So cameras work in Stops and composite packages use Gain. To convert between the two we need to do a bit of log maths. Heres how.

To convert from Stops (f) to Gain

Gain = 2^f

To convert from Gain to stops (f)

f = log₂ Gain

This is equivalent to:

f = ( log₁₀ Gain ) / ( log₁₀ 2 )

If you want to see why then we’ll need to look a little deeper at log maths

The three basic Laws of logarithms.

These three identities give us all the maths we need to know.

log_a X + log_a Y = log_a X * Y

log_a X – log_a Y = log_a ( X / Y )

log_aX^Y = Y log_a X

So if we’re dividing by the a Gain value then:

( log₂ 1 )  – ( log₂ Gain ) = log₂ (1 / Gain)

And since:    log 1 = 0

 – log₂ Gain = log₂ (1 / Gain)

This means that dividing by a Gain value will give a negative f-Stop value.

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Converting the base of the Log.

If your calculator can’t do Log₂ you can use this formula to convert to Log_10.

log_a X = ( log_b X ) / ( log_b a )

So to convert a value from Gain to Stops ( f ) using log₁₀ rather than log₂

f = ( log₁₀ Gain ) / ( log₁₀ 2 )

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