The magnetoelastic coupling in Co films on W(0 0 1) in the range from 3 to 200 monolayers has been measured. The film stress during film growth and the magnetoelastic stress are determined in situ with a highly sensitive bending beam method. The magnetoelastic coupling in Co films as thin as three atomic layers has been determined. We find a strong variation of the magnetoelastic coupling between 32 and 15 MJ/m(3) for films of three monolayers and 30 nm thickness, respectively. This deviation of the magnetoelastic coupling from its bulk value of 37.5 MJ/m(3) is ascribed to the large strain of the film and changes in the crystalline structure. Relations between the magnetoelastic coupling coefficients B-j and the magnetostrictive strains lambda(i) are derived for hexagonal symmetry, which correct misprinted relations found in the literature.