When Does Celsius Equal Fahrenheit? Example Problem 3


Fahrenheit and Celsius thermometer. Credit: Todd Helmenstine

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 = 59(°F – 32)
°F = 95°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 = 95°C + 32

Solve for °C

°C – 95°C = 32
Factor out the °C

(1 – 95)°C = 32

Solve the fraction

(5595)°C = 32
45°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

About Todd Helmenstine

Todd Helmenstine is the physicist/mathematician who creates most of the images and PDF files found on sciencenotes.org. Nearly all of the graphics are created in Adobe Illustrator, Fireworks and Photoshop. Todd also writes many of the example problems and general news articles found on the site.