The rule of thirds is one of the easier elements of composition to master and I like it because it’s easy. Mentally divide the frame into thirds horizontally and vertically and put the subject near the power points. Easy. My kind of rule.
The Golden Ratio is a little more complicated and involves math. For thousands of years artists and intellectuals have studied the Golden Ratio and other constructs based on the Golden Mean and how it applies to art composition. That has yielded tools like the Golden Triangle, the Golden Spiral, and the Golden Rectangle.
This gets deep in a hurry, so I’m going to simplify by saying the Golden Rectangle is one where the short side and long side relate to one another on a ratio of 1.61803. You might recognize the Golden Rectangle by another name, we call it 16:9 (actually a ratio of 1.777, but close enough).
Align the visual elements of a picture to the golden ratio and apparently humans perceive the composition more positively. It’s true. If you look at an older TV show shot in 4:3 it looks boxy compared to a show shot in wide screen format. Once you get used to wide screen it’s hard to go back.
By way of a simple calculation, divide the frame diagonally, corner to corner. Then draw a second line from the lower corner to upper intersection of thirds. That will yield a rough approximation of the Golden Triangle. Do the same drawing a line from the upper left corner to the lower left intersection of the thirds. If you can picture all that in your head, then you’re aligned with the Divine Ratio.
You can see how your pictures measure up to the gold standard at this handy site.