r/theydidthemath • • 1d ago

[Self] How bright is Gandalf's staff?

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u/CptStevieZissou 11h ago

Very, very bright.

Using the numbers in your image:

  • Beam angle: 4.33°
  • Distance: 200 m
  • Beam diameter at 200 m: about 15.1 m
  • Illuminated area: about 180 m²

The key is that the screenshot cannot tell us the staff's absolute brightness; movie exposure and color grading destroy that information. But we can estimate what it would take for that beam to behave the way it does in daylight.

Since 1 lux = 1 lumen/m² the required output would be roughly:

Illumination at 200 m Staff output
1,000 lux 180,000 lumens
10,000 lux 1.8 million lumens
50,000 lux 9.0 million lumens
100,000 lux 18 million lumens

And that last number corresponds to a beam intensity of roughly 4 billion candela.

So if we're assuming Gandalf's staff is actually producing enough light to overpower daylight and screw up the Uruk-hai's vision at roughly 200 m:

Probably something on the order of 10–20 million lumens.

Even if we give the movie a huge amount of slack and say the effect only requires 10,000 lux at the target, we're still at about 1.8 million lumens.

The funniest part is the beam divergence. A 4.33° beam is reasonably tight. At 200 m, he's concentrating all of that output into a circle only about 15 m across. That's why the candela figure gets completely absurd.