The Exposure Triangle, as a Formula

Photographers talk about the exposure triangle like folklore. It's actually just arithmetic in log space, and writing it out made me a better shooter — and, weirdly, a better debugger.

The exposure value

The canonical definition ties aperture $N$ and shutter time $t$ together:

EV = \log_2\!\left(\frac{N^2}{t}\right)

Every full stop is $+1$ to $EV$: halve the light, add a stop. Inline, that means a jump from $$f/2.8$$ to $$f/4$$ is exactly one stop, because $\left(\tfrac{4}{2.8}\right)^2 \approx 2$.

Balancing a change

If you open up the aperture by $\Delta_N$ stops you have to pay it back somewhere — shutter or ISO — to hold exposure constant:

\begin{aligned} EV_{\text{const}} &= (N \text{ stops}) + (t \text{ stops}) + (S \text{ stops}) \\ 0 &= \Delta_N + \Delta_t + \Delta_S \end{aligned}

That conservation law is the whole game: light removed from one term has to reappear in another. Once I saw it as an invariant I stopped guessing.

The debugging parallel writes itself — every system has a budget, and if you take from one place without accounting for it, the exposure blows out somewhere you weren't looking.