This research study presents a novel global index based on harmonic mean theory to jointly evaluate the performance of pan-sharpening algorithms without using a reference image. The harmonic mean of relative spatial information gain and relative spectral information preservation provides a unique global index to compare the performance of different methods. The presented index also facilitates in assigning relevance to either the spectral or spatial quality of an image. The information divergence between the multispectral (MS) bands at lower resolutions and the pan-sharpened image provides a measure of the spectral fidelity and mean-shift. Mutual information between the original pan and the synthetic pan images generated from the MS and pan-sharpened images is used to calculate the relative gain. The relative gain helps to quantify the amount of spatial information injected by the method. A trend comparison of the presented approach with other quality indices using well-known pan-sharpening methods on high resolution and medium resolution datasets reveals that the new index can be used to evaluate the quality of pan-sharpened images at the resolution of the pan image without the availability of a reference image.