Model Railroad Curve & Grade Calculator
What a layout curve is in prototype feet and degrees, what a grade costs in run, and the helix radius that will actually clear itself.
Degrees of curvature are on the arc definition — the angle subtended by 100 feet of track. The clearance figure is railhead to railhead and has to cover the equipment, the roadbed and whatever the upper deck is built on, so measure yours rather than taking 3.5 in on trust. Nothing is uploaded.
A radius scales, and that is bad news for the curve you call broad
A 22-inch curve is generous by layout standards. Scaled up it is a prototype radius of 160 feet — a 36-degree curve, more than 6 times sharper than the 1000-foot curve a railroad would call broad.
| Scale | 22 in is really | Which is | 1000 ft would need |
|---|---|---|---|
| Z (1:220) | 403 ft | 14.2° | 55 in (9 ft across) |
| N (1:160) | 293 ft | 19.5° | 75 in (13 ft across) |
| HO (1:87) | 160 ft | 35.9° | 138 in (23 ft across) |
| S (1:64) | 117 ft | 48.8° | 188 in (31 ft across) |
| O (1:48) | 88 ft | 65.1° | 250 in (42 ft across) |
| G (1:22.5) | 41 ft | 138.9° | 533 in (89 ft across) |
Going the other way is worse. A genuine mainline curve in HO wants 23 feet of clear floor to turn in, and even N scale wants 12.5. This is not a failure of anyone's benchwork — it is why every layout runs curves the prototype would refuse, and why the visual trick is to hide the tightest ones.
A grade does not scale, because a percentage has no units
Rise over run is a ratio of two lengths, so scaling both leaves it exactly alone. Two percent is two percent in Z, in HO and on a real mountain grade — the one number on a layout plan that means precisely what it says. What it costs is run: gaining 3.5 inches at 2% takes 14.6 feet of track, and halving the grade doubles that.
| Helix radius | One turn is | Rise per turn at 2% | Grade to clear 3.5 in |
|---|---|---|---|
| 15 in | 94 in of run | 1.88 in — short | 3.71% |
| 18 in | 113 in of run | 2.26 in — short | 3.09% |
| 22 in | 138 in of run | 2.76 in — short | 2.53% |
| 24 in | 151 in of run | 3.02 in — short | 2.32% |
| 30 in | 188 in of run | 3.77 in — clears | 1.86% |
| 36 in | 226 in of run | 4.52 in — clears | 1.55% |
Which is why a helix at the radius most people have room for does not work at the grade most people quote: at 22 inches, 2% gains 2.76 in a turn and needs 2.53% to clear itself, while at 30 inches it clears under two. The bigger helix is the easier climb and the harder thing to house — both move together, so there is no best radius, only the trade your room decides.
How to use
- Enter your curve radius in inches and your scale.
- Read the prototype radius and its degrees of curvature.
- Enter the rise you need and the grade you want.
- Check whether a helix at that radius clears itself.
Frequently asked questions
What is my curve in prototype terms?
Multiply the radius by the scale. A 22-inch curve in HO is a prototype radius of about 160 feet, which is a 36-degree curve — six times sharper than the 1000-foot curve a railroad would describe as broad.
Can I model a real mainline curve?
Almost certainly not. A 1000-foot prototype radius needs 138 inches in HO, which is 23 feet of clear floor to turn in, and 12.5 feet even in N. Every layout runs curves the prototype would refuse; the skill is in hiding the tightest ones.
Does a grade scale like a radius does?
No, and this is the one thing on a layout plan that means exactly what it says. Rise over run is a ratio of two lengths, so it is dimensionless — 2% is 2% in Z, in HO and on a real mountain grade alike.
What does clearance actually cost?
Run, not height. Gaining three and a half inches at 2% takes 175 inches of track — fourteen and a half feet — and halving the grade to 1% doubles that to nearly thirty. The height is trivial; finding the length is the whole problem.
Will a helix work at 2%?
It depends entirely on the radius, because one turn buys you one circumference of run. At 22 inches a 2% turn gains only 2.76 inches, which does not clear a three-and-a-half-inch deck spacing. You would need about 2.53%.
So should I build a bigger helix?
It is a genuine trade rather than an improvement. A 30-inch helix clears the same spacing under 2%, but it is also a five-foot circle to find room for. Both move together, so there is no best radius — only the one your room allows.
What clearance figure should I use?
Measure yours. The three and a half inches used here is railhead to railhead and has to cover the tallest equipment you run, the roadbed and whatever the upper deck is built from. Double-stack containers alone will break a figure chosen by habit.
Does this send anything anywhere?
No. Every figure is computed in your browser, and nothing is uploaded or stored.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.