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”.
Fahrenheit and Kelvin are equal at 574.59. In other words 574.59 °F equals 574.59 K.
About the Kelvin Temperature Scale
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
About the Fahrenheit Scale
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 re-defined so that now the melting point of water ice is 32 °F and the boiling point of water is 212 °F.
What Temperature Are Fahrenheit and Kelvin Equal?
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 is 574.59 °F.
Solving this problem isn’t that difficult. It just requires a little algebra and knowing how to convert Kelvin to Fahrenheit.
More Temperature Conversion Examples
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