Exposure stops — the f/√2 ladder that governs every camera
A 'stop' is a factor-of-two change in light. Aperture stops go f/1.4, f/2, f/2.8, f/4, f/5.6 — each is √2 apart because area scales with radius². Shutter halves cleanly (1/125 → 1/250). ISO doubles (100 → 200). Change any one by a stop and exposure changes by exactly the same amount.
Photographic exposure is a light-integration problem: total exposure H (lux·seconds at the sensor) = illuminance × time. The camera has three controls that trade off in factor-of-two increments — 'stops' — so a scene metered at f/8, 1/125, ISO 200 is identical in brightness to f/5.6, 1/250, ISO 200 (opened aperture one stop, sped shutter one stop). This equivalence is codified in the APEX system (ISO 2720:1974) via the Exposure Value: EV = log₂(N²/t) where N is f-number and t is shutter in seconds.
The exact math
f-number N = focal_length / entrance_pupil_diameter > Aperture area ∝ 1/N², so one stop = N × √2 > EV₁₀₀ = log₂(N²/t) (at ISO 100) > EV at other ISO: EV_S = EV₁₀₀ + log₂(S/100) > Sunny 16: EV₁₀₀ = 15 in direct summer sun → f/16 at 1/125 s, or f/11 at 1/250 s, etc.
The stop ladders
| Aperture (f) | Shutter (s) | ISO | |---|---|---| | f/1.0 | 1 | 25 | | f/1.4 | 1/2 | 50 | | f/2 | 1/4 | 100 | | f/2.8 | 1/8 | 200 | | f/4 | 1/15 | 400 | | f/5.6 | 1/30 | 800 | | f/8 | 1/60 | 1600 | | f/11 | 1/125 | 3200 | | f/16 | 1/250 | 6400 | | f/22 | 1/500 | 12 800 | | f/32 | 1/1000 | 25 600 |
Each row is one full stop from its neighbour. Modern cameras subdivide into 1/3-stop clicks (f/2, f/2.2, f/2.5, f/2.8) — a 26% light change per click.
Worked example — the reciprocity trade
You meter a portrait at f/5.6, 1/60 s, ISO 400. Subject shifts and you want shallower depth of field.
Open two stops: f/5.6 → f/4 → f/2.8 (+2 stops of light) > To keep exposure equal, drop two stops elsewhere: shutter 1/60 → 1/125 → 1/250, or ISO 400 → 200 → 100. > Choice depends on constraint: subject motion (need faster shutter → drop ISO) or noise budget (need low ISO → drop shutter, but risk motion blur).
EV, LV and the Sunny 16 rule
The Sunny 16 rule (published in every Kodak Data Book since 1948): in direct front sun at midday, correct exposure is f/16 at 1/ISO. At ISO 100 → f/16, 1/125 s (EV 15). Overcast bright: EV 13 (f/8, 1/125). Open shade: EV 12. Indoor daylight window: EV 8–9. Full-moon night: EV −3. A camera's meter reads Light Value (LV) directly and reports EV, so an incident meter reading of EV 14 tells you every legal aperture/shutter combination at your working ISO.
Why f-numbers are irrational
Aperture is the *area* of the entrance pupil relative to focal length. Area = π(f/2N)². Doubling area (one stop) requires N × √2 = 1.414. The full-stop series (1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32) is the powers of √2 rounded to two significant figures. Cinema lenses use T-stops instead, correcting for glass absorption losses (typically 0.1–0.4 stops); a T2.8 zoom might be optically f/2.5 but transmits like f/2.8.
ISO — the odd one out
ISO 12232:2019 defines digital ISO via two methods: Standard Output Sensitivity (SOS) — brightness at 18% grey — and Recommended Exposure Index (REI). Doubling ISO doubles the *gain* applied to the sensor signal, not sensitivity itself. Read-noise-limited cameras see roughly 1 stop of dynamic range lost per stop of ISO gain (measured by Bill Claff's photonstophotos.net). Modern dual-gain sensors (Sony IMX571, Canon R6 II) get a free ~1 stop DR bonus at their second gain point (usually ISO 800 or 1600).
Depth of field and diffraction
Depth of field roughly doubles per stop of aperture closing (f/2.8 → f/4 → f/5.6). But diffraction sets a floor: airy-disc diameter d = 2.44 × λ × N. At λ = 550 nm and f/16, d = 21.5 μm — wider than a 3.7 μm APS-C pixel × 4. Full-frame Bayer sensors soften visibly beyond f/11; APS-C beyond f/8; Micro Four Thirds beyond f/5.6; smartphone 1.4 μm sensors beyond f/2.8, which is why phones use fixed f/1.8 apertures and simulate DoF computationally.
Flash and guide numbers
Flash exposure ignores shutter (up to sync speed, typically 1/200 s). Instead, guide number GN = distance × f-number, at ISO 100. Godox V1 has GN 28 m at ISO 100 — at 4 m, correct aperture is 28/4 = f/7 (round to f/8). Double the ISO, halve √2 the aperture: ISO 200 → f/11 at same 4 m. High-speed sync (HSS) beats sync-speed but drops 2–3 stops of flash power because the burst runs through the entire shutter travel window.
The Zone System bridge
Ansel Adams' 11 zones (0 to X) are exactly one stop apart. Zone V is 18% middle grey (EV = meter reading). Zone III is 'textured shadow with detail'; Zone VII is 'textured highlight with detail'. Modern raw workflow: expose to the right (ETTR) means placing highlights near Zone VIII–IX to capture maximum sensor bits, then pull down in post — an ISO stop of noise saving.
The five-second recap
One stop = 2× light. f/√2 ladder for aperture, halving for shutter, doubling for ISO. Sunny 16: f/16 at 1/ISO in direct sun. Diffraction hurts past f/11 on full-frame; higher ISO trades light for noise 1:1.
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FAQ
Is f/2.8 twice as bright as f/4?+
Yes, exactly one stop = 2×. Aperture areas: π(f/5.6)² vs π(f/8)² — the ratio is 2:1 because 5.6/4 = √2.
Why does my exposure look different when I only change ISO?+
ISO changes signal gain, not scene light. If you underexpose two stops and push in post, the result matches ISO-raised exposure in mid-tones but shows more noise in shadows on non-ISO-invariant sensors (older Canon DSLRs, most phones). Modern Sony/Nikon sensors are near ISO-invariant above ISO 400.
What is the fastest 'safe' handheld shutter?+
Rule of thumb: 1/(focal length × crop factor). 50 mm on full-frame → 1/50 s minimum. In-body stabilization adds 3–7 stops; a Sony A7 IV with 5-stop IBIS at 50 mm can shoot 1/2 s handheld with practice.
Do phone cameras have 'real' apertures?+
Yes, but they're tiny (usually f/1.6–f/2.4 fixed). The 'aperture' setting in phone portrait modes is computational — depth is estimated from sensor data or a second lens, then Gaussian blur is applied. Optically, the lens never changes.
Why do videographers care about the 180° shutter rule?+
Motion blur looks natural when shutter is 1/(2×fps). 24 fps → 1/48 s (rounded to 1/50). Break the rule and motion looks stroboscopic (Saving Private Ryan) or dreamy (Wong Kar-wai). Setting affects exposure by up to 5 stops vs stills defaults — hence ND filters on video shoots.
This article was written by The Turbo Unit Converter engineering desk (Applied radiometry & imaging science) and last reviewed on 2026-07-20 against NIST SP 811 and the BIPM SI Brochure. Read our full editorial policy.