Tonearm Alignment Calculator

The stylus sits on a circle of radius r around the spindle while the arm pivots at a fixed distance d away, so the cartridge is tangent to the groove only at two radii: the null points, where r² − 2·L·sin(offset)·r + (L² − d²) = 0 with L the effective length. Between those two radii the arm's fixed offset angle is more than the groove requires, so the cantilever toes outward toward the record edge (shown as a positive error); outside them it toes inward toward the label (negative), and the positive peak sits at √(L² − d²) between the nulls. A very small offset angle never reaches the tangent at all, which the calculator refuses rather than reporting zero error. This is a static geometry check: it assumes a straight arm, the stylus exactly at the effective length and the offset angle the manufacturer states. Stylus shape, wear, anti-skate, VTA and record eccentricity are not modelled, and it is not a judgement of how a record sounds.