I do not know of any online versions of the calculation, but I will be happy to post it right here for you.
In = the square root of I^A+I^B+I^C-(IA*IB)-(IB*IC)-(IC*IA)
However, I have found that for field calculations, by determining the load of the greatest unbalance of any two phase loads will give you a very accurate value. EX: A=30amp, B=40amp, C=50amp. The greatest difference is 50-30= 20amp. If you perform the above calculation, the value comes to around 17.32amp. Not close enough for an exam question, but plenty clos enough for field calcs.
Bryan P. Holland, ECO. Secretary - IAEI Florida Chapter
gravity, why does that work? I know it does because I used my HP-11C calculator and assumed that the phases were 120 degrees apart and got the same answer. The way I do it is to convert the polar quantities into rectangular and total them, then convert back to polar. Using the HP it only takes a few seconds once you learn how to do it, faster than your method. If the currents are not 120 degrees apart, then there is a lot of difference in doing it my way and your way. For an electrician, probably doesn't matter. I was a substation test engineer commissioning protective relays and had to know very accurately what the residual currents were. But I am intriqued by your method. Thought at first it was symmetrical components, but ruled that out.