In my job as copyeditor of scientific texts, I see within more often than I would like. Perhaps those who write within may think the word makes a text more scholarly. As you can see from the example above, within may look ludicrous.

IN

In is used about place or time:

He was in the kitchen.
My daughter lives in Italy.
This happened in late September.
See you in a minute. 
I haven’t felt this happy in years. 

WITHIN

Within often means inside a certain area, according to particular limits or rules, or during a certain period of time:

An angry voice was heard from within.
After she had left, I had a warm feeling within me.
Don’t place this medicine within the reach of children!
Delivery is free of charge within a thirty-kilometre limit.
From your hotel, the picturesque gardens are within easy reach.
I am not sure we can do this within budget.
Within minutes of arriving at the railway station, I heard a loud voice calling my name.
They had had three burglaries within six months.

IN AN HOUR OR WITHIN AN HOUR?

I’ll be back in an hour means that I ’ll be back in about one hour, perhaps fifty, sixty, or seventy minutes from now.

I’ll be back within an hour means that I’ll be back at any time before an hour has passed but in one hour at the latest.

I hope this has helped you understand the difference between in and within.

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