% · 1 in N · radius · helix
Model railway gradient calculator
How steep is that climb, how tight can the curve be, and will the helix clear the track above?
Gradient
- Gradient2 %1 in 50 · 20 ‰ · 1.15°
- Rise10 cm100 mm · 3.94 in
- Horizontal run5 m5,000 mm · 500 cm · 196.9 in · 16.4 ft
NEM 101 recommended maximums, standard gauge
Branch lines 3% (1 in 33): withinMain lines 2.5% (1 in 40): withinTracks in stations 0.4% (1 in 250): steeper
Narrow gauge
Branch lines 4% (1 in 25): withinMain lines 3.3% (1 in 30): withinTracks in stations 0.5% (1 in 200): steeper
Transitions at HO (1:87.1): Round off the change from level over at least 99 mm · 3.9 in of track (NEM 101 minimum, G = 16.5 mm); 165 mm · 6.5 in is recommended for branch lines and 231 mm · 9.09 in for main lines. Vertical curve radius at least 4.95 m, ideally 8.25 m (branch) or 11.55 m (main).
Minimum curve radius
| Class | Layout type | Minimum radius | Minimum turnout frog |
|---|---|---|---|
| E formerly E/J | Old-time pikes, small 60° curve, 100 ft prototype | 356 mm 14 in | No. 4 |
| F formerly F/K | Branch and feeder lines 50° curve, 118 ft prototype | 419 mm 16.5 in | No. 4½ |
| G | Branch and feeder lines 45° curve, 131 ft prototype | 457 mm 18 in | No. 5 |
| H formerly G/L | Branch and feeder lines 40° curve, 146 ft prototype | 508 mm 20 in | No. 5 |
| I | Branch and feeder lines 36.5° curve, 158 ft prototype | 559 mm 22 in | No. 5 |
| J formerly H/M | Standard trunk lines 35° curve, 166 ft prototype | 584 mm 23 in | No. 6 |
| K | Standard trunk lines 33° curve, 176 ft prototype | 622 mm 24.5 in | No. 6 |
| L formerly N | Standard trunk lines 30° curve, 193 ft prototype | 673 mm 26.5 in | No. 6 |
| M | Standard trunk lines 27° curve, 214 ft prototype | 749 mm 29.5 in | No. 6 |
| N formerly O | Standard trunk lines 25° curve, 231 ft prototype | 813 mm 32 in | No. 6 |
| O | Standard trunk lines 22° curve, 262 ft prototype | 914 mm 36 in | No. 6 |
| P formerly P | Standard trunk lines 20° curve, 288 ft prototype | 1,016 mm 40 in | No. 7 |
| Q | Standard trunk lines 18° curve, 320 ft prototype | 1,118 mm 44 in | No. 8 |
Helix
- Rise per turn94.2 mm9.42 cm · 3.71 in
- Needed per turn92 mm77 mm clearance (RP-7.1 H, classic, 22 ft) + 15 mm deck
- Clearance checkClears2.26 mm to spare (0.09 in)
- Smallest radius at 2%732 mm28.82 in to the track centre
- Gentlest grade at this radius1.95 %1 in 51.2
- Track per turn4.712 m15.46 ft (185.5 in)
NEM 101 advises not reaching its maximum gradients on tight curves, as curves on a grade cut the load a locomotive can pull: test a helix with your longest train.
How to use it
Gradient is rise over horizontal run: 100 mm up over 5 m is 2%, or 1 in 50. Choose what to work out, fill in the other two, and switch the gradient box between percent and 1 in N. MOROP's NEM 101 recommends at most 2.5% (1 in 40) on standard-gauge main lines, 3.0% on branch lines and 0.4% in stations, with 3.3%, 4.0% and 0.5% for narrow gauge.
Where a gradient starts or ends, NEM 101 asks for the change to be rounded off over a length in multiples of the track gauge G: at least 6 G for a 2% change, 10 G recommended on branch lines and 14 G on main lines. The calculator scales that to your gradient and gauge.
The curve table is NMRA RP-11's minimum radius for each class of equipment, from old-time short wheelbases to long modern cars; use the largest radius your space allows. In a helix, one turn of track must climb at least the overhead clearance plus the thickness of the deck above, so the calculator compares the rise per turn with NMRA RP-7.1's bridge height for your era.
Questions
How do I turn 1 in N into a percentage?
Divide 100 by N: 1 in 40 is 2.5% and 1 in 50 is 2%. To go back, divide 100 by the percentage.
What radius does a helix need?
Enough that one turn climbs past the clearance and deck at a gradient your trains can manage. At 2% in HO with classic-era clearance and a 15 mm deck, that is at least 732 mm to the track centre.
Why is my train fine on the straight but stalls on the curve?
A curve on a grade adds drag, and NEM 101 notes that tight radii on inclines cut the load a train can haul, so it advises not reaching the maximum gradient on tight curves. Ease the grade on curves or widen the radius.
Sources
- Recommended maximum gradients and the rounding of gradient changes (300 G minimum vertical radius; 6, 7.5 and 12 G minimum for 2%, 2.5% and 4% changes): MOROP NEM 101, Inclinations and changes of inclination (Recommendation, 2025).
- Minimum radius and turnout frog by equipment class for O, S, OO, HO, TT and N: NMRA RP-11, Curvature and Rolling Stock (March 2018). RP-11 prints two cells where its inch and millimetre rows disagree (N class G: 10 in and 248 mm; OO class M: 33.75 in and 851 mm); both are shown as printed.
- Overhead clearance (dimension H, bridge height above the rail: 17, 22, 22 and 23 ft for the four eras): NMRA RP-7.1, Tangent Track Centers and Clearance Diagrams (January 2019).
- Track gauges: MOROP NEM 010 (2011) and the targets in NMRA S-3.2 (2026).