Practical tools for measured work
Model Railroad Grade Calculator & Riser Heights
Find the grade, vertical easements and riser heights for a climb, or the run needed for a target grade.
Calculate the layout, check the diagram, then print the result for the shop or jobsite.
Height gained from the starting railhead to the finishing railhead.
Horizontal distance covered by the ramp. Used when solving for the gradient.
Used when solving for the horizontal length.
Model length. Each vertical easement is 1.5 times this.
Distance between vertical supports along the run.
Heights are measured up from the starting railhead level, along the track centre line. Cut each support to the listed height before adding roadbed and track.
Support heights
| Distance from the bottom | Height above the start |
|---|---|
| 0 in | 0 in (0 in) |
| 12 in | 0.314 in (5/16 in) |
| 24 in | 1.132 in (1 1/8 in) |
| 36 in | 1.994 in (2 in) |
| 48 in | 2.856 in (2 7/8 in) |
| 60 in | 3.719 in (3 11/16 in) |
| 72 in | 4.581 in (4 9/16 in) |
| 84 in | 5.443 in (5 7/16 in) |
| 96 in | 5.965 in (5 15/16 in) |
| 100 in | 6 in (6 in) |
How it works
Gradient (called grade in North America) is rise divided by run, as a percentage. A 6 in rise over 100 in of straight track is 6%. Adding easements changes that, because each easement is a curve where the grade builds up gradually from level.
Vertical easement: a common guide is to make the change of grade at least 1.5 times the length of your longest car or locomotive, so long equipment does not bridge the crest or sag. Each end is a parabolic curve, and the constant-grade section between them covers rise divided by (run minus one easement length). That is why the grade with easements is steeper than the plain rise over run.
Measuring: measure the run along the horizontal projection of the track, not along the sloping rail. Measure rise from railhead to railhead. Then cut the supports to the listed heights and cut the subroadbed to follow the profile.
Current-input example
The result above uses these exact values. This snapshot is included when the page is printed so the output can be checked against the original measurements.
- Measurement unit
- Inches
- What to solve
- Gradient from the horizontal length I have
- Total rise
- 6
- Available horizontal length
- 100
- Target gradient
- 2 %
- Longest car or locomotive
- 11
- Vertical easements
- At the bottom and the top
- Support spacing
- 12
Primary result: Track gradient: 7.19 %.
Before using the result
- Measure from the datum or reference edge described by this tool, and do not mix inside, outside and centerline dimensions.
- Keep inputs in the displayed units and preserve more precision than the final cutting or purchasing tolerance requires.
- When the result is close to a limit, verify it with a test piece, field measurement, manufacturer drawing or qualified project professional.
Limitations
The 1.5 times longest car guide is a rule of thumb, not a standard. This tool covers straight grades. A grade that continues through a curve loses effective pulling ability, and a helix should be checked in the helix calculator. Always test your longest train on a mock-up before fixing the profile.
Frequently asked questions
Why is my gradient higher than the rise divided by the horizontal length?
The easements at each end use up run without gaining their share of the rise, so the constant-grade section has to climb a little faster. Turn easements off to see the straight-ramp value.
How steep is too steep?
It depends on locomotive power and train length. Test your heaviest train on a mock-up, and keep the grade lower where trains must start on the slope.
Related tools
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Easement Template
Print a full-size spiral easement and curve template for model railroad track, with the exact offset from the tangent.
Curve Template
Print a full-size circular curve template for one or two tracks, with chord, sagitta and radial tick marks.