Why does my friend's 1.7 carat round look bigger than my 1.8 carat round diamond?

Carat is a measure of weight, and may correspond roughly to the diameter of the stone, but not perfectly.

Depending on the quality of the diamond, it might be cut a little deeper which could result in a smaller diameter.

It may also be cut a little shallower, which would make it have a larger diameter.

A stone that is cut to ideal proportions will always have more brilliance than a stone that is cut a little too deep or a little too shallow, both of which are undesirable.

A 1.75 carat Round Diamond with Excellent proportions should measure 7.8 MM at the girdle.

Finally, how a stone is set can affect it's appearance.