Start with the calendar, not the number
A Julian calendar date has a year, month, and day under the older Julian leap-year rule. It is not the same as a Julian Day Number, even though both names contain Julian.
Before converting, copy the date as written and identify whether the source explicitly says Old Style, Julian calendar, ecclesiastical calendar, or another phrase tied to civil calendar usage.
If the source only says Julian date, pause before entering values. A historical date written as 12 March 1700 belongs in the Julian Calendar Converter; a value such as 2451545 belongs in the Julian Date Converter.
Use a neutral day count as the bridge
The reliable arithmetic pattern is to convert the source Julian calendar date to a neutral day count, then convert that same day count into the target Gregorian calendar. This avoids hand-counting month lengths or memorizing the date gap for every century.
The visible result should still be a calendar date. The day count is the bridge used by the calculation, not necessarily the value a historian would cite in the final note.
Separate arithmetic conversion from local adoption history
A converter can produce the corresponding Gregorian date under a rule set, but adoption dates varied by country, church, and record office. A date near reform may need local historical context before you decide which calendar the original writer used.
For careful notes, preserve the original Julian calendar date and add the converted Gregorian date with a statement of the rule used. That makes later review much easier.