How to convert Fahrenheit to Celsius in your head

The actual formula is

T_{C} = \frac{T_{F} - 32}{1.8}

But dividing by 1.8 is annoying. It's easier to divide by 2 instead, then add back the extra factor. So if we divide by 2 instead of 1.8, how much are we missing?

\begin{aligned} \frac{T_{F} - 32}{1.8} \div \frac{T_{F} - 32}{2} \\ = & \frac{2}{1.8} \\ = & 1.111 \dots \end{aligned}

So to easily convert from Fahrenheit to Celsius in our heads, we may subtract 32, divide by 2, and add 11% (or roughly and easily, 10%).

For example, 70ºF take 32 yields 38, divided by 2 yields 19, adding 10% (1.9) gives 20.9, adding 1% (if you're a try-hard) of 19 (0.19) gives 21.09. You can keep adding 0.1%, 0.01%, ... to get further accuracy.

Back the other way

Let's come up with an easy way (ie leaning towards small whole-number factors) to go from C to F.

\begin{aligned} T_{F} & = 1.8 \cdot T_{C} + 32 \\ = (2 - 0.2) \cdot T_{C} + 32 \\ = 2 \cdot T_{C} + 32 - \frac{T_{C}}{5} \end{aligned}

So to convert 30ºC to Fahrenheit, multiply it by 2 to yield 60, add 32 to yield 92, and subtract 6 (30/5) to reach 86ºF.

The pattern

This pattern generalises to "how to make formulas conducive to in-your-head-arithmetic". In general, for any formula: replace multiplication or division by a non-whole factor like 1.8 with its nearest whole number (2), then add/subtract the difference. 2/1.8 is 1.11111..., so you can simply add back 10%, 1%, 0.1%, ... to get closer to the true answer.