To compute and test the significance of the Spearman rank correlation coefficient, the differences between ranks are used, and the Spearman correlation coefficient is used as a test statistic. This study has introduced an efficient rank correlation formula like the method earlier derived by Spearman. The formula is based on a new statistic that depends on the sum of the ranks rather than their difference, as in Spearman's formula. The formula was derived and tested with real data. Hence, if there are no ties in the data, the result shows that the formula gives the same result as Spearman's formula. The formula is simple to use and does not include a negative sign during calculation. we clarify the relationship between the new test statistic and the Spearman rank correlation coefficient and establish the exact distribution of the new test statistic using the exact distribution of the Spearman rank correlation coefficient. When there are no ties, it is advised to follow this formula.