But, how do you know the temperature where the two scales are the same? This is a common homework question for students when they are learning unit conversions. This example problem shows how to calculate when the reading on a Celsius thermometer would equal the reading on on a Fahrenheit thermometer.
Find Where Fahrenheit and Celsius Are Equal
Start with one of the two conversion factors between °C and °F.
The two conversion formulas are:
°C = 5⁄9(°F – 32)
°F = 9⁄5°C + 32
It doesn’t matter which one you use since they are two forms of the same equation. Let’s use the second one. We want to know when °C = °F, so the equation becomes:
°C = 9⁄5°C + 32
Solve for °C
°C – 9⁄5°C = 32
Factor out the °C
(1 – 9⁄5)°C = 32
Solve the fraction
(5⁄5 – 9⁄5)°C = 32
–4⁄5°C = 32
Multiply both sides by 5
-4°C = 160
Divide both sides by -4
°C = -40
°C = °F = -40.
Celsius equals Fahrenheit at -40°. You use the same method to find the point at which other temperature scales are equal, too.
For more help, try these other temperature conversion example problems:
Convert Celsius to Fahrenheit Example Problem
Convert Fahrenheit to Celsius Example Problem
Convert Celsius to Kelvin Example Problem
Convert Kelvin to Celsius Example Problem
What Temperature Are Fahrenheit and Kelvin Equal?