I meant how much angular movement would be involved from the sum of his body parts to "just miss" the light, but I'll just post what I would do if I were doing the calc.
We know the distance between the two and how far the light has already traveled since we see Naruto begin to react when the light is at the staff. That tells us all we need to know for exactly where the light would be relative to Naruto's face position. The light breaks the staff in 1.698ns and would reach Naruto in 3.088ns, and Naruto has 1.39ns to move a
minimum of 3.5cm after the staff is broken (see below), or else he's pierced. How people choose to find the distance depends on what's agreed upon.
At a
minimum, from what we are properly shown, Naruto moves at least 0.107c, which is already more distance than the bare minimum he would have had to cover to laterally dodge the jutsu (
which we know he didn't do.) Using OP's green line in his
calc, and assuming Naruto's head drags along the green line in a 2D plane (not the 3D direction we've just been discussing), that gives us 0.268c. The light moved over 55% of the distance between Naruto and Madara (still FTL perception) before Naruto could move 10%.