Model railroad helix calculator.

How the helix is calculated

A helix is a spiral ramp, and the arithmetic is geometry. One turn at centreline radius r is a circle, so the track length per turn is 2πr. A grade is rise divided by the length of track, so one turn rises 2πr times the grade. Dividing the height you want to climb by that rise per turn gives the number of turns, and the turns times 2πr give the track length. The page treats the track length as the run, which is exact for the grade as defined here and a very small approximation if you measure grade against the horizontal.

The clearance check compares the rise per turn with the headroom each turn must leave. The headroom is NMRA RP-7.1 dimension H, the clearance height for bridges and obstacles measured from the top of the railhead, scaled to your model, plus the thickness of the deck above the lower track, which you supply. RP-7.1 gives H as 17 feet for the Old-Time era, 22 feet for Classic and Early Modern, and 23 feet for Modern. In HO those are 2.34, 3.03, 3.03 and 3.17 inches. The radius line reads RP-11's model radius table for your scale. The NMRA's index lists no standard or recommended practice on helix grades, so there is no published limit for the grade here; the tool does not make one up.

It does not add extra grade for the drag of the curve, and it does not allow for easing into and out of the helix. Check the locomotives you run on the steepest part before committing to a grade.

Worked examples with real numbers

• HO, 18 inch radius, 2% grade. The circumference is 113.1 inches and one turn rises 2.26 inches. Climbing 12 inches takes 5.31 turns and 600 inches of track, which is 50 feet.
• Does that clear? Modern-era H in HO is 3.17 inches. With 0.5 inch of deck, each turn must rise 3.67 inches, but 2% gives only 2.26 inches. At 18 inches radius you would need a grade of about 3.24%, or a bigger radius.
• Same helix at 3.25%. Rise per turn is 3.68 inches, enough for the 3.67 inches needed. Climbing 12 inches takes 3.26 turns.
• Radius check. 18 inches is RP-11 class G in HO (18 inches), so the radius meets classes E, F and G only.

What this calculator leaves out

It does not know your locomotives' pulling power, the friction of your track, or how long your trains are. It works out one single-track helix, not a double-track one with a larger outer radius. It does not produce a plan: you still lay out the supports, the transitions at each end and the access for rerailing.