Find the hour everyone is awake
Add the cities. The amber column is when all of them are at work. Drag the line to read every clock at once.
Why time-zone maths goes wrong even when you are careful
Converting one time to another is arithmetic, and people are generally good at arithmetic. The errors come from somewhere else. They come from the fact that the offset you are adding is not a constant: it depends on the date, on whether either country happens to be observing daylight saving at that moment, and on whether the two hemispheres are shifting in opposite directions — which for half the year, they are.
A meeting set between London and Sydney in September is a different number of hours apart than the same meeting in November, because Britain falls back while Australia springs forward, and the gap moves by two hours in the space of a few weeks. Neither party did anything wrong. The arithmetic was correct when it was done.
Seeing it instead of calculating it
This tool shows day and night as a band per city, all laid on one timeline. Because each band is offset by that city's real current position, they visibly fail to line up — and the shape of that misalignment is the thing you are actually trying to understand. You are not converting a number. You are looking at where the daylight is.
The amber column marks the hours when every city on the list is inside 9am–6pm locally. When that column is narrow, you can see immediately that there is not much room. When there is no column at all, the tool says so, rather than proposing a time that requires somebody to take a call at four in the morning and pretending that counts as a solution.
The cases that break other converters
Half-hour and quarter-hour offsets are the usual casualty. India runs 5 hours 30 minutes ahead of UTC, Nepal 5 hours 45, and any tool that stores offsets as whole numbers gets both wrong. So are the places that opt out of daylight saving inside a country that observes it: Arizona keeps Mountain Standard Time all year, and Queensland keeps Australian Eastern Standard Time, so both agree with their neighbours for half the year and differ for the other half.
None of that is handled here by special-casing. The browser you are reading this in ships the full IANA time-zone database because it needs it to format dates, and this page reads offsets out of that. The consequence is that the rules are as current as your browser, and there is no offset table on this site that could ever be wrong.