The following is an excerpt from Miles and Banyard's (2007) "Understanding and Using Statistics in Psychology --- A Practical Introduction" on "Calculating the exact significance of a Pearson correlation in MS Excel":
Inconveniently, this is not completely straightforward - Excel will
not give us the exact p-value for any value of r. However, it will
give the exact $p$-value for any value of $t$, and it’s not too hard to
convert $r$ to $t$. The formula you need is this one:

And then you use the tdist()
function in Excel. So, we have a value of
$r = 0.44$, and $N = 19$. We can use Excel to turn the $r$ into $t$, so in the
Excel sheet (at Cell A1, let’s say) we type:
=(0.44 * sqrt(19 – 2))/(sqrt(1-0.44^2))
This gives a value of $t = 2.02$. We then use the
tdist()
function to find the associated $p$. We need to tell Excel 3
things. First, the value of $t$, second, the degrees of freedom, which
are equal to $N – 2 = 17$, and third, the number of tails – either 1 or
2, and we always use 2 tails. If the value from the first calculation
is stored in cell A1, we can write:
=tdist(A1, 17, 2)
Which gives a result of $p = 0.059$.
Should you ever want to calculate a critical value for a Pearson
correlation, the process is reversed. You first calculate the critical
value for $t$, and then you convert this into $r$. Let’s say we wanted to
know the critical value for a correlation for $p = 0.05$. We first find
the value of $t$ that gives a $p$ of $0.05$. We use the excel function
tinv()
. We need to tell Excel two things, the probability that we
are interested in, and the degrees of freedom. Into cell A1 We type:
=tinv(0.05, 17)
Excel tells us that the answer is $2.11$. We then need
to turn that into a value of r. The formula is the reverse of the one
above, which takes a bit of algebra, so we’ll tell you what it is:

We type the formula into Excel =A1/(SQRT(A1 * A1 + 19 - 2 ))
And we
get the answer that the critical value is 0.0456.
References:
"Understanding and Using Statistics in Psychology: A Practical Introduction" Google Books
How to Calculate the P-Value & Its Correlation in Excel ehow