Described are instruments for measuring troll depths of a line, of a known length, drawn through water and having a proximal line end out of the water and a weighted, distal line end in the water. The instruments include a reference to align with the line near the proximal line end to sense the insertion angle of the line. A nonlinear depth scale marks troll depths as a polynomial function of the length and angle of insertion, the angle of insertion measured relative to e.g. a horizontal or vertical reference.