The formulas for converting between degree Celsius and degree Fahrenheit are:

°F = (°C * 9/5) + 32

°C = (°F – 32) * 5/9

To find the temperature when both are equal, we use an old algebra trick and just set ºF = ºC and solve one of the equations.

°C = (°C * 9/5) + 32

°C – (°C * 9/5) = 32

-4/5 * °C = 32

°C = -32 * 5/4

°C = -40

°F = (°F * 9/5) + 32

°F – (°F * 9/5) = 32

-4/5 * °F = 32

°F = -32 * 5/4

°F = -40

So the temperature when both the Celsius and Fahrenheit scales are the same is -40 degrees.