We evaluate synchrotron radiation for a circular orbit using Graf's addition theorem for Bessel functions. Using Debye's and Olver's asymptotic expansions, the exact radiation fields can be calculated without recourse to assuming large distance from the tangent point and without using truncations as in Schwinger's work. Thus, the present results should be both numerically robust and efficient, requiring no numerical integration. The results are applied to assessing the accuracy of the Schwinger formula for radiometric applications. The formulas are particularly well suited for long wavelengths and for measurements at end stations close to the storage ring. Application areas are typically UV and x-ray instrument calibration for such purposes as found on environmental satellites. By carrying out this work, we can gain a quantitative sense on the accuracy of various approximations that can be made, and hence their consequential suitability.