What temperature are Fahrenheit and Kelvin equal to each other? This question is similar to the popular homework question “When does Celsius equal Fahrenheit?” where the two different temperature scales read the same value. This example problem not only gives you the answer, it shows step by step, how to solve the question of “What temperature are Fahrenheit and Kelvin Equal”.

The Kelvin temperature scale, also known as the absolute temperature scale, is the SI unit of measuring temperature. The scale starts at absolute zero, where molecular energy is at its minimum value and rises from that where each unit is equivalent in size to the Celsius degree. The difference between Celsius and Kelvin is expressed by the formula:

K = °C + 273.15

where

K = temperature in Kelvin

°C = temperature in Celsius

If we solve this for °C, we get

°C = K – 273.15

Fahrenheit is a temperature scale originally used to measure a temperature range of real-life things. The zero point was the temperature of an equal mix of salt and ice water and 100 degrees above that was the temperature of a human being. Over the years, this temperature scale was defined by the melting point of water ice (32 °F) and the boiling point of water (212 °F) and the size of the individual units have not changed much. We can relate Fahrenheit to Kelvin by converting Fahrenheit to Celsius using the formula:

°C = ^{5}⁄_{9}(°F – 32)

where °F and °C are the temperatures in Fahrenheit and Celsius respectively.

Since these two equations equal the same thing (°C), they equal each other.

K – 273.15 = ^{5}⁄_{9}(°F – 32)

Now you have the formula to convert between Kelvin and Fahrenheit. We want to know when K = °F, so plug in K for °F in the formula.

K – 273.15 = ^{5}⁄_{9}(K – 32)

Solve for K. First, get rid of the parenthesis

K – 273.15 = ^{5}⁄_{9} K – 17.78

Subtract ^{5}⁄_{9} K from both sides

K – ^{5}⁄_{9} K – 273.15 = 17.78

Add 273.15 to both sides

K – ^{5}⁄_{9} K = 17.78 + 273.15

K – ^{5}⁄_{9} K = 255.37

^{9}⁄_{9} K – ^{5}⁄_{9} K = 255.37

^{4}⁄_{9} K = 255.37

Multiply both sides by ^{9}⁄_{4}

K = (255.37)^{9}⁄_{4}

K = 574.59

At 574.59 Kelvin, the Fahrenheit temperature will be 574.59 °F.

Solving this problem wasn’t that difficult. It just required a little basic algebra and knowing a way to convert Kelvin to Fahrenheit.

If you’d like to see some other temperature conversion examples, check out

Convert Kelvin to Celsius Example Problem

Convert Celsius to Fahrenheit Example Problem

Convert Fahrenheit to Celsius Example Problem