Inclusive and exclusive counting
From 1 March to 10 March there are 9 days of difference, but 10 days if both endpoints are counted. Neither is wrong — they answer different questions.
Use exclusive counting for intervals and deadlines ("how long until"), inclusive counting for durations where both ends are occupied ("how many nights booked", "how many days of leave").
Month lengths and leap years
Months range from 28 to 31 days, which is why mental arithmetic across month boundaries goes wrong. February gains a 29th day in leap years: those divisible by 4, except century years not divisible by 400. 2000 was a leap year; 1900 was not.
"One month later" is ambiguous
Adding a month to 31 January has no clean answer — there is no 31 February. Different systems resolve this differently, some clamping to 28 or 29 February and others rolling into March. Contracts and software disagree on this more often than people expect.
Where precision matters, express the interval in days rather than months.
Business days
Ten business days is not two calendar weeks if a public holiday falls inside it. Holidays also vary by country and frequently by region or state, so a deadline counted in working days can resolve to different dates for parties in different places.
Common uses
Contract and notice periods, project scheduling, interest accrual over an exact number of days, visa and travel durations, age in days, counting down to an event, and working out how many nights a booking covers.