Shutter angle, shutter speed and ND filters
The 180-degree rule at any frame rate, and which ND filter to put on to keep it while opening the aperture you want. The two settings that decide whether motion looks like cinema or like a phone.
Shutter speed at every frame rate
The whole table comes out of one division, so nothing here is a recommendation — it is arithmetic. The row you want is almost always 180°.
| Angle | 23.976 | 24 | 25 | 29.97 | 30 | 50 | 60 fps |
|---|---|---|---|---|---|---|---|
| 45° | 1/191.8 | 1/192 | 1/200 | 1/239.8 | 1/240 | 1/400 | 1/480 |
| 90° | 1/95.9 | 1/96 | 1/100 | 1/119.9 | 1/120 | 1/200 | 1/240 |
| 172.8° | 1/49.9 | 1/50 | 1/52.1 | 1/62.4 | 1/62.5 | 1/104.2 | 1/125 |
| 180° | 1/48 | 1/48 | 1/50 | 1/59.9 | 1/60 | 1/100 | 1/120 |
| 270° | 1/32 | 1/32 | 1/33.3 | 1/40 | 1/40 | 1/66.7 | 1/80 |
| 360° | 1/24 | 1/24 | 1/25 | 1/30 | 1/30 | 1/50 | 1/60 |
The 29.97 column is not a typo: at 29.97 fps a 180° shutter really is 1/59.94 s, and 23.976 gives 1/47.95. Cameras label those settings 1/60 and 1/48, and that is what you dial in — but the exposure underneath is the number shown here.
172.8° is the odd one out, and it is there on purpose: at 24 fps it lands on exactly 1/50 s — and on 1/49.95 at 23.976, near enough — which is what stops 50 Hz lights from flickering while you still shoot 24p. A shutter angle is the only control that can do that without touching exposure or frame rate.
What each ND filter takes away
An ND is named after the factor by which it divides the light. ND8 divides by eight, which is three stops, because 2³ = 8. The optical density printed on some filters is simply the number of stops multiplied by 0.3.
| Filter | Stops | Optical density | Light divided by |
|---|---|---|---|
| ND2 | 1 | 0.3 | 2 |
| ND4 | 2 | 0.6 | 4 |
| ND8 | 3 | 0.9 | 8 |
| ND16 | 4 | 1.2 | 16 |
| ND32 | 5 | 1.5 | 32 |
| ND64 | 6 | 1.8 | 64 |
| ND128 | 7 | 2.1 | 128 |
| ND256 | 8 | 2.4 | 256 |
| ND512 | 9 | 2.7 | 512 |
| ND1000 | 10 | 3.0 | 1024 |
The ten-stop filter is sold as “ND1000” but divides the light by 1024. The name is rounded; the glass is not.
Common aperture jumps, in stops
| From | To | Stops | Filter that fits |
|---|---|---|---|
| f/4 | f/2.8 | 1 | ND2 |
| f/5.6 | f/2.8 | 2 | ND4 |
| f/8 | f/2.8 | 3 | ND8 |
| f/11 | f/2.8 | 3.9 | ND8 |
| f/16 | f/2.8 | 5 | ND32 |
| f/16 | f/1.4 | 7 | ND128 |
| f/22 | f/1.4 | 7.9 | ND128 |
The two formulas, so you can check us
shutter speed = angle ÷ (360 × frame rate)
stops = 2 × log₂(aperture measured ÷ aperture wanted)
Both are exact, and both are worth knowing by heart. The first says a 180° shutter at 24 fps is 1/48 s — half the frame. The second says the jump from f/8 to f/2.8 is three stops, because light passes through an area: doubling the f-number quarters the light.
What the shutter angle actually changes
Not the exposure you are chasing — the motion you are recording. A narrow angle freezes each frame and turns pans into a stutter. A wide angle drags. 180° sits where an audience stops noticing the camera and starts watching the scene.
Which is why, outdoors, the shutter is the one setting you do not trade. You have the aperture, the ISO, and the light in front of the lens. The ND is the third one.
The filter suggested is the strongest one that does not exceed what you need — being slightly under is a half-turn of the iris away, being over costs you the aperture you came for.
Frequently asked
Why 180 degrees?
Because it exposes each frame for half its duration, and that is the amount of motion blur a century of cinema has trained everyone to read as “film”. Go narrower and movement turns stroboscopic — the Saving Private Ryan look, at 45°. Go wider and it smears. Neither is wrong; both are decisions.
How is the shutter speed worked out?
Exactly: shutter speed = angle ÷ (360 × frame rate). At 24 fps and 180°, that is 1/48 s. Nothing is approximated — a mechanical shutter really is a disc with an opening of that angle.
Why do I need an ND filter at all?
Because outdoors, keeping a 180° shutter and shooting at f/2.8 means far too much light. You cannot close the shutter without changing how motion looks, and you do not want to stop down if you came for that depth of field. So you take the light out in front of the lens. That is the whole job of an ND: it buys you an aperture without touching anything else.
How many stops is one aperture from another?
stops = 2 × log₂(f₁ ÷ f₂). The square comes from the area of the pupil — light goes through a surface, not a diameter. From f/8 to f/2.8 is 3 stops, which is an ND8.
Why does the tool never round the filter up?
Because being one notch short is fixable and being one notch over is not: you close the iris a touch and you are back. Over-filtered, you either open past the aperture you wanted or raise the ISO. So it picks the strongest filter that does not exceed the need, and tells you what is left.