The relationship between beam quality factor β and wavefront error was analyzed in this paper. Approximate formulas to calculate β from room-mean-square (RMS) of wavefront error were deduced. The relationship between β and several Zernike polynomials was obtained by numerical calculation through fast Forier transform (FFT) method. The approximate formula to estimate β from atmosphere disturbed wavefront error was given too. These approximate formulas were compared and verified well with the results of numerical calculation.