Q:

What is the salesforce turnaround time for API usage refresh

We have just exceeded our API usage limit. Need to check when will be the turnaround time for the refreshment. I think it is refreshed hourly but can't find the related document. 
Is there any document stating this? 

A:

It's a moving window - last 24 hours. If you've been doing callouts for the last 24 hours continuously, chances are you can make more callouts in a few minutes, as the ones older 24 hours will stop count. Though, if you made all the callouts in the last 5 minutes and you've exceeded the limit, then you'll have to wait 24 hours before you can make more callouts. So the limit applies to callouts made within that 24h window.
Documentation (Page 35):

The DebuggingHeader has an extra usage limit of 1,000 calls per
24-hour period.
Limits are enforced against the aggregate of all API
calls made to the org in a 24-hour period. Limits are not on a
per-user basis. When an org exceeds a limit, all users in the org can
be temporarily blocked from making additional calls. Calls are blocked
until usage for the preceding 24 hours drops below the limit.
For Unlimited Edition and  Performance  Edition orgs, it ’ s likely that
other limiting factors, such as system load, can prevent you from
using your entire allocation of calls in a 24-hour period.

