Electron cyclotron emission (ECE) is a standard diagnostic in present day tokamak devices for temperature measurement. When the plasma density is high enough the emission at some frequencies is cut off. Of these cutoff frequencies, the first frequency to cut off depends on the shape of the density profile. If the density profile can be described by a few parameters, in some circumstances, this first cutoff frequency can be used to obtain two of these parameters. If more than two parameters are needed to describe the density profile, then additional independent measurements are required to find all the parameters.We describe a technique by which it is possible to obtain an analytical relation between the radius at which the first cutoff occurs and the profile parameters. Assuming that the shape of the profile does not change as the average density rises after the first cutoff, one can use the cutoffs at other frequencies to obtain the average density at the time of these cutoffs. The plasma densities obtained with this technique using the data from a 14 channel ECE diagnostic on COMPASS-C tokamak are in good agreement with those measured by a standard 2 mm interferometer. The density measurement using the ECE cutoffs is an independent measurement and requires only a frequency calibration of the ECE diagnostic.