The area under a correctly phased absorption-mode spectral peak is a direct measure of the number of oscillators (ions, spins, molecules) in Fourier transform spectrometry (ion cyclotron resonance, magnetic resonance, interferometry absorbance). However, phase correction can prove difficult when (as in broad-band Fourier transform ion cyclotron resonance (FT/ICR] detection is considerably time-delayed after excitation. In the absence of noise, Huang, Rempel, and Gross showed that a "complex area" method yields the correct absorption-mode peak area, for an unphased noiseless spectrum. In this paper, we show that the number of oscillators may also be obtained from a least-squares fit to a magnitude-mode (i.e., phase-independent) spectrum. In the presence of noise and in the absence of peak overlap, the magnitude-mode method offers precision superior to that based on magnitude-mode peak height, "complex area", or even direct digital integration of a correctly phased absorption-mode peak, as demonstrated by both theoretical derivation and experimental FT/ICR results. The present method thus appears to offer the best available determination of the relative abundances of ions of different mass-to-charge ratio in FT/ICR mass spectrometry.