freezing point of water, 0 degrees Celsius, is equivalent to 32 degrees Fahrenheit.

The boiling point of water, 100 degrees Celsius, is equivalent to 212 degrees Fahrenheit. As we can see, Fahrenheit and Celsius are measuring the same temperature, but they do it with very different number scales.

The Kelvin scale is the SI unit of temperature developed by Lord Kelvin as an absolute temperature scale.

0 kelvins is the absolute lowest temperature an object can have in the universe.

Unlike the cumbersome conversion between Celsius and Fahrenheit, a change in temperature in kelvins has the same magnitude change in Celsius. This means that for a one unit increase in kelvins, there is a one unit increase in Celsius.

Let’s look at an example.

### Example 1: Converting from Celsius to Kelvin

A pan of water is heated from to . By how much has the temperature of the water increased in kelvins?

### Answer

Every unit increase in kelvins is an increase in Celsius. The temperature in the pan increases as such.

In Celsius, the change in temperature is

So, the temperature has increased by .

Changes in kelvins and Celsius are of the same magnitude, so the temperature of the water in the pan has increased by the same amount in kelvins (though we do not call it degrees nor use the degree symbol).

Thus, the temperature of the water in the pan has increased by 48 kelvins.

Though the magnitude change between Celsius and kelvin is the same, they still differ. The table below shows several different temperatures comparing Celsius, kelvin, and Fahrenheit.

Celsius | |||
---|---|---|---|

Kelvin | 373 K | 273 K | 0 K |

Fahrenheit | |||

Physical Significance | Boiling point of water | Freezing point of water | Absolute zero |

The exact difference between Celsius and kelvin, as shown in the table above, is 273. Expressed as an equation, where are kelvins and are degrees Celsius.

Let’s look at some sample conversions of other temperature points. Say we have a lukewarm mug of coffee at . To find its temperature in kelvins, we need to merely add 273 to it: which gives us

So, the temperature in kelvins is 273 more, 308 K.

Let’s look at some more examples.

### Example 2: Converting between Celsius and Kelvin

What is in kelvins?

### Answer

We have that

in kelvins is thus 255 K.

### Example 3: Converting between Kelvin and Celsius

What is 330 K in degrees Celsius?

### Answer

Instead of being given the initial temperature in Celsius, we instead are given it in kelvins. To convert, we must then subtract 273, rather than add it:

To get Celsius, we subtract 273 from both sides:

is 330 K, so

Subtracting gives

Now let’s look at converting Fahrenheit to kelvin. Since the Celsius and Kelvin scales are related, this is just a matter of converting the Fahrenheit measurement to Celsius, then converting to kelvin. The conversion form Fahrenheit to Celsius is

The reverse, converting Celsius to Fahrenheit, is

For example, for a temperature of , which becomes

Multiplying through yields

Now that we have this in Celsius, we can use this to convert to kelvins.

Let’s look at an example.

### Example 4: Converting from Fahrenheit to Kelvin

What is in kelvins? Give your answer to the nearest kelvin.

### Answer

We first convert the degrees Fahrenheit to degrees Celsius using

Putting in the value of gives

Subtracting gives

Multiplying the gives

Now that we have our value in Celsius, all we have to do is add 273:

Since we want our answer to the nearest degree, we round up to an even 300 K.

We can also convert the other way, kelvins to Fahrenheit.

Let’s look at an example.

### Example 5: Converting from Kelvin to Fahrenheit

What is 400 K in degrees Fahrenheit? Give your answer to the nearest degree Fahrenheit.

### Answer

We first convert the kelvin to Celsius by subtracting 273:

We then use the equation to convert Celsius to Fahrenheit:

We put in our value of Celsius, :

Multiplying with 127 gives

Adding gives us the value in Fahrenheit:

We need the answer to the nearest degree, so we round up to .

Now that we have seen how kelvin is related to the other temperature scales, we can interpret graphs containing them.

Let’s look at an example.

### Example 6: Understanding the Linear Relationships between Celsius, Fahrenheit, and Kelvin

The graph shows the Celsius and Fahrenheit temperature scales against the kelvin temperature scale, where the kelvin temperature is shown on the horizontal axis. Which line represents the Fahrenheit temperature scale?

### Answer

Between Celsius and Fahrenheit, Fahrenheit increases more rapidly. We should thus expect the line representing Fahrenheit to have a higher slope, which appears to be the orange line.

Using the numbers on the graph to double check, we know that since 0 K is degrees Celsius, we just have to find which line is at degrees Celsius when the temperature is 0 K. The blue line is at around , and the orange line is at around .

Thus, the blue line represents Celsius, and the orange line represents Fahrenheit.

Let’s summarize what we have learned in this explainer.

### Key Points

- The three most common temperature scales are Celsius, Fahrenheit, and kelvin.
- The kelvin is the base SI unit of temperature.
- Absolute zero is the lowest temperature possible.
- To convert kelvin to Celsius, add 273. To convert the other way, subtract 273.
- To convert kelvin to Fahrenheit, use the following equation:
- To convert Fahrenheit to kelvin, use the following equation: