Scale ratio: 1 : 87.1
Any unit works (mm, cm, m) — the result uses the same unit you entered.
1000 ÷ 87.1 = model size
Results are design guidelines. Real running also depends on locomotive pulling power, track condition and train length.
Three layout-design calculations in one tool. • Scale conversion: convert between real and model sizes for HO (1:87), N (1:160) and other scales. • Grade: turn rise and run into grade (%), angle and ratio, with a ramp you can see. • Helix: from radius, clearance and total rise, find the number of turns, the grade, the track needed and the footprint. It lets you spot an unworkable grade early and avoid layout mistakes.
1. Pick a mode (Scale Convert, Grade or Helix). 2. For scale conversion, choose the scale and direction, then enter a length. 3. For grade, enter rise and run. Turn on curve compensation to also see the effective grade for a given radius. 4. For the helix, enter radius, clearance between levels, total rise and roadbed width to get the turns and grade, shown on a diagram.
Scale: model size = real size ÷ ratio, real size = model size × ratio. Grade: grade (%) = rise ÷ run × 100. Angle = arctan(rise ÷ run). Helix: circumference = 2 × π × radius. Rise per turn = clearance + roadbed thickness. Grade (%) = rise per turn ÷ circumference × 100. Turns = total rise ÷ rise per turn.
A 2% grade is moderate; above 2.5% most locomotives lose pulling power and you'll need to shorten trains. 3% and up suits short consists only. In a helix, a larger radius lengthens the circumference and eases the grade, but takes more space. Make sure clearance leaves enough room for cars to pass under the level above.
HO is a 1:87 scale and the most popular model railroad scale worldwide. Models are 1/87 the size of the real thing and run on track 16.5 mm wide. Its balance of detail and size makes it a favorite for beginners and experts alike.
It depends on car length and scale, but in HO a radius of at least 18 in (about 457 mm) is recommended, with 22–30 in preferred. Tight radii cause steeper grades, derailments and coupler problems. Longer cars need a larger radius.
Aim for 2% or less on a model; above 2.5% is considered steep. Real railroads usually sit around 1–2%, and on a model you should keep grades gentle to allow for pulling power, train length and curve drag.
Curves add sideways friction between wheels and rails, so the same physical grade feels steeper. Tighter radii add more drag, so it's safest to design with a gentler grade to leave room for this compensation.
N gauge is 1:160 (9 mm track), smaller than HO (1:87), so you can fit a larger layout or broader curves in the same space. It saves room, while HO is easier to detail and handle. Choose based on space and purpose.