Why date arithmetic is harder than it looks
Counting days seems like the simplest calculation on this site and produces more wrong answers than any other. The reasons are structural rather than difficult.
Months are not a fixed length. "Three months from January 31" has at least three defensible answers, and different systems pick different ones. Any calculation expressed in months is carrying a convention, and the convention should be stated rather than assumed.
Inclusive and exclusive counting both exist. A hotel booking from the 3rd to the 7th is four nights and five days. A notice period, a contractual deadline and a return window may each count differently, and the difference is exactly one day -- which is the amount by which deadlines are usually missed.
Days are not always 24 hours. Daylight saving transitions produce a 23-hour and a 25-hour day each year in most of the United States and Europe, and time zones mean two people can disagree about today's date in good faith.
Leap years follow three rules, not one. A year is a leap year if it is divisible by 4, except centuries, except centuries divisible by 400. The year 2000 was a leap year; 1900 was not.
What these tools do about it
Each calculator here states the convention it uses and offers the alternative where a genuine choice exists. The date difference tool lets you include or exclude the final day, and reports both a plain day count and a years-months-days breakdown, because those two answers are legitimately different rather than one being a rounded version of the other.
The time card calculator converts clock times to decimal hours, which is what payroll systems use and where a great deal of confusion starts: seven hours and forty-five minutes is 7.75 hours, not 7.45. It handles shifts that cross midnight, and it separates paid hours from time on site so that an unpaid break is visible rather than absorbed.
The age calculator borrows days and months the way a person does when counting on their fingers, which is why its answer differs slightly from dividing total days by 365.25. Both methods are correct for different questions, and the page explains which is which.
What no calendar tool can know
Public holidays vary by country, state and sometimes by employer, and there is no universal list to apply. Business-day counts here exclude Saturdays and Sundays only; if your count has to be exact, subtract the holidays that actually apply to you.
Nor can a calculator know which convention a particular contract, statute or policy intends. When a date determines a legal right or a payment, the governing document is the authority and this is a cross-check.