{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"equivalent-exposure"},"result":{"entity_type":"calculator","id":"equivalent-exposure","calculator_id":"equivalent-exposure","canonical_url":"https://tttkmbb.com/photography/equivalent-exposure","name":"Equivalent Exposure Calculator","title":"Equivalent Exposure Calculator – Shutter Speed for a New Aperture or ISO at Constant Exposure","category":"photography","category_name":"Photography & Optics","tool_name":"calculate_equivalent_exposure","featured_mcp_tool":false,"description":"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.","use_when":"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).","inputs":[{"name":"aperture_f","label":"Aperture (f-number)","type":"number","required":true,"min":0.5,"max":128,"description":"Current f-number, e.g. 8 for f/8.","example":8},{"name":"shutter_seconds","label":"Current shutter speed","type":"number","unit":"s","required":true,"max":86400,"exclusive_min":0,"description":"Exposure time in seconds. Enter fractions as decimals: 1/125 s = 0.008, 1/60 s = 0.016667, 1/1000 s = 0.001.","example":0.004},{"name":"iso","label":"ISO","type":"number","required":false,"default":100,"min":1,"max":10000000,"description":"ISO sensitivity setting (100, 200, 400, ...).","example":100},{"name":"target_aperture_f","label":"Target aperture (f-number)","type":"number","required":false,"min":0.5,"max":128,"description":"Optional new f-number; leave empty to keep the current aperture.","example":4},{"name":"target_iso","label":"Target ISO","type":"number","required":false,"min":1,"max":10000000,"description":"Optional new ISO; leave empty to keep the current ISO. At least one of target_aperture_f / target_iso is required.","example":100}],"outputs":[{"name":"target_shutter_seconds","label":"Target shutter speed","type":"number","unit":"s","decimals":6,"description":"Shutter speed that gives the same exposure with the target aperture and ISO."},{"name":"target_shutter_text","label":"Target shutter speed (text)","type":"string","decimals":4,"description":"The same value as a conventional fraction or seconds, e.g. '1/1000 s' or '2 s'."},{"name":"stops_from_aperture","label":"Stops from aperture change","type":"number","unit":"stops","decimals":2,"description":"2·log2(aperture_f / target_aperture_f); positive means the new aperture admits more light."},{"name":"stops_from_iso","label":"Stops from ISO change","type":"number","unit":"stops","decimals":2,"description":"log2(target_iso / iso); positive means the new ISO is more sensitive."},{"name":"net_stops","label":"Net stops","type":"number","unit":"stops","decimals":2,"description":"Sum of both; the shutter becomes 2^net_stops times faster."},{"name":"ev","label":"EV of current setting","type":"number","unit":"EV","decimals":2,"description":"log2(aperture_f² / shutter_seconds)."},{"name":"target_ev","label":"EV of target setting","type":"number","unit":"EV","decimals":2,"description":"log2(target_aperture_f² / target_shutter_seconds); differs from ev only by the ISO change."},{"name":"ev100","label":"Scene light value (EV100)","type":"number","unit":"EV","decimals":2,"description":"ISO-normalised exposure value, identical for both settings."}],"input_schema":{"type":"object","properties":{"aperture_f":{"description":"Current f-number, e.g. 8 for f/8.","type":"number","minimum":0.5,"maximum":128,"examples":[8]},"shutter_seconds":{"description":"Exposure time in seconds. Enter fractions as decimals: 1/125 s = 0.008, 1/60 s = 0.016667, 1/1000 s = 0.001. Unit: s.","type":"number","maximum":86400,"exclusiveMinimum":0,"examples":[0.004],"x-unit":"s"},"iso":{"description":"ISO sensitivity setting (100, 200, 400, ...).","type":"number","minimum":1,"maximum":10000000,"default":100,"examples":[100]},"target_aperture_f":{"description":"Optional new f-number; leave empty to keep the current aperture.","type":"number","minimum":0.5,"maximum":128,"examples":[4]},"target_iso":{"description":"Optional new ISO; leave empty to keep the current ISO. At least one of target_aperture_f / target_iso is required.","type":"number","minimum":1,"maximum":10000000,"examples":[100]}},"additionalProperties":false,"required":["aperture_f","shutter_seconds"]},"output_schema":{"type":"object","properties":{"target_shutter_seconds":{"description":"Shutter speed that gives the same exposure with the target aperture and ISO. Unit: s.","type":"number","x-unit":"s"},"target_shutter_text":{"description":"The same value as a conventional fraction or seconds, e.g. '1/1000 s' or '2 s'.","type":"string"},"stops_from_aperture":{"description":"2·log2(aperture_f / target_aperture_f); positive means the new aperture admits more light. Unit: stops.","type":"number","x-unit":"stops"},"stops_from_iso":{"description":"log2(target_iso / iso); positive means the new ISO is more sensitive. Unit: stops.","type":"number","x-unit":"stops"},"net_stops":{"description":"Sum of both; the shutter becomes 2^net_stops times faster. Unit: stops.","type":"number","x-unit":"stops"},"ev":{"description":"log2(aperture_f² / shutter_seconds). Unit: EV.","type":"number","x-unit":"EV"},"target_ev":{"description":"log2(target_aperture_f² / target_shutter_seconds); differs from ev only by the ISO change. Unit: EV.","type":"number","x-unit":"EV"},"ev100":{"description":"ISO-normalised exposure value, identical for both settings. Unit: EV.","type":"number","x-unit":"EV"}}},"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)","method":"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.","sources":[{"name":"Wikipedia – Exposure value","url":"https://en.wikipedia.org/wiki/Exposure_value","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Exposure (photography)","url":"https://en.wikipedia.org/wiki/Exposure_(photography)","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"f/8, 1/250 s, ISO 100 → f/4","inputs":{"aperture_f":8,"shutter_seconds":0.004,"iso":100,"target_aperture_f":4},"expected":{"target_shutter_seconds":0.001,"target_shutter_text":"1/1000 s","stops_from_aperture":2,"stops_from_iso":0,"net_stops":2},"url":"https://tttkmbb.com/api/v1/calculate/equivalent-exposure?aperture_f=8&shutter_seconds=0.004&iso=100&target_aperture_f=4"},{"name":"f/8, 1/250 s, ISO 100 → ISO 400","inputs":{"aperture_f":8,"shutter_seconds":0.004,"iso":100,"target_iso":400},"expected":{"target_shutter_seconds":0.001,"stops_from_iso":2,"net_stops":2,"ev":13.97,"target_ev":15.97},"url":"https://tttkmbb.com/api/v1/calculate/equivalent-exposure?aperture_f=8&shutter_seconds=0.004&iso=100&target_iso=400"}],"faq":[{"q":"Why does a two-stop aperture change quadruple the shutter speed?","a":"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."},{"q":"Why does the target EV change when only ISO changes?","a":"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."}],"tags":["equivalent exposure","exposure triangle","reciprocity","stops","shutter speed","aperture iso"],"related":[{"calculator_id":"exposure-value","reason":"Exposure value and lighting description of a single setting."},{"calculator_id":"nd-filter-exposure","reason":"The same stop arithmetic for neutral-density filters."}],"links":{"html":"https://tttkmbb.com/photography/equivalent-exposure","markdown":"https://tttkmbb.com/photography/equivalent-exposure.md","json":"https://tttkmbb.com/photography/equivalent-exposure.json","api":"https://tttkmbb.com/api/v1/calculate/equivalent-exposure","schema":"https://tttkmbb.com/api/v1/calculators/equivalent-exposure","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:45:08Z"}