The calculator below displays the grade as a percent when you enter the rise and run.
Grade expresses the incline of a length of track as a percentage. Grade is independent of scale; a grade in N-scale is measured and calculated the same as a grade for HO, S, G, O, or even a full-size railroad.
Rise is the change in height from the beginning to end of the grade.
Run is the horizontal distance from the beginning to end of the grade.
The formula for calculating grade is:
Rise and run must use the same units of measure. You can use inches, millimeters, feet, miles, etc., as long as both rise and run use the same units. If you use inches, convert fractions to decimals. Example: 2 3/8 inches = 2.375 inches.
The formula divides rise by run, yielding a small number. The formula then multiplies by 100 to convert the number to a percent.
Example 1 (a model railroad):
A grade rises 2.375 inches in a run of 165 inches. Dividing 2.375 by 165 = 0.01439. Multiply by 100 = 1.439% or slightly more than 1.4%.
Example 2 (a full size railroad):
A grade rises 578 feet in a run of 10 miles. First convert 10 miles to feet so that rise and run are in the same units:
10 x 5280 = 52800 feet.
Now use the formula.
578 divided by 52800 = 0.01094. Multiply by 100 = 1.094%. See? The formula works for any scale!
Railroad Boy Tip: It can sometimes be awkward to measure the run. Scenery and structures may interfere. Fortunately, your grade calculation will be accurate enough if you simply measure the track length from the beginning to end of the grade. For the percentage grades we use in railroading, measuring the track length instead of the run introduces only a very small error — one you can safely ignore. It's easily good enough for (model) railroad work!
The steeper the grade, the fewer cars a given locomotive can pull up the incline without stalling or slipping its wheels. As a general rule, grades on model railroad mainlines should be limited to 2% or less. Branch lines are often steeper: 3%-5%. Certain special lines such as mining branches may be steeper still.
Curves are also a factor. A grade on a curve is effectively steeper than the same grade on a straight section of track. The calculator below assumes a straight track.
If grades are excessive, locomotives may have trouble pulling cars up the incline. This is true for both model and full-size railroads. In both cases, steep grades can be managed by reducing the length of the train or using more than one locomotive per train. Sometimes that means two or more engines at the head of a train, but you can also use helper engines at the end or even in the middle of a train, just as real railroads do.