Can I set up a formula field so that a user can overwrite the information when in edit mode?

Can you describe your set up a little more?  as far as tables and fields you are using.

You could possibly modify the button to write the value to the field when you first load the page, but give you the option to override it in the same field.  But this depends on your set up, and where the data is coming from.

Here is my specific situation...
I have a stipend field and a benefits field.  Both are currency.
Once I enter the stipend amount, I want the benefits field to be auto-populated as 25% of the stipend.  This is our estimate.  
Once the stipend has been processed and paid, I will know the actual benefits dollar amount.
I would like to overwrite the auto-populated benefit amount with the exact benefits amount in the same field.

This can be done with a formula which does that 25% calculation and a form rule

When [Benefits] is blank
Change [Benefits] to the value in the field [Stipend arstinsted]

You will have to have the [Benefits Estimated] field on the form, even if it's in a hidden section.

You can experiment with that rule or else a rule based on
"when the record is saved

So I tried
Estimated Benefit = Stipend * 25%

And a form rule that says
If Estimated Benefit is not blank
Then Benefit = Estimated Benefit

However, this doesn't work because Estimate Benefit is a formula field.  If I make it a non-formula field than the form rule works.

On further testing, it does work for new records added but not for existing records.

Did you uncheck the box on the form rule at the bottom so that it always fires and not just when the conditions become true?

Thanks.  Had not done that.