model buildings

 

 


Use This Model Railroad
Track Grade Calculator

 

TRACK GRADE CALCULATOR

Rise

Run

Grade

%

This tool for calculating train track grades is free to use, and is a quick way for model railroaders to accurately determine track gradients based on track lengths and required rises to haul a train to a higher or lower level on the railroad.

train track grades


The RISE is the vertical height change from where the grade starts to where it ends.

The RUN is the distance horizontally from the start to the end of the grade.

Enter the RISE and RUN numbers using the same units (example inches, feet, miles, km, cm, or mm etc.). Enter only numbers, not fractions. To enter fractions of an inch simply alter them to a decimal format:

1/8 = 0.125
1/4 = 0.25
3/8 = 0.375
1/2 = 0.5
5/8 = 0.625
3/4 = 0.75
7/8 = 0.875

Example: 2 5/8 = 2.625

Share this page with your friends
Facebook Twitter Google Bookmarks Digg Yahoo My Web

You are welcome to share the link to these free track calculators with friends in the hobby. This grade calculator is for measuring a straight track. You’ll find a more comprehensive explanation on how to do the math, how track grades function, what impact curves have, and the advantages/disadvantages of various track grades etc below.

NOTE: With scenery and structures in the way, it is sometimes difficult to measure the exact run. However, with most model railroads, it is generally accurate enough to simply measure the length of track from the start to the end of the grade. The difference is usually minimal.

What is a track grade?

In model railroad terms a grade is basically a slope, incline, or gradient. Grades exist on full-size railroads, so it makes sense for model railroaders to include them too. Grades will generally add realism to a model railroad, but they do pose some operational and space issues that will require careful consideration at the planning stage.

train track grades

The amount of slope on a track grade is based on the rise (in feet) per 100 foot of track length, and is expressed as a percentage e.g. 1ft in a 100ft = 1%. You can calculate in metrics as long as the same units are used to measure the RISE and RUN (see blow).

Grades are calculated and measured using the same formula regardless of whether it’s a real full-sized railroad, or a scale model railroad. It doesn’t matter if the scale is HO, N, OO, Z, O, or some other scale, the same principles apply.

What is the optimal gradient for a railroad?

Unfortunately the world is not perfect, so railroad grades need to vary according to the terrain. If a train needs to pass over or through hills, mountains, or valleys, then it’s likely to change levels and/or travel through tunnels and over bridges to reach its destination.

Although today’s modern locomotives are extremely powerful, there are still limits to how much each engine can pull especially if it’s climbing a slight rise. The steeper the rise, the fewer cars the locomotive will be able to haul up the incline without it stalling or the wheels slipping. The downward pressure on the track is lessened the steeper the incline gets.

For a particularly steep section of track a train may require more than one loco. This could mean having two (or more) engines at the front of the train, or hooking up “helper engines” in the middle or behind the train. This is precisely what happens on real railroads, so the same applies with scale models.

The other option is to minimize the train length if it is to climb a steep gradient. In the real world a railroad would consider the various financial, efficiency, and safety ramifications for increasing or reducing the length of a train, or for adding extra engines to a service. Real railroads are expensive to operate, so delays and extra costs caused by inefficiency or accidents are avoided. The model railroader has the advantage of simply picking up a derailed train and placing it back on the track, however this would be a dangerous and expensive outcome in the real world.

Where possible, mainline grades for scale model railroads (and real railroads), are generally kept at or below 2%. This however is not always possible especially on branch lines, where the grade could reach or exceed 3 to 5 percent. A line servicing a mining town might even rise higher.

As with real railroads, the track on a model railroad does not always run in a straight line. This is even more likely when a train is climbing and winding through a mountain range. That’s why the model railroader needs to understand a gradient on a curved track is, in every practical sense, steeper than a similar gradient on a straight track section.

How do you calculate track grade manually?

Here is the formula:

calculate track grades

As already mentioned; the RISE and RUN doesn’t need to be measured in feet. You can measure in inches, miles, millimeters, centimeters etc., provided the RISE and RUN are measured using the same units.

If you are working in inches, use the free fractions to decimals calculator above. Example: 2 5/8 inches = 2.625 inches.

Here is an example where the grade on a model railroad is just over 1.4%

track grade formula

The grade rises by 2.375-inches on a run of 165-inches. You therefore divide 2.375 by 165. The answer is 0.01439. Then multiply by 100 to get 1.439%.

On a full-sized railroad the same formula works:

railroad grades

Here the grade rises 526 feet on a 5 mile run. Firstly convert 5 miles into feet so then the RUN and RISE are in feet:

1 Mile = 5,280 feet

5 Miles x 5,280 feet = 26,400 feet

Now using the formula:

526 divided by 26,400 = 0.01992 x 100 = 1.99% (roughly 2%)

How powerful are locomotives?

In today’s world locomotive is more important than ever. For trains to compete with other freight and passenger services the locomotive(s) need to be able to haul a big load quickly and safely and keep to a schedule.

To be efficient the locomotive doesn’t necessarily need to be the biggest, the heaviest, the longest, have the most cylinders, be the most powerful, or have the most wheels. The locomotive just needs to be suited to the type and weight of load it is hauling taking into consideration the required speed and terrain it will pass through. So a number of factors could take precedence. For example; the overall weight will provide traction over the driving axles. The actual power could be measured in “raw” horsepower, and the available axle power (shaft horsepower). With steam engines it would be important to know how much steam the engine will generate on a sustained basis. There would be no advantage for a long distance steam train to have to stop every few miles for water.

The most powerful locomotives ever built include: the Union Pacific Railroad’s DDA40X diesel-electric loco (with 2 diesel engines) which operates at 6,600 hp; the EMD SD90MAC, the GE AC6000CW, and China Railway’s DF8C locomotives.

How do locomotives operate?

Until recent times, locomotives generally pulled the cars behind them. However these days it’s becoming more common (in certain countries) to see locomotives both pushing and pulling trains. This is called “push-pull operation”, and is when one engine is positioned in front to pull the train and another locomotive is positioned behind the train to push the cars. To avoid mishaps, the rear locomotive is controlled from a cab in the front locomotive.

Also, these days, some engines are specifically designed to operate on steep grade railroads. They will typically have extra braking mechanisms especially to cope with steep downward grades. A diesel-electric loco might be fitted with ‘dynamic brakes’ that utilize the traction motors for electrical generators when braking. This helps with controlling the train speed on a downward grade.