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Equivalent Exposure Calculator

Solves the shutter speed that keeps the exposure unchanged when the aperture and/or ISO are changed, using the reciprocity relation t2 = t1 × (N2/N1)² × (ISO1/ISO2), and reports the stop changes involved.

When to use

You have a correctly exposed setting and want to open up or stop down the aperture, or change ISO, without changing the image brightness.

Do not use when: You only need the exposure value of one setting (use exposure-value), or the change comes from a neutral-density filter (use nd-filter-exposure).

Formula

target_shutter_seconds = shutter_seconds × (target_aperture_f / aperture_f)² × (iso / target_iso); net_stops = 2·log2(aperture_f / target_aperture_f) + log2(target_iso / iso)

Assumes reciprocity (exposure depends only on the product of intensity and time), which holds for digital sensors; film shows reciprocity failure for exposures longer than about 1 s. Cameras round shutter speeds to the nearest 1/3 stop.

Inputs

Parameter	Type	Unit	Required	Description
`aperture_f`	number		yes	Current f-number, e.g. 8 for f/8. Range: ≥ 0.5, ≤ 128
`shutter_seconds`	number	s	yes	Exposure time in seconds. Enter fractions as decimals: 1/125 s = 0.008, 1/60 s = 0.016667, 1/1000 s = 0.001. Range: > 0, ≤ 86400
`iso`	number		default 100	ISO sensitivity setting (100, 200, 400, ...). Range: ≥ 1, ≤ 10000000
`target_aperture_f`	number		no	Optional new f-number; leave empty to keep the current aperture. Range: ≥ 0.5, ≤ 128
`target_iso`	number		no	Optional new ISO; leave empty to keep the current ISO. At least one of target_aperture_f / target_iso is required. Range: ≥ 1, ≤ 10000000

Outputs

Output	Type	Unit	Description
`target_shutter_seconds`	number	s	Shutter speed that gives the same exposure with the target aperture and ISO.
`target_shutter_text`	string		The same value as a conventional fraction or seconds, e.g. '1/1000 s' or '2 s'.
`stops_from_aperture`	number	stops	2·log2(aperture_f / target_aperture_f); positive means the new aperture admits more light.
`stops_from_iso`	number	stops	log2(target_iso / iso); positive means the new ISO is more sensitive.
`net_stops`	number	stops	Sum of both; the shutter becomes 2^net_stops times faster.
`ev`	number	EV	log2(aperture_f² / shutter_seconds).
`target_ev`	number	EV	log2(target_aperture_f² / target_shutter_seconds); differs from ev only by the ISO change.
`ev100`	number	EV	ISO-normalised exposure value, identical for both settings.

Example

f/8, 1/250 s, ISO 100 → f/4: {"aperture_f":8,"shutter_seconds":0.004,"iso":100,"target_aperture_f":4} → {"target_shutter_seconds":0.001,"target_shutter_text":"1/1000 s","stops_from_aperture":2,"stops_from_iso":0,"net_stops":2}

f/8, 1/250 s, ISO 100 → ISO 400: {"aperture_f":8,"shutter_seconds":0.004,"iso":100,"target_iso":400} → {"target_shutter_seconds":0.001,"stops_from_iso":2,"net_stops":2,"ev":13.97,"target_ev":15.97}

GET https://tttkmbb.com/api/v1/calculate/equivalent-exposure?aperture_f=8&shutter_seconds=0.004&iso=100&target_aperture_f=4

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/equivalent-exposure (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/equivalent-exposure · Markdown: https://tttkmbb.com/photography/equivalent-exposure.md · JSON definition: https://tttkmbb.com/photography/equivalent-exposure.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="equivalent-exposure"
OpenAPI operationId: calculate_equivalent_exposure
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Exposure value (reference)
Wikipedia – Exposure (photography) (reference)

FAQ

Why does a two-stop aperture change quadruple the shutter speed?

Light admitted scales with the square of the f-number ratio: f/8 → f/4 is (8/4)² = 4× more light, so the shutter must be 4× shorter to compensate.

Why does the target EV change when only ISO changes?

EV counts only aperture and shutter, so the faster shutter raises it; the ISO-normalised EV100 stays the same, which is what 'equivalent exposure' means.

Related calculators

Exposure Value Calculator — Exposure value and lighting description of a single setting.
ND Filter Exposure Calculator — The same stop arithmetic for neutral-density filters.