Count cells that contain odd numbers

If you need to count cells that contain only odd numbers, you can use a formula based on the SUMPRODUCT function together with the MOD function.

In the example shown the formula in cell E6 is:

 
=SUMPRODUCT(--(MOD(rng,2)=1))

This formula returns 4 since there are 4 odd numbers in the range B6:B11 (which is named range, “rng” in the formula).
How this formula works
The SUMPRODUCT function works directly with arrays.
On thing you can do quite easily with SUMPRODUCT is perform a test on an array using one or more criteria, then count the results.
In this case, we are running a test for an odd number, which uses the MOD function:
 
MOD(rng,2)=1

MOD returns a remainder after division. In this case, the divisor is 2, so MOD will return a remainder of 1 for any odd integer, and a remainder of zero for even numbers.
Inside SUMPRODUCT, this test is run on every cell in B6:B11, the result is an array of TRUE / FALSE values:
{FALSE;TRUE;TRUE;TRUE;FALSE;TRUE}
After we coerce the TRUE/FALSE values to numbers using the double negative, we have:
{0;1;1;1;0;1}
SUMPRODUCT then simply sums these numbers up and returns 4.