When does Celsius equal Fahrenheit? The temperature is -40°.

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.

Start with one of the two conversion factors between °C and °F.

The two conversion formulas are:

°C = ^{5}⁄_{9}(°F – 32)

and

°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

What Temperature Are Fahrenheit and Kelvin Equal?