Grade & Gradient Calculator
Enter a rise and a run to get percent grade, the angle from horizontal, the slope length, and the “1 in X” ratio notation used on incline spec sheets.
Grade & angle
Why funiculars quote grade so many different ways
A cliff railway or funicular’s incline is usually its headline statistic, and it shows up described in at least three different ways across brochures, engineering drawings, and Wikipedia infoboxes: as a percentage, as an angle in degrees, or as a “1 in X” ratio inherited from railway engineering tradition. All three describe exactly the same slope — they’re just different units for the same rise-over-run relationship.
This calculator converts between all of them at once, and adds the slope length — the actual track or cable distance covered — which is what the ascent-time and rope-length calculators on this site use as their input.
Frequently Asked Questions
What does a percent grade actually mean?
A grade of X% means the track climbs X units of height for every 100 units travelled horizontally. A 50% grade — steep for a funicular, and roughly what several of the world's steepest funiculars run — rises 50 meters for every 100 meters of horizontal run. It's a ratio, so it applies at any scale: the same 50% grade describes 5 meters of rise over 10 meters of run.
How is grade different from the angle in degrees?
Percent grade is rise divided by run; angle is the arctangent of that same ratio. They track together but aren't proportional — a 100% grade isn't a 90° angle, it's 45°, because rise equals run at that point. Past very steep grades the two numbers diverge quickly, so always check which one a spec sheet is quoting.
What is the '1 in X' ratio notation for?
Railways and funiculars often describe grade as '1 in X' — a 1-unit rise for every X units of run — which is just the reciprocal of the rise/run ratio. A grade of 1:2.5 is the same incline as 40%. This notation is common on historical and engineering documentation for cliff railways and rack railways, so this tool reports it alongside the more familiar percentage.
Why does slope length matter separately from rise and run?
Rise and run describe an incline's shape, but the actual length of track or cable needed to cover it is the hypotenuse of that triangle — the slope length, found with the Pythagorean theorem. On a steep line the slope length can be meaningfully longer than the horizontal run, which matters for cable, rail, and travel-time calculations.
Educational conversion tool. Published grade figures for a specific line come from its operator or engineering documentation — use this to understand and compare those figures, not to replace them.