When does Celsius equal Fahrenheit? is a common homework question that appears when learning metric conversions. This example problem shows how to calculate when the reading on a Celsius thermometer would equal the reading on on a Fahrenheit thermometer.
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 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°.
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