Abstract. Errors in the sun photometer calibration constant lead to artificial diurnal variations, symmetric around solar noon, of the retrieved aerosol optical depth (AOD) and the associated Ångström exponent α and its curvature γ. We show in simulations that within the uncertainty of state-of-the-art Langley calibrations, these diurnal variations of α and γ can be significant in low AOD conditions, while those of AOD are negligible. We implement a weighted Monte Carlo method of finding an improved calibration constant by minimizing the diurnal variations in α and γ and apply the method to sun photometer data of a clear day in Innsbruck, Austria. The results show that our method can be used to improve the calibrations in two of the four wavelength channels by up to a factor of 3.6.