We evaluate the logarithmic derivative of the depth of the solar convective zone (CZ) with respect to the logarithm of the radiative opacity, ln R sub(CZ)/ ln . We use this expression to show that the radiative opacity near the base of the solar CZ must be known to an accuracy of c1% in order to calculate the CZ depth to the accuracy of the helioseismological measurement, R sub(CZ) = 0.713 c 0.001 R sub( ). The radiative opacity near the base of the CZ that is obtained from OPAL tables must be increased by 621% in the 2004 Bahcall-Pinsonneault solar model if one wants to invoke opacity errors in order to reconcile recent solar heavy abundance determinations with the helioseismological measurement of R sub(CZ). We show that the radiative opacity near the base of the CZ depends sensitively on the assumed heavy-element mass fraction, Z. The uncertainty in the measured value of Z is currently the limiting factor in our ability to calculate the depth of the CZ. Different state-of-the-art interpolation schemes using the existing OPAL tables yield opacity values that differ by 64%. We describe the finer grid spacings that are necessary to interpolate the radiative opacity to c1%. Uncertainties due to the equation of state do not significantly affect the calculated depth of the CZ.