Short answer
Usually minutes to a few hours, occasionally a day or two. Nothing is actually being pushed around the internet. Resolvers hold on to the old answer until its time to live (TTL) runs out, and name server changes can take longer because the old delegation is cached too. Lower the TTL before a planned change to make it faster.
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What is really happening
When you change a DNS record, nothing is sent out to the world. Your DNS provider simply starts giving the new answer. The delay comes from everyone who asked recently: their internet provider's resolver, public resolvers and your own device have all stored the old answer and will keep using it until it expires.
That is why it looks like a slow spread. Different people see the change at different moments, depending on when their copy expires.
TTL: the number that sets the wait
Every record carries a time to live, in seconds. A TTL of 300 means resolvers may keep the answer for five minutes. A TTL of 86400 means a full day.
The wait after a change is roughly the old TTL, not the new one. That is the whole trick to fast changes, covered below.
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Why name server changes take longer
Pointing a domain at new name servers is a change at the registry for the domain ending, such as .com or .in, and those records are cached for much longer. A day or two is common, and it is the main reason people say DNS takes 48 hours.
Changing an A record or an MX record at your existing DNS host is far quicker, governed by that record's own TTL.
How to check whether it has reached the resolvers
Ask several public resolvers and compare. Our free DNS checker asks Cloudflare, Google, AdGuard and DNS.SB directly and shows whether their answers match. If all four agree on the new value, the large public resolvers have it.
It does not cover every resolver in the world, and no tool can. Treat it as a quick, honest sample rather than a global map.
If you still see the old site
Your own device may be holding the old answer. Restart the browser, then clear the operating system's DNS cache. On a Mac that is a restart of the DNS responder, and on Windows the command is ipconfig /flushdns.
Try the site on mobile data, which uses a different resolver. If that shows the new site, the change is live and only your own copy is stale.
How to make the next change fast
A day or two before a planned move, lower the TTL on the records you will change to something like 300. Wait for the old, longer TTL to pass. Make the change, confirm it, then raise the TTL again.
Keep the old server running for a few days after the move. Visitors whose resolvers are slow to update still reach the old copy instead of an error.