Why does Lightroom XMP store f/8 as exif:ApertureValue="6/1"?

Question

In a Lightroom XMP sidecar, I see `exif:ApertureValue="6/1"` for a photo that was shot at f/8. All other tools show the aperture as f/8 correctly. Why does XMP/EXIF store aperture this way? Is `6/1` Lightroom-specific, or is it defined by the EXIF/XMP standard? If possible, how do you convert between this value and the usual f-number?

user14028 · Accepted Answer

The Exif:ApertureValue is stored as an APEX value as mandated by various EXIF standards.

The APEX system is a way to calculate exposure and works using base-2 logarithms. The use of base-2 means a rise of one in the value equates to a doubling, which we know as 1 stop; which makes it pretty handy for photographers if they're good with logarithms (which we don't use much nowadays). Do note, however, that 1 stop in aperture means doubling of the square of the F-number -- for example, going from f/2.8 to f/4 is 1 stop because 4² = 2 * 2.8² (approximately).

To convert from APEX to F-numbers, use the following equation:

ApertureValue (Av) = log₂ (F-number)² = 2 log₂ (F-number)
⇒ F-number = 2^{Av / 2}

To convert f/8.0 to it's APEX value 6/1...

Log2(8) = 3
3 * 2 = 6 (or 6/1 as a fraction)

To convert the 6/1 APEX value back to f/8...

6/2 = 3
2^3 = 8 giving us back f/8.0

See also:

ExifTool: Exif Tags
APEX—The Additive System of Photographic Exposure (PDF) – Contains tables and equations, but no calculation examples.
JEITA CP-3451 Exif 2.2 (PDF) – Contains conversion equations.

Why does Lightroom XMP store f/8 as exif:ApertureValue="6/1"?

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