sigma-bonds are the first bond between atoms. pi-bonds are those built up on top. A double bond is a sigma and a pi; a triple bond is a sigma and 2 pi bonds.
C_2H_4 is also known as ethene and has a double bond equivalent (DBE) of 1.
DBE is calculated using the formula
1/2 (A - X),
where A is the potential number of hydrogen and X is the actual number. A is calculated using
2n + 2
where n is the number of carbons in the molecule.
Therefore, when n = 2,
1/2 (A - X) = 1/2 (6 - 4) = 1/2 * 2 = 1
Although double bond equivalents are not necessarily double bonds, as they could be triple bonds or cyclic structures, in a molecule this small there is no opportunity for those.
Since double bonds have one sigma and one pi, this is the total number of pi-bonds: 1.
