A stop is the unit, not the f-number
The f-number is the confusing part of photography, and it is confusing for one specific reason: it is not the quantity anyone cares about. The quantity is light, and light goes as the square of the f-number, inverted.
A lens gathers light through an opening whose area is proportional to the square of its diameter. The f-number is the focal length divided by that diameter, so light gathered goes as 1/N². To halve the light you multiply the f-number by √2, not by 2.
The standard aperture series, and what each step costs| Marked | Exact | Light vs f/1 | Stops from f/1 |
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| f/1 | 1.000 | 1 | 0 |
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| f/1.4 | 1.414 | 1/2 | 1 |
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| f/2 | 2.000 | 1/4 | 2 |
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| f/2.8 | 2.828 | 1/8 | 3 |
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| f/4 | 4.000 | 1/16 | 4 |
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| f/5.6 | 5.657 | 1/32 | 5 |
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| f/8 | 8.000 | 1/64 | 6 |
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So moving f/2.8 → f/4 changes the number by 43% and the light by 50%. Neither figure is wrong; they are answers to different questions, and the reason the series looks arbitrary is that people read it as a linear scale of light when it is a geometric scale of ratio.
Once the series is recognised as powers of √2 it stops being a list to memorise. Every second entry doubles — 1, 2, 4, 8, 16 — and the ones between are those multiplied by 1.4. That is the whole pattern.
The numbers on the barrel are rounded
A small thing that explains a surprising amount: the printed f-numbers are not the exact series. f/2.8 is really 2.8284, f/5.6 is 5.6569, and f/11 is 11.3137.
Every second position is exact, because those are whole powers of two — 1, 2, 4, 8, 16, 32. The intermediate positions carry a √2 and get rounded to two significant figures for the barrel.
The consequence is measurable. Compute f/2.8 → f/4 with the printed numbers and you get 0.49 of the light rather than 0.50 — about 0.03 EV. So f/2.8 at 1/250 and f/4 at 1/125, which every photographer would call equivalent, differ by three hundredths of a stop on paper.
That is far below anything visible, and well below the third-of-a-stop increments most cameras offer. It matters only because it explains a discrepancy people notice in calculators and assume is a bug. This one keeps both the nominal and the exact value and reports the difference, rather than silently picking a convention.
Worth knowing that real lenses depart from the marked figure by more than this anyway. Manufacturing tolerance, vignetting at wide apertures and light lost to the glass itself all mean the transmitted light differs from the geometric prediction — which is why cinema lenses are marked in T-stops, measured rather than calculated.
Why three different scales are interchangeable
Aperture moves in √2, shutter in 2 and ISO in 2. Three different-looking scales, and one stop of each is exactly the same change in exposure. That equivalence is what the exposure triangle is actually claiming, and it is not obvious.
One stop, on each control| Control | One stop is | Bigger number means | What it costs |
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| Aperture | × √2 in f-number | Less light | Depth of field |
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| Shutter | × 2 in time | More light | Motion blur |
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| ISO | × 2 in sensitivity | More light | Noise |
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The aperture row is the odd one twice over: its factor is √2 rather than 2, and its number runs backwards — a bigger f-number means less light. Both follow from the same fact, that the f-number is a divisor and the light goes as its square.
What makes the triangle useful is that the three costs are unrelated. Trading a stop of shutter for a stop of aperture keeps the exposure identical and swaps motion blur for depth of field — that is a compositional decision with no exposure consequence, which is exactly why photographers talk in stops rather than in the underlying numbers.
The calculator names the direction explicitly, because “trade shutter for aperture” is genuinely ambiguous in words. Giving up light on one control and taking it back on the other is the operation; which control surrenders and which gains determines every sign in the answer.
The f-number is a ratio
It is written as a fraction because it is one: the f-number is the focal length divided by the diameter of the entrance pupil. “f/2” literally means the focal length over two.
What f/2 requires, physically| Lens | Pupil at f/2 | Relative glass area |
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| 24 mm | 12 mm | 1× |
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| 50 mm | 25 mm | 4.3× |
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| 100 mm | 50 mm | 17× |
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| 200 mm | 100 mm | 69× |
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All four give identical exposure. The 200 mm needs sixty-nine times the glass area of the 24 mm to do it, which is the entire explanation for why a 24 mm f/2 is a pocketable lens and a 200 mm f/2 is a thing you carry with both hands and insure separately.
It also explains the f-number’s peculiar usefulness. Because it is a ratio, the same f-number gives the same exposure on any lens on any camera — the geometry cancels. A meter reading of f/8 at 1/250 is a complete instruction, and nothing about the lens needs to be known.
And it explains why fast long lenses hit a physical wall. A 400 mm f/2.8 needs a 143 mm entrance pupil, so the front element must be at least that across in good glass, ground accurately. Going one stop faster to f/2 would require 200 mm, which is why that lens is rare and costs what a car does.
Reading EV against real light
Exposure value collapses the three controls into one number: EV is the base-two logarithm of the aperture squared over the shutter time, referenced to ISO 100. Each whole EV is one stop, so it is the natural unit for comparing settings that share nothing else.
Familiar light levels, at ISO 100| Scene | EV | Stops below full sun |
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| Bright sun, distinct shadows | 15 | — |
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| Hazy sun | 14 | 1 |
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| Overcast | 12 | 3 |
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| Open shade | 11 | 4 |
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| Bright indoor room | 8 | 7 |
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| Lit street at night | 4 | 11 |
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| Full moon on a landscape | −3 | 18 |
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The range is the striking part. Sunlight to moonlight is eighteen stops, which is a factor of about a quarter of a million — and the eye handles it without noticing, while a camera needs every one of those stops accounted for across three controls.
The sunny-16 rule falls straight out of the top row: in bright sun, f/16 at one over the ISO is a correct exposure. At ISO 100 that is 1/100 second, which is EV 15. It is worth carrying because it is a check on the meter rather than a replacement for it — if a reading in open sun comes back several stops from EV 15, something is wrong with the settings rather than with the light.
Sources and methodology
All three facts this page turns on are standardised: the aperture scale is a geometric series that lenses mark in rounded form, exposure value is defined logarithmically against ISO 100, and ISO speed is linear in sensitivity. That last one is why ISO and shutter share a stop factor of two while aperture does not — a difference that looks arbitrary until the definitions are read side by side.