Explanation
What this measures
A UTC offset is how far a local clock is ahead of or behind Coordinated Universal Time. Subtracting the source offset gives UTC; adding the target offset gives the target local time.
How to use it
Enter the local hour and minute, then pick the offset of each place for that date. New York is UTC−05:00 in winter and UTC−04:00 in summer; India is UTC+05:30 all year. The answer is the local time at the target, with the day shift when the date changes.
t = 60h + m − o₁ + o₂; R = t − 1440 × ⌊t ÷ 1440⌋
| R | target time in minutes after midnight |
|---|---|
| h | source hour |
| m | source minute |
| o₁ | source UTC offset in minutes |
| o₂ | target UTC offset in minutes |
| t | total minutes; ⌊t ÷ 1440⌋ is the day shift |
Next day at 01:30
| Hour | 23 |
|---|---|
| Minute | 30 |
| From offset | UTC±00:00 |
| To offset | UTC+02:00 |
| Result | 01:30 next day |
60 × 23 + 30 − (0) + (120) = 1,530 min. 1,530 − 1440 × 1 = 90 min after midnight, which reads 01:30 with a day shift of 1.
Previous day at 23:00
| Hour | 1 |
|---|---|
| Minute | 0 |
| From offset | UTC+02:00 |
| To offset | UTC±00:00 |
| Result | 23:00 previous day |
60 × 1 + 0 − (120) + (0) = -60 min. -60 − 1440 × -1 = 1,380 min after midnight, which reads 23:00 with a day shift of -1.
A UTC+05:30 offset at 17:30
| Hour | 12 |
|---|---|
| Minute | 0 |
| From offset | UTC±00:00 |
| To offset | UTC+05:30 |
| Result | 17:30 |
60 × 12 + 0 − (0) + (330) = 1,050 min. 1,050 − 1440 × 0 = 1,050 min after midnight, which reads 17:30 with a day shift of 0.
Diagram of this result
The diagram lays the two clocks side by side as 24-hour scales, shifted by the difference between the offsets, and marks the converted moment on both.
A text summary gives the source time and offset, the converted time and offset, and the day shift.
Common mistakes
A city’s offset can change with daylight saving time and with history. Do not treat an offset as a named time zone or assume it holds all year. Keep the minus sign for places west of UTC.
Limits and assumptions
Offsets from UTC−12:00 to UTC+14:00, including half- and quarter-hour offsets, and a 24-hour source clock. The day shift ranges from −2 to +2. There is no time zone database or daylight saving lookup; check the offsets for your date first.
Sources
UTC offset arithmetic; one day has 1440 minutes. Checks cover moving into the next day, back into the previous day and a half-hour offset.
Does this handle daylight saving time?
No. It converts the offsets you pick. Choose the summer offset for dates when daylight saving time is in effect.