Counting working days without the off-by-one
Three things make project date arithmetic go wrong, and all three are avoidable once you can see them.
The off-by-one, and where it comes from
There are two reasonable meanings of "finish": the last day worked, and the moment work stops. They differ by one day. Scheduling software mostly means the second; people mostly mean the first.
Mix them and a five-day task starting Monday "finishes Saturday". The fix is to compute in one form consistently and convert once at the end — which is why a one-day task starting Monday correctly finishes Monday, not Tuesday.
The working week is not always five days
Monday to Friday is a default, not a fact. Sunday to Thursday is standard across much of the Middle East, four-day weeks are increasingly common, and construction and manufacturing frequently work six. A calculator that assumes Mon–Fri gives the wrong answer for everyone else, and the error compounds with every week of duration — a ten-week project on a six-day week finishes nearly two weeks earlier than a five-day assumption suggests.
Backward planning is not forward planning reversed
Once holidays exist, counting ten working days forward from a date and ten working days back from another step through different holidays. So a backward answer worked out by subtracting from a forward one can be several days out.
This matters most in exactly the situation where backward planning is used: a fixed external deadline where being wrong is expensive. The reliable approach is to walk the calendar in reverse rather than negate a forward result.
A start on a non-working day
If a project start lands on a Saturday, work does not begin on Saturday. It begins on the next working day, and a calculator that silently counts from the Saturday will run a day or two ahead of reality for the entire plan.
What this tool will not do
It calculates from the figures you enter and nothing else. It cannot tell you whether your estimates are honest, whether your dependencies reflect how the work really flows, or whether the plan is achievable with the people you have. Those are judgements, and a schedule that looks precise can still be built on all three being wrong.