TIL that nobody knows how to convert nits to lumens properly.

If you search the question, the AI overview is wrong. nits are a unit of brightness per area, so first of all, you need to multiply by screen area (in square meters).

1 nit = 3.426 lm/m² (?)

But where does that constant come from anyway? If you search around, you will find various websites using that number. Others say it is just 1.

Apparently the 3.426 factor has to do with conversion from foot-lamberts... so completely unrelated.

1 nit = 1 cd/m^2. 1 cd = 1 lm/sr. So 1 nit = 1 lm/sr⋅m^2. For a perfectly uniform Lambertian surface, the integral over 180 degrees (the screen only emits forward) works out to π (3.14). So 3.426 is impossibly large.

But of course, real screens aren't uniform emitters. For OLED screens it would be a fairly small factor, since they tend to maintain brightness at steeper angles. LCD screens have much stronger falloff, which depends on the specific technology.

You'd have to integrate the brightness curve for a specific display to arrive at a number. Eyeballing and extrapolating the graphs in the previous link and plugging into Wolfram Alpha, I get around a factor of 2.9 for OLED and 2.2 for IPS, give or take. Probably a lot worse for TN. Take these numbers with a grain of salt, but that's the ballpark.

So, for a screen, lumens = k * nits * area (m² ), where k is in the ballpark of 2.9 for OLED, 2.2 for IPS, and pi ideal.