Model Railroad Helix Design Calculator
Enter the usable radius, vertical clearance, deck thickness, and desired rise to lay out a buildable helix. The results preserve clearance while rounding the plan to whole construction segments and show every riser elevation.
Inner-track grade (in inputs)2.49%
- Minimum rise per turn (in)
- 3.75
- Buildable segment count
- 32
- Actual turns
- 4
- Actual rise per turn (in)
- 3.75
- Rise per segment (in)
- 0.47
- Outer-track grade
- 2.3%
- Minimum radius for target grade (in)
- 29.84
- Inner-track length (in)
- 603.37
- Helix footprint diameter (in)
- 56
- Center opening diameter (in)
- 44
Riser elevation schedule
| Segment | Cumulative rotation (degrees) | Elevation above entrance (in) |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 45 | 0.47 |
| 2 | 90 | 0.94 |
| 3 | 135 | 1.41 |
| 4 | 180 | 1.88 |
| 5 | 225 | 2.34 |
| 6 | 270 | 2.81 |
| 7 | 315 | 3.28 |
| 8 | 360 | 3.75 |
| 9 | 405 | 4.22 |
| 10 | 450 | 4.69 |
| 11 | 495 | 5.16 |
| 12 | 540 | 5.63 |
| 13 | 585 | 6.09 |
| 14 | 630 | 6.56 |
| 15 | 675 | 7.03 |
| 16 | 720 | 7.5 |
| 17 | 765 | 7.97 |
| 18 | 810 | 8.44 |
| 19 | 855 | 8.91 |
| 20 | 900 | 9.38 |
| 21 | 945 | 9.84 |
| 22 | 990 | 10.31 |
| 23 | 1,035 | 10.78 |
| 24 | 1,080 | 11.25 |
| 25 | 1,125 | 11.72 |
| 26 | 1,170 | 12.19 |
| 27 | 1,215 | 12.66 |
| 28 | 1,260 | 13.13 |
| 29 | 1,305 | 13.59 |
| 30 | 1,350 | 14.06 |
| 31 | 1,395 | 14.53 |
| 32 | 1,440 | 15 |
The schedule includes the entrance at segment 0 and the final elevation at the last segment.
Single-track calculations ignore track spacing; all geometry is centerline geometry.
How to use this calculator
- Choose inches or millimeters, then enter every length in that same unit.
- Enter the inner track centerline radius and choose single or double track.
- Add the clearance, deck assembly thickness, total rise, and the number of construction segments in one turn.
- Use the grades, footprint, and target-radius result to compare layouts before cutting deck segments.
- Read the riser schedule from segment 0 through the final segment when setting elevations.
How the helix grade is calculated
A helix needs enough vertical space for a train on the lower level, plus the material from the underside of the next deck to the railhead. Let c be clearance above the lower railhead and d be deck, roadbed, and track thickness. The minimum rise in one full turn is H = c + d.
The calculator keeps the construction practical by using whole deck segments. With total rise D and S segments per turn, it finds the largest whole segment count that does not make a full turn rise less than H:
N = floor(D x S / H)
The actual turns are T = N / S, the actual rise per turn is P = D / T, and each segment rises D / N. Rounding down the segment count can make P slightly greater than the clearance-driven minimum. That is why the displayed grade can be steeper than a first division of the total rise might suggest.
For inner centerline radius r, the level circumference is C = 2 x pi x r. The inner-track grade is 100 x P / C. A double-track helix uses an outer radius of r + s, where s is track-center spacing, so its longer circumference produces a lower grade. The tool also solves the relationship backward for the radius needed at a selected maximum grade: R = 100 x P / (2 x pi x G).
What changes a helix most
Radius and rise per turn dominate grade. A larger radius lengthens every turn and lowers the grade, while more clearance or a thicker deck increases the rise that each completed turn must gain. More segments per turn do not directly change the smooth geometric grade; they give the construction layout more places to land and can change the rounded segment count. Double track needs its center spacing added to the outer radius when sizing the footprint.
The footprint is 2 x (outermost track radius + deck-edge margin). The center opening is max(0, 2 x (inner radius - deck-edge margin)). A margin equal to or larger than the inner radius therefore leaves no opening in this simple plan.
What this calculation leaves out
These are ideal centerline dimensions. The calculation does not predict locomotive traction, train length, coupler force, wheel slip, or the extra resistance of tight curves. It also does not choose scale-specific clearances, account for equipment overhang, superelevation, wiring, fasteners, guard rails, rerailing access, transition grades, or the structural design of the risers and deck. Measure your actual rolling stock, allow working access, and prove the plan with a full-size mock-up and test train before making the complete set of parts.
Worked example
Consider a double-track helix in inches with a 24 in inner centerline radius, 2 in track centers, 3 in railhead clearance, 0.75 in of deck assembly, 15 in total rise, and 8 segments per turn. The required rise is 3 + 0.75 = 3.75 in. The segment count is floor(15 x 8 / 3.75) = 32, which makes exactly 4 turns.
The actual rise per turn is 15 / 4 = 3.75 in, or 0.46875 in per segment. The 24 in inner circumference is about 150.80 in, so the inner grade is about 2.49%. The 26 in outer track is about 2.30%. At a 2% target, the same 3.75 in pitch requires an inner radius of about 29.84 in. With a 2 in deck-edge margin, the footprint is 56 in across and the center opening is 44 in.
Common questions
How is model railroad helix grade calculated?
Divide the rise in one complete turn by the track centerline circumference, then multiply by 100. For a 24 inch radius, the circumference is about 150.8 inches, so a 3.75 inch rise per turn is about a 2.49% grade. The inner track is the limiting grade because it has the shorter circumference.
Why can segment rounding make the grade steeper?
Deck pieces are normally made as whole segments. The calculator rounds the number of segments down far enough to preserve the required clearance on every complete turn, then divides the fixed total rise by the remaining number of turns. That can make the actual rise per turn greater than the clearance minimum.
What radius is needed for a 2 percent helix?
The required radius depends on the actual rise per turn after segment rounding. Divide 100 times that rise by 2 pi times 2 to find the minimum inner centerline radius. For a 3.75 inch rise per turn, the result is about 29.84 inches.
Which radius should I enter for a double-track helix?
Enter the centerline radius of the inner track. Then enter the center-to-center spacing between tracks. The calculator uses the spacing to calculate the outer track grade and the full deck footprint, while the inner track remains the steeper one.
Does the calculation include plywood and roadbed thickness?
Yes, enter their combined thickness with the track thickness in the deck assembly field. That thickness is added to the railhead clearance to establish the minimum rise in a complete turn. Include any layers that sit between the underside of one deck and the railhead above it.
How do I use the riser elevation schedule?
The table starts at segment 0 at the entrance elevation and adds one equal rise for each construction segment. Use its cumulative rotation and elevation to mark support locations around the helix. Confirm the final row reaches the intended entrance-to-entrance rise before building the deck.