A method calculates mean speed of a fluid flowing in an open channel or a partially filled duct. Fluid having a free surface of width L1 extending between walls of the channel or duct includes local speed measurements at the surface of the fluid over a zone of width L2, the set of local measurements generating a spectrum of discrete data expressed in a temporal domain. The spectrum of discrete data is converted into a spectrum of data expressed in a frequency domain via a Fourier transform. A Gaussian curve is fitted to the spectrum and the mean μ and the standard deviation σ of the Gaussian curve are calculated. L2 and σ enable calculating the distribution of speeds over L2. The ratio L2/L1 is calculated and the mean speed of the fluid within the channel or duct is determined based on the Gaussian curve and the ratio L2/L1.