Please do not block ads on this website.

No ads = no money for us = no free stuff for you!

## Temperature Conversions: Kelvin, Celsius, Fahrenheit

Let's compare three common temperature scales: Kelvin, Celsius and Fahrenheit:

Water: (1 atm) |
freezing point |
liquid water |
boiling point |

Celsius (°C) |
0 |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
80 |
90 |
100 |

Kelvin (K) |
273.15 |
283.15 |
293.15 |
303.15 |
313.15 |
323.15 |
333.15 |
343.15 |
353.15 |
363.15 |
373.15 |

Fahrenheit (°F) |
32 |
50 |
68 |
86 |
104 |
122 |
140 |
158 |
176 |
194 |
212 |

The divisions in the Celsius scale and the Kelvin scale are the same size:

For example, the difference between the temperature at which water boils and freezes at 1 atm:

In °C: 100°C − 0°C = 100°C

In K: 373.15 K − 273.15 K = 100 K

A difference of 1°C is the same as a difference of 1K, the only difference is the starting point (at 1 atm, the freezing point of water is 0°C or 273.15 K).

This makes converting between temperatures in °C and K straight-forward.

If you have a temperature in °C we can just add 273.15 to arrive at a temperature in Kelvin (K):

T (K) = T (°C) + 273.15

To convert 25°C to a temperature in Kelvin (K):

T (K) = T (°C) + 273.15 = 25 + 273.15 = 298.15 K

If we have a temperature in Kelvin (K) we can just subtract 273.15 to arrive at a temperature in °C

T (°C) = T (K) − 273.15

To convert 0 K to a temperature in Celsius (°C):

T (°C) = T (K) − 273.15 = 0 − 273.15 = −273.15 (°C)

If you need to convert a temperature in Fahrenheit to a temperature in °C or K, it is a little bit trickier because not only is the starting point different (freezing point of water) but also the size of the divisions are also different, so that a difference of 1°F is NOT the same size as a difference of 1°C.

A difference of 10°C = 10 K = 18°F

A difference of 1°C = 1 K = 1.8°F

Or, we can put this another way:

A difference of 1.8°F = 1°C = 1 K

A difference of (1.8°F ÷ 1.8) = (1°C ÷ 1.8) = (1 K ÷ 1.8)

A difference of 1°F ≈ 0.55555555°C ≈ 0.55555555 K

The "5"s after the decimal point will just keep on repeating forever, so this is not a satisfactory way of converting Fahrenheit to Celsius or Kelvin!

So we express the value as a fraction:

1.8 = ^{9}/_{5}

So, a difference of 1.8°F = ^{9}/_{5}°F = 1°C = 1 K

And, a difference of 1°F = ^{5}/_{9}°C = ^{5}/_{9} K

So if we are given a temperature in Fahrenheit and we need to convert it to Celsius, first we need to subtract 32 from the temperature in °F (that is, the freezing point of water) and then multiply this by ^{5}/_{9}

T (°C) = (T (°F) − 32) × ^{5}/_{9}

To convert 68°F to Celcius:

T (°C) = (T (°F) − 32) × ^{5}/_{9} = (68 − 32) × ^{5}/_{9} = 36 × ^{5}/_{9} = 20°C

If we need to convert a temperature in °C to a temperature in °F; first we multiply the temperature in °C by ^{9}/_{5} and then we add 32 (freezing point of water):

T (°F) = [^{9}/_{5} × T (°C)] + 32

To convert 25°C to Fahrenheit:

T (°F) = [^{9}/_{5} × T (°C)] + 32 = [^{9}/_{5} × 25 °C)] + 32 = [45] + 32 = 77°F

To summarise:

## Worked Examples of Temperature Conversions: Celsius and Kelvin

**Question 1:** Convert 30°C to a temperature in Kelvin (K)

Solution:

Kelvin (K) = °C + 273.15 = 30 + 273.15 = 303.15 K

**Question 2:** Convert −15°C to a temperature in Kelvin (K)

Solution:

Kelvin (K) = °C + 273.15 = −15 + 273.15 = 258.15 K

**Question 3:** Convert 300 K to a temperature in Celsius (°C)

Solution:

°C = K − 273.15 = 300 - 273.15 = 26.85°C

**Question 4:** Convert 25 K to a temperature in Celsius (°C)

Solution:

°C = K − 273.15 = 25 - 273.15 = −248.15°C

## Worked Examples of Temperature Conversions: Fahrenheit, Celsius and Kelvin

**Question 1:** Convert 30°C to a temperature in Fahrenheit (°F)

Solution:

°F = (^{9}/_{5} × °C) + 32 = (^{9}/_{5} × 30) + 32 = 54 + 32 = 86°F

**Question 2:** Convert 300 K to a temperature in Fahrenheit (°F)

Solution:

Convert K to °C

°C = K − 273.15 = 300 - 273.15 = 26.85°C

Convert °C to °F

°F = (^{9}/_{5} × °C) + 32 = (^{9}/_{5} × 26.85) + 32 = 48.33 + 32 = 80.33°F

**Question 3:** Convert 60°F to a temperature in Celsius (°C)

Solution:

°C = ^{5}/_{9} × (°F − 32) = ^{5}/_{9} × (60 − 32) = ^{5}/_{9} × (28) = 15.56°C

**Question 4:** Convert −20°F to a temperature in Kelvin (K)

Solution:

Convert temperature in °F to temperature in °C:

°C = ^{5}/_{9} × (°F − 32) = ^{5}/_{9} × (−20 − 32) = ^{5}/_{9} × (−52) = −28.89°C

Convert temperature in °C to temperature in K:

Kelvin (K) = °C + 273.15 = −28.89 + 273.15 = 244.26 K