How can I increase label distance(see attachment) in contour?
, there's no contour setting that controls the density of the labels.
You can try adjusting the scale of your map. The scale can really impact how your contours appear. A smaller scale can make your contours less dense over all, which may also help with the labels.
You can easily change the scale of your map by drawing a base map and changing the scale in the first dialog.
Map tools > Base Map > Draw Base Map.
Redraw your contours after changing the scale.
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AGS Res2DInv & Res3DInv