# Converting between Gain and f-Stops

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 = 2f

To convert from Gain to stops (f)

f = logGain

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.

logX + logY = logX * Y

logX – logY = loga ( X / Y )

logaXY = Y loga X

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

( log1 )  – ( logGain ) = log(1 / Gain)

And since:    log 1 = 0

– logGain = log(1 / Gain)

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

### Converting the base of the Log.

If your calculator can’t do Log2 you can use this formula to convert to Log10.

logX = ( logX ) / ( loga )

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

f = ( log10 Gain ) / ( log10 2 )