Easement Curve Calculator

Description

Snapping straight track directly onto a curve makes a sudden kink where the straight ends and the curve's full radius begins. A real train eases into a curve gradually — a sharp kink instead causes a visible jolt, and can even cause longer cars to bind or derail. An easement (also called a transition curve) fixes this by tapering the radius gradually from straight to full curve over a short length, instead of jumping straight to it.

Pick your track's gauge and your curve's radius, and this calculator gives you the easement's length and offset — the two numbers you need to lay it out on your benchwork, either by eye with a flexible guide or by marking the intermediate points from the source standard below. By default it uses that standard's recommended offset for your gauge; switch to "choose the length myself" if you'd rather pick a specific transition length (useful if space is tight) and have the offset computed for it instead.

Sources

• NEM 113 "Transition Curve", Standards for European Model Railroads (MOROP), Edition 2016 — publishes the recommended offset f per track gauge, the closed-form length formula L = √(f · 24 · R), and the alternate offset formulas for a freely chosen length (f = L²/(24R), L²/(23R), or L²/(22R), depending on the L:R ratio). This calculator implements that formula directly; it does not estimate or round.

Disclaimer: NEM 113 recommends keeping the transition length under the curve's radius (ideally under 0.8×) and at least as long as your longest car. Always check the result against your available space and equipment.