You don't use a formula to make soap with wood ash lye. There is way too much variability involved for calculations to be accurate. If you want to calculate, then use ingredients that are sufficiently consistent so calculations make sense. If you want wood ash lye, then you gotta deal with it as it is, not what you'd like it to be.
The time honored way to make soap with wood ash lye -- Cook part of the fat with some of the lye, stirring often, until the soap starts to emulsify the mixture. Test the mixture for zap or no zap. Add more lye or more fat as is appropriate, cook it some more, test, add more lye or fat, etc. until you've used up all the fat you want to saponify and a zap test of the finished soap tells you the soap is just slightly zappy. Then, if you want, you can add a slight bit more fat until the zap disappears. The old makers left the soap slightly alkali heavy. There were reasons why soap makers were an honored trade in a community -- it requires skill to do well.
Wood ash lye is not KOH, it's mostly K2CO3, which saponifies more slowly than KOH. You can convert the carbonate to the hydroxide by treating it with slaked lime.
