Aperture and Shutter Speed Calculator: Find Exposure

An aperture and shutter speed calculator converts a known exposure into equivalent aperture-and-shutter settings, using the same ISO and brightness. Enter the starting f-number and shutter time, then choose a new aperture or shutter speed; the calculator returns the matching setting and the exposure difference in stops.

Formula

For the same scene brightness and ISO, exposure is proportional to shutter time divided by the square of the f-number. Therefore, when changing aperture from f to n, the equivalent shutter time is:

v = t × (n ÷ f)²

When changing shutter time from t to u, the equivalent f-number is:

w = f × √(u ÷ t)

The exposure difference between the new settings (n, u) and the starting settings (f, t) is:

x = log₂[(t ÷ u) × (n ÷ f)²]

• f: starting aperture f-number, with no physical unit.
• t: starting shutter time in seconds.
• n: new aperture f-number.
• u: new shutter time in seconds.
• v: shutter time that keeps exposure equivalent after changing aperture, in seconds.
• w: aperture that keeps exposure equivalent after changing shutter time, as an f-number.
• x: exposure difference in stops; positive means the chosen new settings are brighter, negative means darker.

A stop is a doubling or halving of exposure. This calculation assumes that the scene, lighting, ISO, and lens transmission remain unchanged. Real lenses may transmit slightly less light than their marked f-number suggests, but that does not alter the standard exposure-equivalence calculation.

Worked Example

The defaults are a starting aperture of f/8, a shutter time of 0.01 seconds (1/100 second), a new aperture of f/4, and a new shutter time of 0.0025 seconds (1/400 second).

1. Matching shutter time for f/4: v = 0.01 × (4 ÷ 8)² = 0.01 × 0.25 = 0.0025 seconds, or 1/400 second.
2. Matching aperture for a 0.0025-second exposure: w = 8 × √(0.0025 ÷ 0.01) = 8 × 0.5 = f/4.
3. Exposure difference for the chosen new settings: x = log₂[(0.01 ÷ 0.0025) × (4 ÷ 8)²] = log₂(4 × 0.25) = log₂(1) = 0 stops.

The new settings are equivalent to the starting exposure: opening from f/8 to f/4 admits four times as much light, while shortening the shutter time from 1/100 to 1/400 second admits one quarter as much. Together, the changes cancel.

How Aperture and Shutter Speed Work

Aperture is the adjustable opening in a lens. Its f-number is the focal length divided by the diameter of the entrance pupil. A lower f-number represents a wider opening and more light; a higher f-number represents a narrower opening and less light. The scale is nonlinear: one full stop changes the opening area by about a factor of two, so the f-number changes by a factor of √2.

Shutter speed is the time the sensor or film receives light. A longer time increases exposure; a shorter one decreases it. Common full-stop shutter times include 1/30, 1/60, 1/125, 1/250, and 1/500 second. Camera settings often use fractions, while this calculator uses decimal seconds: for example, 1/250 second is 0.004 seconds.

ISO affects how the camera records or amplifies a given exposure. The calculator holds ISO constant; changing ISO introduces another exposure variable. In practical photography, exposure compensation, metering, and post-processing can also affect the final image, but they do not change the basic relationship between aperture and shutter time.

When to Use the Calculator

Use an exposure-equivalence calculator when you want to preserve overall brightness but change how the image looks. A wider aperture can blur the background more, while a faster shutter can reduce motion blur. The calculator helps compensate for one change with the other.

• For a portrait, you might open the lens from f/8 to f/4 and shorten the shutter time by two stops to keep exposure steady.
• For moving subjects, you might choose a faster shutter and calculate the wider aperture needed to compensate.
• For a tripod landscape, you might use a longer shutter time and a narrower aperture, while checking that movement in trees or water is acceptable.

The results are mathematical equivalents, not recommendations for every scene. The best setting depends on subject movement, desired depth of field, available light, lens limits, and camera stability.

Reading Results and Common Mistakes

The calculator reports exposure time in seconds. Convert seconds to the familiar shutter notation by taking the reciprocal: 0.005 seconds is 1/200 second. A displayed value may not match a camera’s selectable shutter steps exactly; choose the nearest available setting and assess exposure.

• Confusing f-number direction: f/2.8 is wider and lets in more light than f/5.6. Moving to a numerically larger f-number reduces exposure.
• Forgetting the square: Aperture changes do not scale linearly. From f/4 to f/8 is two stops less light, not merely a one-step change.
• Mixing time units: Enter seconds, not a denominator such as 100 for 1/100 second. Use 0.01.
• Rounding too early: Keep the calculated value until the final step, then round to a shutter speed or aperture the camera supports.
• Changing more than one assumption: If ISO or scene brightness changes, the calculated pair alone no longer guarantees the same recorded brightness.

At very short or long times, the camera may not offer the exact calculated value. Long exposures can also encounter reciprocity failure with film or other equipment-specific behavior; those effects are outside this simple model.

Frequently Asked Questions

How do I calculate an equivalent shutter speed?
Multiply the starting shutter time by the square of the new f-number divided by the starting f-number: t × (new f-number ÷ starting f-number)². Keep ISO and lighting unchanged.

What happens to shutter speed when I open the aperture?
Opening the aperture lets in more light. To maintain the same exposure, shorten the shutter time. For example, opening from f/8 to f/4 is two stops, so use a shutter time four times shorter.

Does a lower f-number mean a smaller aperture?
No. A lower f-number means a wider aperture. The f-number is a ratio, so its direction can feel counterintuitive: f/2 admits more light than f/8.

Can aperture and shutter speed alone determine exposure?
They determine exposure only when ISO, scene brightness, and other relevant conditions are fixed. If ISO changes, or the light changes, the same aperture and shutter time may produce a different image brightness.

Why is the calculator result not an available camera setting?
Cameras offer shutter speeds and aperture values in discrete steps, and the exact options depend on the camera and lens. Select the nearest setting; a small difference may be corrected with another exposure adjustment.

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in f | Starting f-number | - | 8 | 0
in t | Starting shutter time | s | 0.01 | 0
in n | New f-number | - | 4 | 0
in u | New shutter time | s | 0.0025 | 0
out v | Matching shutter time | s | t * (n / f) ^ 2 | 4
out w | Matching f-number | - | f * sqrt(u / t) | 2
out x | Exposure difference | stops | log2((t / u) * (n / f) ^ 2) | 2