The arithmetic behind it
Two exposures match when this quantity matches, where N is the f-number, t is the shutter time in seconds and S is the ISO:
| Relationship | Formula |
|---|---|
| Equivalence | N² / (t · S) is constant |
| Exposure value | EV = log₂(N² / t) |
| EV at ISO 100 | EV₁₀₀ = log₂(N² / t) − log₂(S / 100) |
| Stops between two exposures | log₂(N₂²/N₁²) − log₂(t₂/t₁) − log₂(S₂/S₁) |
That is the entire exposure triangle. Everything else — sunny 16, the reciprocal rule, ND filter maths — is this identity wearing a hat.
Sunny 16, the meterless meter
Set the shutter to one over your ISO. Then pick the aperture from the sky:
| Light | Aperture | At ISO 100 | At ISO 400 |
|---|---|---|---|
| Snow or bright sand, hard shadows | f/22 | 1/100 | 1/400 |
| Bright sun, distinct shadows | f/16 | 1/100 | 1/400 |
| Slight haze, soft-edged shadows | f/11 | 1/100 | 1/400 |
| Cloudy bright, barely any shadow | f/8 | 1/100 | 1/400 |
| Overcast, no shadow at all | f/5.6 | 1/100 | 1/400 |
| Heavy overcast or open shade | f/4 | 1/100 | 1/400 |
| Sunset, subject front-lit | f/2.8 | 1/100 | 1/400 |
Each row is one stop from the row above, which is exactly what the calculator does — the chart is just the calculation memorised. It is accurate to about a stop, which negative film forgives entirely and digital raw mostly forgives, as long as you protect the highlights.
Which leg should you let go of?
The calculator will happily solve for any of the three. Deciding which one is the actual craft, and it comes down to what would ruin the frame:
- Hold the shutter when motion is the risk — sport, kids, handheld long lenses, anything moving. Let ISO float.
- Hold the aperture when depth of field is the risk — portraits where the eyes must be sharp and the background must not be, or landscapes that need front-to-back sharpness.
- Hold the ISO when noise is the risk — long exposures, night skies, anything destined for a large print.
That decision is the entire design of Lucid Camera. Instead of hunting through modes, you pick the letter that names what you are protecting — A, M, S or I — and the camera floats the rest live as the light changes. This calculator is that idea, standing still.
Common questions
Why doesn't the answer land on a normal shutter speed?
Because the exact solution is a continuous number and camera dials are quantised to thirds of a stop. The readout shows both: the exact answer, and the nearest setting your camera actually offers, along with how far off it is. Anything under about a sixth of a stop is invisible.
Is ISO really part of exposure?
Purists say no: exposure is light per unit area at the sensor, which only aperture and shutter time control. ISO is amplification applied afterwards. In practice it trades exactly like a stop of light, so it belongs in the arithmetic even if it does not belong in the physics.
What about reciprocity failure?
That is a film problem. On exposures longer than about a second, film needs more time than the maths predicts, and the correction is emulsion-specific. Digital sensors are linear, so this calculator applies to them directly. For very long digital exposures, see the ND filter calculator.
Does this work with exposure compensation?
Yes — exposure compensation is measured in stops, so read the difference readout as your compensation. Two-thirds of a stop brighter is +0.7 EV on the dial.
Why do phone cameras have so few apertures?
Most have exactly one. iPhone lenses use a fixed physical aperture, so the triangle collapses to shutter and ISO. That is why Lucid Camera has no aperture control — a dial that changes nothing is worse than no dial.
Related tools
Hold one leg. Let the camera float the rest.
Lucid Camera puts A, M, S and I on your iPhone with real shutter and ISO dials, a live exposure readout, and a viewfinder that shows exactly what will save.