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 = ^{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

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