What's the relationship between flash power expressed as a fraction and as EV?

Question

I'm looking around for a second flash to play around with for off-camera stuff. Some flash specs I'm reading say that I get an adjustment range of plus or minus 2 EV or similar, while others say I get ½, ¹⁄₄, ¹⁄₁₆, and so on as manual settings.

What's the relationship between these different measurements? How do I convert from one to the other?

Answer

+-EV is used to measure compensation of automatically determined flash power (using either TTL or light sensor on flash). Fractions are used in manual mode and refer to how much of maximum power the flash is using.

Since these measures are used in different modes and there is no easy way to determine exactly how much power your flash uses in auto mode, you can't directly convert from compensation value to a manual setting. First, you'll have to determine flash power for correct exposure.

When you have determined manual flash power that gives you correct exposure, you have the equivalent of 0 EV. Now, if you double the power, that is +1EV; similarly, if you halve the power, it gives you -1EV. The amount of EVs gained by such compensation can be calculated as

log2( current setting / correct exposure setting )

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