Adding months is where date arithmetic stops being obvious, because months are not a fixed length. The rule used here is the calendar one: adding a month keeps the day number and moves to the next month, so 15 January plus one month is 15 February. Where the day number does not exist in the target month, the result falls back to the last day of that month — 31 January plus one month gives 28 February, or 29 in a leap year.
That fallback is not reversible, and it is worth understanding why. Take 31 January, add a month to reach 28 February, then subtract a month again: you arrive at 28 January, not where you started. Nothing has gone wrong; there is simply no arrangement of calendar months in which every day number survives the round trip. Systems that need reversibility count in days instead, which is why some contracts specify 30 days rather than one month.
British usage adds one more wrinkle. A period stated as "one month" from a date generally means the corresponding date in the following month, whereas one stated in days means exactly that many days — and for periods around the end of the month the two produce different answers. Where a deadline, a notice period or an anniversary matters, it is worth reading which of the two the document actually says before relying on either figure.
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