Turnout Design Calculator
Whole numbers 5-20. AREA (TN-12's source) publishes no data for frog No. 4.
Whether the switch (point) rails themselves are curved or straight — independent of the closure rail, which is curved either way.
Also designing a crossover? Add parallel-track spacing
Description
A turnout's diverging route is not one constant-radius curve: it's a straight kink at the switch points, a curved (or, for a straight-switch turnout, straight-then-curved) switch rail, a curved closure rail, and finally a straight run through the frog. NMRA Technical Note TN-12, "Engineering Analysis and Geometric Design of Model Railroad Turnouts," works through the full prototype-railway-engineering geometry of all of these pieces and adapts it to model scale. This calculator runs that full equation set for a given frog number, scale, and switch type (curved- or straight-switch rails), rather than estimating a single "equivalent radius" the way a frog-number-only shortcut would.
Frog geometry: the frog (divergence) angle from the frog number, plus the frog's toe and heel lengths, overall length, toe/heel spread, and wing-rail extension — all measured from the frog's geometric "theoretical point" (where the two rails would meet with zero practical point width), per TN-12 Part IV.
Switch design: the switch heel spread (how far apart the stock and switch rails must sit at the heel, per TN-12's narrower, prototype-realistic "Method 2," which this calculator uses exclusively); the switch point and heel angles; the switch rail length, radius (curved switch only) and mid-ordinate; and the closure rail connecting the switch heel to the frog toe. TN-12 solves these switch angle equations by root-finding — they have no closed form — so this calculator does the same numerically.
Closure rail & gauge points: the straight and curved closure-rail lengths, three evenly-spaced gauge points along the diverging route with their lateral offset from the straight route (useful for laying out or checking a curved closure rail by hand), and the distance from the frog to where the diverging and straight centerlines cross.
Crossover spacing (optional): for two turnouts built into a crossover between parallel tracks, the straight-leg and diagonal track-center distances for a given track spacing, plus how much each changes per unit change in spacing — useful for checking how much a change in track centers shifts a crossover's overall length.
This calculator deliberately covers only the turnout geometry itself: TN-12's overall Planning Template (a full-turnout dimensioned diagram) and its 4 Tie Spacing Methods are left out, because TN-12 itself describes both as "not part of the turnout RPs" — i.e. not part of the geometric standard, just drafting aids layered on top of it. Guard rail design (setback, length, bevels) is also out of scope here, to keep this calculator focused on the switch/frog/closure-rail geometry that actually determines whether a turnout's diverging route is correctly shaped.
Sources
Core geometry, all switch and closure-rail equations, and the AREA frog toe/heel length, wing-rail-extension, and lead data are from NMRA Technical Note TN-12, "Engineering Analysis and Geometric Design of Model Railroad Turnouts" (Van S. Fehr, Revised March 5, 2015), Parts I and IV. Per-scale minimum gauge, maximum flangeway width, and maximum switch point spread are from NMRA Standard S-3.2, "Track, Standard Scale."
TN-12's AREA-sourced lead figures are the actual (practical) lead to the frog's 1/2-inch point; this calculator converts that to the theoretical lead the switch and closure-rail equations need, by inverting TN-12's own actual-lead equation (I-66).
The switch heel/point angle equations (IV-39, IV-40, IV-48) use TN-12's own empirically-averaged switch-angle ratio (its constant "k," averaged from its own Table 8) to reduce a true two-unknown system to one solvable equation. That averaging carries a small inherent error — amplified by the switch-rail-length equation's sensitivity at small switch angles — so this calculator's curved-switch rail length and radius can run a percent or two off TN-12's own worked example, even though every other quantity here (frog dimensions, lead, switch heel spread, gauge points, crossover spacing) was checked to match TN-12's Appendix A worked examples closely. Frog numbers 13, 17, and 19 are not in AREA's own published tables; TN-12 says it fills those gaps by linearly interpolating the adjacent frog numbers, and this calculator does the same (flagged in the result below).
Disclaimer: this is a geometric design calculation, not a substitute for building and testing an actual turnout. Check clearances, wheel/flangeway fit, and switch-point operation against your own stock before committing to a design.