Relation between Resolution and Peak separation?

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The resolution is represented as a numeric value, such as 0.8, 1.0, or 3.0. But what is the relationship between the number representing the resolution and the actual peak separation? 

 At a resolution of 1.0, if the two peaks are assumed to have a Gaussian distribution and have the same peak height and peak width, then the difference in retention time from equation  become 1.0W, or 1.0 × 4σ = 4 σ. 

 In the case of a Gaussian distribution, 4 σ encompasses 95.4 %, such that the peaks overlap by 2.3 % ((100 % - 95.4 %)/2). 
This indicates that 2.3 % of the peak intrudes into the other peak from a perpendicular line drawn in the trough. 

 Similarly, a resolution of 1.5 indicates a difference in retention time of 1.5× 4σ = 6σ, which corresponds to an overlap of 0.15 % ((100 % - 99.7 %)/2).

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