A simple formula, using the quantum numbers of solar system planets and some quantized extra-solar planets, to estimate the periods, is done. The quantum numbers, calculated by other authors, have been used to find the orbital periods of solar system planets and some extra-solar planets. Observed periods have been used to compare them with the estimated periods from the given formula. It is found that the given relation is applicable perfectly for the solar system planets. Some extra-solar planets, of stars having approximately the same mass as the sun, are chosen to apply the same relation. The differences between the observed and calculated periods for the extra-solar systems have been calculated and tabulated. It is found that the percentage errors between the predicted values and the corresponding observed values for extra-planetary systems are controlled by the star’s mass and its quantum number. The percentage error decreases by increasing the quantum number, for quantum numbers over 4. When the quantum number is less than or equal 4, it is found that the percentage error decreases by decreasing the quantum number.