A stop is a doubling, and that is the whole system
Exposure has three controls and one unit. The unit is the stop, and one stop is a factor of two in the light reaching the sensor. Shutter time is the easy one: double the time, double the light, one stop. ISO is nearly as easy: double the number, one stop more sensitivity, with the caveat that ISO amplifies rather than collects, so it buys brightness and not signal.
Aperture is the one that trips people, because the f-number is a ratio of focal length to pupil diameter, and light passes through an area. Area goes as the square of the diameter, so the light changes as the square of the f-number ratio. That is why the standard series steps by a factor of √2 — 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22 — and why each of those steps is one stop even though the numbers look irregular. In formula terms, the stops between two apertures is 2 × log₂(N₂ ÷ N₁).
Once everything is in stops, exposure becomes addition. Close down two stops, slow the shutter two stops, and the brightness is unchanged. This calculator does that arithmetic and then converts back to a shutter speed you can dial in.
ND filters and the labelling mess
An ND filter of N stops multiplies the required shutter time by 2ᴺ. Three stops turns 1/125 into 1/15. Ten stops turns 1/125 into eight seconds. That doubling is the entire physics; the confusion is purely in how filters are named.
| Stops | Light passed | Common markings | 1/125 s becomes |
|---|---|---|---|
| 1 | 1/2 | ND2, 0.3 | 1/60 s |
| 2 | 1/4 | ND4, 0.6 | 1/30 s |
| 3 | 1/8 | ND8, 0.9 | 1/15 s |
| 6 | 1/64 | ND64, 1.8 | 1/2 s |
| 10 | 1/1024 | ND1000, 3.0 | 8 s |
Three naming systems coexist: the stop count, the transmission denominator, and the optical density where each 0.3 is one stop. Variable ND filters are labelled least reliably of all, and most of them drift by a fraction of a stop across the frame near the ends of their range. Whatever the ring says, take a frame and check the histogram.
Reciprocity, and what actually breaks it
The reciprocity assumption is that halving the light and doubling the time gives the same result. Digital sensors hold to it well across almost every exposure a normal shoot will use. Where it fails on digital is at very long exposures, where thermal noise accumulates independently of the light — which is a noise problem, not a brightness problem, and the fix is dark-frame subtraction or a cooler sensor rather than more exposure.
Film is where genuine reciprocity failure lives. Past roughly a second, many emulsions need meaningfully more exposure than the arithmetic says, and the correction is specific to each stock and published by its manufacturer. Colour films can also shift colour as they fail, because the three layers fail at different rates. This calculator does the linear arithmetic only. If you are shooting film long exposures, run the number here and then apply your stock manufacturer figures on top.
Which control to spend
All three routes to a given brightness produce different pictures, so the choice is compositional rather than technical. Aperture decides how much is sharp, which the depth of field calculator quantifies. Shutter decides whether motion is frozen or smeared, and in video it is largely spoken for — the conventional shutter angle puts you at about one over double the frame rate, which is why ND filters are standard equipment on a video shoot in daylight rather than an effect. ISO decides how much noise you accept.
The usual working order is to fix whichever one the shot demands, fix the second one according to what the subject needs, and let the third one land wherever it lands. Deciding all three at once is how people end up with a technically correct exposure of the wrong picture. If the light itself is what you are adjusting, the inverse-square falloff calculator covers moving the lamp instead of moving the settings.
Questions people ask
Why is f/2 to f/2.8 one stop rather than a third?
Because the f-number is a diameter ratio and light passes through an area. Doubling the area needs the diameter multiplied by the square root of two, about 1.414, and 2 × 1.414 is 2.83, which gets marked as 2.8. That is the whole reason the aperture series looks like a strange set of numbers: it is powers of the square root of two, rounded for the barrel engraving. The general form is that the difference between two apertures in stops is 2 × log₂(N₂ ÷ N₁).
Does raising ISO add noise?
Raising ISO does not create noise so much as reveal it. The noise floor is largely set by how few photons the sensor collected, which is decided by aperture and shutter. ISO amplifies whatever was collected, so a high-ISO frame looks noisy because it is a thin signal amplified, not because amplification is dirty. The practical consequence is worth knowing: at a fixed aperture and shutter, raising ISO and getting a properly bright frame usually beats underexposing at low ISO and lifting it afterwards on most modern sensors, though the margin is small and varies by camera.
Can I stack ND filters?
Stop values add, so a 3-stop and a 6-stop together give 9 stops, and the arithmetic here handles that if you enter 9. The costs of stacking are optical rather than mathematical: more glass surfaces means more flare and more chance of a colour cast, deep stacks vignette on wide lenses, and any polariser in the stack becomes very hard to judge. One filter of the right strength beats two of the wrong ones.
What shutter speed do I need for video?
The convention is roughly one over double the frame rate — about 1/48 at 24 fps, 1/60 at 30 fps — which comes from a 180 degree shutter angle and produces the motion blur audiences read as normal. Because that shutter is fixed and video ISO options are limited, the only remaining exposure control outdoors is aperture, and aperture is compositional. That is why ND filters are treated as basic equipment on video shoots rather than as a special-effects item.
How accurate is the one-over-focal-length handheld rule?
It is a starting point from the film era, calibrated against print sizes nobody uses anymore, and it is optimistic on a high-resolution sensor where shake is visible at magnifications film never reached. Treat it as the slowest speed worth attempting rather than a safe one, and shoot a burst when it matters. Image stabilisation genuinely buys several stops against your own movement, and buys exactly nothing against a subject that is moving — a stabilised 1/8 second frame of a walking person is a sharp background and a blurred person.