Reciprocity shutter speed calculator for aperture stop changes

This reciprocity shutter speed calculator starts with the original exposure time and an aperture change measured in stops, then returns the new time required to preserve exposure. Positive stops mean closing the aperture and therefore lengthening the exposure; negative stops mean opening it and shortening the exposure. The result includes seconds, a readable shutter-speed label, and the exact exposure multiplier used in the calculation.

Describe the starting exposure and aperture change

Enter the original shutter speed as a duration in seconds. A camera setting written as 1/125 second is 0.008 seconds, while a two-second exposure is simply 2. Then enter the aperture movement in stops. Use a positive value when closing the aperture, because less light passes through the lens and the shutter must remain open longer. Use a negative value when opening the aperture, because more light reaches the image plane and the exposure time must become shorter. Whole stops are common, but the calculator also accepts fractional changes such as 0.3, 0.5, or 1.5 stops. The sign convention is important: moving from f/4 to f/8 closes the aperture by two stops, so enter 2. Moving from f/8 to f/4 opens it by two stops, so enter -2. This explicit convention avoids relying on f-number interpretation and also works when the stop difference was obtained from a meter, filter calculation, or lens transmission test. Inputs must be finite numbers within the published ranges.

Understand the reciprocity calculation

Each full stop represents a factor of two in exposure. The calculator raises two to the aperture-change value and multiplies the original shutter duration by that factor. Closing by one stop doubles the required time; closing by two stops multiplies it by four. Opening by one stop halves the time because two raised to minus one equals one half. Fractional stops follow the same exponential relationship, so half a stop uses the square root of two rather than a rough linear adjustment. The response reports the original duration, signed stop change, exposure multiplier, new duration in seconds, and a formatted shutter-speed label. Numeric results are rounded to a stable precision so identical inputs produce identical JSON across environments. The readable label is a convenience: durations below one second are shown as a reciprocal when practical, while longer durations remain in seconds. Use the numeric seconds field for downstream calculations, camera-control software, or comparisons, since actual camera dials may offer only standardized increments and may require choosing the nearest available setting.

Apply the result without changing the exposure target

The computed time preserves the mathematical exposure implied by the starting settings. It is useful when changing depth of field, moving between lens apertures, or planning a sequence in which aperture changes but brightness should remain consistent. It does not account for every physical effect. Very long film exposures can exhibit reciprocity failure, and some film manufacturers recommend additional time or color correction beyond the ordinary stop relationship. Digital sensors may introduce thermal noise during long exposures, while neutral-density filters can have real transmission values that differ slightly from their labels. Camera shutter controls also quantize times into full-, half-, or third-stop steps. Treat the returned value as the exact reciprocal target, then select the closest supported shutter speed or use a timed bulb exposure when precision matters. If another variable changes at the same time, such as ISO or filter density, combine all changes into a net stop adjustment before calculating. The endpoint is deterministic and performs no network requests, so it can also serve as a reliable building block in exposure-planning tools, shot lists, and repeatable testing workflows.