Time & Dates
How To Convert Time Zones
A time zone conversion is two arithmetic steps around a shared reference. The day shift that comes out of it is the part people get wrong, not the arithmetic.
Quick Answer
target local time = local time - source offset + target offset
- t_s
- Local time in the source zone
- o_s
- UTC offset of the source zone, in hours
- o_t
- UTC offset of the target zone, in hours
- t_t
- Local time in the target zone
14:30 in Shanghai at UTC+8 is 06:30 UTC and 01:30 the same day in New York at UTC-5, so New York is 13 hours behind. The two sides can also straddle midnight, which is where a day shift appears.
What Is How To Convert Time Zones?
A time zone is a region that keeps the same clock time. Each one is defined by its offset from Coordinated Universal Time, which is the shared reference every conversion goes through.
Converting between two zones is two steps. Subtract the source offset to reach UTC, then add the target offset to reach the destination. Nothing else is involved.
The offsets are signed. UTC+8 means eight hours ahead of UTC, so the local time is eight hours later than the UTC clock, and converting out of it means subtracting those eight hours.
The direction of the subtraction is the usual source of error. Converting from a positive offset to a negative one subtracts both offsets, which moves the clock back by their sum rather than by their difference.
Some zones use half-hour and quarter-hour offsets. India is UTC+5:30, Nepal is UTC+5:45 and Newfoundland is UTC-3:30, so the arithmetic has to carry minutes rather than whole hours.
A day shift happens whenever the destination time crosses midnight relative to the source. Going west from a positive offset usually lands on an earlier clock reading and can land on the previous day.
The day shift is found by dividing the destination minutes by the number of minutes in a day and taking the floor, which gives -1, 0 or +1 for any realistic conversion.
Summer time, called daylight saving time in some places, adds an hour to a zone during part of the year. Both zones can be on it, only one can, or neither, and the offsets in use are not the standard ones.
Summer time rules are not global. The northern and southern hemispheres are on opposite schedules, and the changeover dates move slightly every year, so a fixed table is wrong twice a year.
This is why the converter asks which zones are on summer time rather than guessing. An explicit tick is honest about a rule that changes annually, while a hidden guess is silently wrong for months.
The international date line produces the largest shifts. Crossing it can change the date by a whole day, which is why a call from London to Auckland can land on tomorrow.
Time zones are political, not astronomical. A country can move its offset, abandon summer time or split itself across two zones, and a converter built on a static table is only as current as the table.
The military and aviation use a letter-based system where Z stands for the UTC offset of zero and each other letter is an hour away. It is the same arithmetic with different labels.
The converter asks for a source zone, a local time and a target zone, subtracts the source offset, adds the target offset, and reports the destination clock, the UTC clock and the day shift.
Formula
target time = source time - source offset + target offset
Both offsets are signed hours from UTC. Subtracting the source offset reaches UTC and adding the target offset leaves UTC, and the two steps compose into one line.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| t_s | Source local time | time | The clock reading in the source zone. |
| o_s | Source offset | hours | Hours the source zone is ahead of UTC. |
| o_t | Target offset | hours | Hours the target zone is ahead of UTC. |
| t_t | Target local time | time | The clock reading in the target zone. |
day shift = floor(target minutes / 1440); local minutes = target minutes - 1440 x day shift
Total minutes past midnight can be negative or exceed a day. Taking the floor of the division by the minutes in a day gives the day shift, and subtracting it back gives the clock within the day.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| m_t | Total minutes | minutes | Target time as minutes, possibly out of range. |
| d | Day shift | days | How many days the destination has moved. |
| m_L | Local minutes | minutes | Minutes within the destination day. |
difference = source offset - target offset
The gap between the two clocks is the difference of the offsets. A positive value means the source zone is ahead, which is the gap to quote for a call or a meeting.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| o_s | Source offset | hours | Hours the source zone is ahead of UTC. |
| o_t | Target offset | hours | Hours the target zone is ahead of UTC. |
| Δ | Difference | hours | How far ahead the source zone is. |
How To Calculate How To Convert Time Zones
- 1
Write down both offsets
Read the offset for each zone, including any summer-time hour. Both are signed, and UTC+8 is a larger offset than UTC+5:30 by two and a half hours.
- 2
Convert the local time to UTC
Subtract the source offset from the local clock. Fourteen thirty at UTC+8 becomes six thirty UTC, and the result can be negative or beyond a day.
- 3
Add the target offset
Add the target offset to the UTC figure. Six thirty UTC plus UTC-5 becomes one thirty, which is on the same day because the sum stayed positive.
- 4
Take the day shift
Divide the destination minutes by 1440 and take the floor. A -1 means the destination fell on the previous day and a +1 means the next one.
- 5
Check the difference the other way
The gap between the two clocks is one offset minus the other. Quoting it in the right direction is what makes a meeting invitation unambiguous.
Examples
Example 1: 14:30 in Shanghai to New York, neither on summer time
- Source zone
- Shanghai (UTC+8)
- Local time
- 14:30
- Target zone
- New York (UTC-5)
- Summer time
- Neither zone
| Step | Calculation | Result |
|---|---|---|
| Source time in minutes | 14 x 60 + 30 | 870 |
| Coordinated Universal Time | 870 - 8 x 60 | 390 |
| UTC as a clock time | 390 minutes past midnight | 06:30 |
| Target time in minutes | 390 + (-5) x 60 | 90 |
| Target clock time | 90 minutes past midnight | 01:30 |
| Day shift | floor(90 / 1440) | 0 days |
Result: Fourteen thirty in Shanghai at UTC+8 is six thirty UTC and one thirty the same day in New York at UTC-5. The day shift is 0 days, so the date is unchanged, and New York is 13 hours behind Shanghai.
Example 2: 22:00 in London to Sydney, neither on summer time
- Source zone
- London (UTC+0)
- Local time
- 22:00
- Target zone
- Sydney (UTC+10)
- Summer time
- Neither zone
| Step | Calculation | Result |
|---|---|---|
| Source time in minutes | 22 x 60 | 1320 |
| Coordinated Universal Time | 1320 - 0 | 1320 |
| Target time in minutes | 1320 + 10 x 60 | 1920 |
| Day shift | floor(1920 / 1440) | 1 |
| Target clock time | 1920 - 1440 minutes | 480 |
| Target local time | 480 minutes past midnight | 08:00 |
Result: Ten pm in London is twenty one hundred minutes, and adding Sydney's ten-hour offset gives nineteen twenty, which is one full day ahead. Sydney reads 08:00 the next day, so the day shift is +1.
Calculator
Prefer a full-width tool? Open the How To Convert Time Zones calculator page.
Common Mistakes
Subtracting the offsets instead of one
Only the source offset is subtracted. Going from UTC+8 to UTC-5 moves the clock back by thirteen hours, which is the sum, but only because one is subtracted and the other is added.
Adding the source offset instead of subtracting it
The source offset brings the local clock to UTC, so it is always subtracted. Adding it sends the answer in the wrong direction by twice the offset.
Forgetting that offsets can be half hours
India is UTC+5:30 and Nepal is UTC+5:45, so the conversion has to carry minutes. Rounding to whole hours puts the answer out by up to three quarters of an hour.
Assuming summer time applies to both zones
The two hemispheres run opposite schedules, so for half the year only one zone is on summer time. The offsets in use have to be checked for each side separately.
Using a fixed summer-time table
The changeover dates drift every year, so a table that was right last March is wrong this March. Asking whether summer time is in effect beats guessing from the date.
Dropping the day shift
A clock reading of 01:30 without the date is ambiguous when the conversion crossed midnight. The day shift is part of the answer, not decoration.
Quoting the difference in the wrong direction
New York being 13 hours behind Shanghai and Shanghai being 13 hours ahead of New York are the same fact, but a meeting invitation that states it backwards is a meeting at the wrong time.
FAQ
How do I convert a time between two time zones?
Subtract the source zone's UTC offset from the local time to reach UTC, then add the target zone's offset. The result may cross midnight, in which case the day shifts by one.
Which direction do I subtract?
Always subtract the source offset and add the target one. Both are signed, so moving from a positive offset to a negative one moves the clock back by their sum.
Why do some time zones have half-hour offsets?
Because the offset is political rather than astronomical. India uses UTC+5:30 and Nepal UTC+5:45, so the arithmetic has to carry minutes rather than whole hours.
What is the international date line?
It is the line of longitude where the calendar date changes by a whole day. Crossing it going west moves to the next date and going east moves to the previous one.
Why does the converter ask about summer time instead of working it out?
Because the changeover dates move every year and the two hemispheres run opposite schedules. An explicit tick is honest about a rule that changes annually, while a guess is silently wrong for months.
What is the largest time difference between two zones?
Twenty-six hours, between UTC-12 and UTC+14. That is a whole day and two hours, which is why a date as well as a clock time is needed to make an appointment unambiguous.
References
- [1]Time and Date AS, Coordinated Universal Time and time zones — https://www.timeanddate.com/worldclock/
- [2]IANA Time Zone Database, UTC offsets by country — https://www.iana.org/time-zones
- [3]National Institute of Standards and Technology, Understanding time zones — https://www.nist.gov/pml/time-and-frequency-division/nist-time-frequently-asked-questions