Turntable Alignment Protractor Generator (Printable)

How the numbers are calculated

The sheet is a two-point protractor. A two-point protractor marks the two record radii, called null points, where the cartridge should sit exactly tangent to the groove.

• Inputs: pivot-to-spindle distance d (the distance from the spindle center to the tonearm pivot center), and the two null radii a (inner) and b (outer).
• Effective length: L = sqrt(d² + a × b). This follows from the triangle spindle, pivot and stylus at a null point, where the stylus sits at radius r and the arm makes a right angle with the radius line once the offset angle is allowed for. Each null radius is a root of r² − 2L sin(β) r + (L² − d²) = 0, so a × b = L² − d².
• Overhang: L − d.
• Offset angle: β = arcsin((a + b) / (2L)).
• Tracking error angle at record radius r: arcsin((r − a)(r − b) / (2rL)). It is zero at both null points. The generator reports it at the inner and outer groove radii and the largest value in between.
• Groove radii: the inner groove radius is 60.325 mm and the outer groove radius of a 12-inch record is 146.05 mm, the radii listed for the IEC 1958 / RIAA 1963 standard (IEC 60098) by The Listening Suite .

The null points for each geometry are published values, not computed here:

These come from The Listening Suite’s tonearm geometry page . Other calculators quote Stevenson’s outer null as 117.4 mm; the difference moves the overhang by about 0.01 mm. As a cross-check of the formulas above, Bool Audio’s alignment calculator shows a table for a 211 mm mounting distance that lists Baerwald at 18.13 mm overhang and 24.07 degrees, Löfgren B at 18.60 mm and 24.02 degrees and Stevenson at 16.17 mm and 23.03 degrees, and this page’s formulas give the same figures. You can also type custom null points into the generator.

Assumptions: the arm is a pivoted arm with a fixed offset angle and no linear tracking, the stylus moves on a circle of radius L about the pivot, and the record radii are the IEC ones. A sheet printed in the wrong scale, a pivot distance that is measured to the wrong point, or a cartridge whose stylus is not on the headshell’s line will all give a wrong result that the sheet cannot detect. Follow your tonearm and cartridge maker’s alignment instructions where they differ.

Factory tonearm geometry from the makers’ manuals

Each row is copied from the maker’s own manual or specification page and carries its source. A blank cell means the maker does not publish that value in the cited document; the generator never fills it in from a guess. Pivot-to-spindle distance is entered where the maker states it, as Rega’s “mounting distance” and Pro-Ject’s Align it S guide do. For other decks, the generator subtracts the published overhang from the published effective length, which is the relationship Pro-Ject’s guide states: effective length is the pivot-to-spindle distance plus the overhang. The row’s link opens the generator with that deck filled in.

This table is deliberately short. It lists the decks whose makers’ documents we could open and check, not every popular turntable. Audio-Technica’s pages did not load for our research tools, so the AT-LP120X and its relatives are not in it yet; Audio-Technica’s own alignment answers are the right source for those decks. For how the factory overhang compares with the Baerwald overhang on the decks listed, see factory overhang vs Baerwald .

For tool choices and what to set on a fixed-cartridge deck, see cartridge alignment tools for first-time installs .

Sources

• The Listening Suite: tonearm geometry and terms for the groove radii and the three sets of null points.
• Each deck’s maker document, linked in its row of the table above.