A camera takes an image by exposing a light sensitive detector to light for some amount of time, in a digital camera this light is stored as charge and then added up to give the image. The shutter speed is simply how long you let the sensor collect light before stopping and reading off the data.
Shutter angle comes about when shooting video/ movie film because sometimes you don’t care about how long the actual exposure time is, you care about it’s length relative to the frame rate of the footage. Motion looks most natural when the shutter speed is half of the frame rate (so 25 fps means you want 1/50th shutter speed). This corresponds to a 180 degree shutter angle, it’s useful because even if you vary the frame rate the shutter angle stays the same so motion still looks natural.
It’s called shutter angle because in the days of film it was achieved by using a rotating disk with part of it open and part closed, the shutter angle corresponded to the angle of the open part. This disc rotated around once every frame which is why 180 degrees corresponds to it being open for half of the frame interval.
Shutter speed is the amount of time a camera shutter is open, usually measured in seconds. Typical figures are 1/100 s (0.01 s) or 1/1000 s (0.001 s).
Shutter angle is used for motion cameras. It tells you how much of the time the shutter is open with 360° (a full circle) meaning open all the time (impossible) and 180° meaning open half the time (typical for cinema movies). If you have a 24 frame-per-second movie camera then a shutter angle of 180° implies a shutter speed of 1/48 s. This is relatively slow and it means that fast-moving objects appear blurry which helps to hide the low frame rate.
Keeping a constant shutter angle means that motion blur stays matched to the frame rate you’re shooting at. So using a shutter speed of 1/120 s for 60 fps is a reasonable choice. Using lower shutter angles can result in stuttery motion.
The use of shutter angle terminology comes from cinema cameras in which the shutter was a rotating disc, so it actually had an angle that was open to control the exposure.
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