Subtracting two times feels like subtracting two numbers, and for two times on the same day it is exactly that. The complications arrive at the boundaries: an interval that crosses midnight, a difference between two dates, and a difference between two places. Each boundary has its own rule, and each rule is a version of the same idea — convert to a single scale, subtract on that scale, and convert back. The single scale for clock times is minutes since midnight; for dates it is days since an epoch; for places it is UTC. This guide works all three, with the borrowing rule that is the only arithmetic a clock subtraction needs.

Same-day differences: borrowing 60

On one day, convert both times to minutes since midnight and subtract. 14:20 is 860 minutes; 09:45 is 585 minutes; the difference is 275 minutes, or 4 hours 35 minutes. When the minutes of the later time are smaller than the minutes of the earlier time, borrow: 16:15 minus 11:50 is 4 hours and (15 − 50) minutes, so borrow one hour — 3 hours and 75 minutes, minus 50, is 3 hours 25 minutes. The borrowing rule is the whole arithmetic of clock subtraction, and it is the same rule as borrowing 10 in decimal subtraction, with 60 in place of 10.

Twelve-hour times need conversion before subtraction, and the conversion is where the errors hide: 12:00 a.m. is midnight (00:00), 12:00 p.m. is noon (12:00), and every other hour keeps its number with 12 added for p.m. times. 12:30 a.m. is 00:30, not 12:30; 12:30 p.m. is 12:30, not 00:30. Convert to 24-hour notation first, subtract second, and the a.m./p.m. ambiguity disappears before it can do damage.

Crossing midnight: add 24 hours

An interval that crosses midnight — a night shift from 22:30 to 06:45 — subtracts to a negative number on one day’s scale: 06:45 is 405 minutes, 22:30 is 1,350 minutes, and 405 − 1,350 = −945. The negative result is the signal, not the answer: the end time belongs to the next day, so add 24 hours (1,440 minutes) to it before subtracting. 1,845 − 1,350 = 495 minutes, or 8 hours 15 minutes. The same interval in decimal hours is 8.25 hours, and the decimal form is what payroll uses — 8 hours 15 minutes at $20 an hour is $165.00, and the quarter-hour is worth $5.00, which is why the minutes matter and why rounding them away is a pay cut in disguise.

Intervals longer than 24 hours need dates, not just times: the difference between Monday 22:30 and Wednesday 06:45 is 32 hours 15 minutes, which no clock-only subtraction can produce, because the clock scale repeats every 24 hours. The time-difference calculation on this site takes dates as well as times for exactly this reason, and any difference that might span more than a day should be entered with dates, not inferred from the clock faces.

Differences between dates: borrow days, not hours

Between two dates, the unit is the day, and the borrowing rule moves up a level: borrowing a month means borrowing the number of days in that month, which varies. 15 March to 10 May is not 2 months minus 5 days by any fixed rule — March has 31 days, so 15 March to 15 April is 31 days and 15 April to 10 May is 25 days, for 56 days in total. Calendar arithmetic that treats every month as 30 days is wrong by days, and the error compounds across months. The reliable method is the same as for clock times: convert both dates to a day count (days since a fixed epoch, as every date library does internally), subtract, and convert the difference back into years, months and days only if a calendar breakdown is needed.

Two conventions need stating when a date difference is reported. The difference between 1 January and 2 January is 1 day, but the count of dates touched inclusive of both ends is 2 — and contracts, subscriptions, and leave balances each choose one convention, usually without saying so. State the convention when the number matters: “elapsed days” for the subtraction, “days inclusive” for the count, and never one number doing both jobs.

Differences between places: subtract in UTC

Two places’ local times differ by their UTC offsets, and the difference between two events in two places is found by converting both to UTC and subtracting. 15:00 in London in winter (UTC+0) is 15:00 UTC; 15:00 in New York in winter (UTC−5) is 20:00 UTC; the events are 5 hours apart, with New York’s 15:00 coming 5 hours after London’s. In summer the offsets are UTC+1 and UTC−4, and the difference is 4 hours — the same two cities, a different difference, because daylight saving moves the offsets independently. Subtracting local clock faces directly gives the right answer only when the offsets are known and constant, which across a daylight-saving transition they are not.

The International Date Line adds a day to the same arithmetic: 15:00 Monday in Tokyo (UTC+9) is 06:00 Monday UTC, and 15:00 Monday in Honolulu (UTC−10) is 01:00 Tuesday UTC — the Honolulu event is 19 hours after the Tokyo event, not 5 hours before it, and the date line is the reason the day changes. The time-zone calculation on this site carries the offset tables and the date-line arithmetic; the rule to remember is that the conversion to UTC is where the complexity lives, and the subtraction after it is trivial.

Frequently asked questions

How do you calculate the difference between two times?

Convert both times to minutes since midnight and subtract, borrowing 60 minutes when the minutes go negative. If the interval crosses midnight, add 24 hours (1,440 minutes) to the end time first: 22:30 to 06:45 the next day is 8 hours 15 minutes. Convert 12-hour times to 24-hour notation before subtracting, remembering that 12:00 a.m. is midnight (00:00) and 12:00 p.m. is noon (12:00).

What is the time difference between 22:30 and 06:45?

Eight hours 15 minutes (495 minutes, or 8.25 hours), if 06:45 is the next morning. On one day’s scale the subtraction is negative, which is the signal that midnight was crossed — add 24 hours to the end time and subtract again. At $20 an hour, the interval is worth $165.00.

How do you find the difference between two dates?

Convert both dates to a day count and subtract. Borrowing a month means borrowing the number of days in that month, which varies — 15 March to 10 May is 56 days, because March has 31 days. State whether the result counts elapsed days or days inclusive of both ends; the two differ by one, and contracts and leave balances each choose one convention.

Why does the time difference between two cities change during the year?

Because daylight saving time moves the two cities’ UTC offsets independently. London and New York differ by 5 hours in winter (UTC+0 and UTC−5) and 4 hours in summer (UTC+1 and UTC−4). Subtracting local clock faces works only when the offsets are known and constant; converting both times to UTC first handles the transitions correctly.

What is the difference between elapsed time and clock time?

Clock time is a position on the dial; elapsed time is the distance between two positions. The dial repeats every 12 or 24 hours, so positions alone cannot express an interval longer than the dial’s cycle — dates are needed. Elapsed time is measured in hours and minutes (or decimal hours for payroll), and it is the quantity that is paid, billed, and scheduled.

How do you convert a time difference to decimal hours?

Divide the minutes by 60: 8 hours 15 minutes is 8 + 15/60 = 8.25 hours. Payroll uses decimal hours, so the conversion matters — 15 minutes is 0.25 hours and 45 minutes is 0.75 hours, and rounding the minutes away before converting understates the pay.