Highpoints by Steepness (Tim Worth)

Quoting from Tim Worth’s “Summit Steepness” website: “In contrast to plugging geographical information into a complex formula to get a numerical rating, angle-based calculation reports steepness of the terrain surrounding a summit in terms of easy to understand figures: angle and vertical drop. […] The calculations above are related of the concept of Spire Measure, with the main difference here being that fixed distances from the summit are analyzed.”

Three key metrics are calculated:

  • Max Drop/Angle – Steepest single line in any direction outward from summit at a given distance (100m, 800m)
  • Min Drop/Angle [*] – Least steepest single line in any direction outward from summit at a given distance (100m, 800m)
  • Avg Drop/Angle – Average steepness over all directions outward from a summit at a given distance (100m, 800m). Quoting “At 100m, sharp spires are identified, 800m/1600m favor large mountains with great vertical drop“.

* Note that the Min Drop/Angle can be negative. For example, the 3DEP spot elevations can be inaccurate. This is especially bad if the central summit elevation is wrong, or taking measurements on a flat plateau (Oklahoma). Another example is with Boundary Peak, NV, where the 800m lines extend across the NV/CA state border (towards Wheeler Peak, CA).

Tables with gory details are below, but first, let’s look at some summary graphics. The first one shows the Max/Avg/Min drops at 100m and 800m.

We can also compare the Max drop (left) and Avg drop (right) at 100m versus 800m in scatter plots.

These scatter plots allow us to see which peaks are “flatter” near the summit (100m) versus near the shoulder (800m). These are the peaks to the left of the ratio line. Peaks to the right of the ratio line will be “steeper” near the summit (100m) versus near the shoulder (800m).

Looking at Massachusetts we see its a fairly flat top near the summit (100m)

as compared to Montana which has a fairly steep summit area.

This map tries to present the data in a visual manner. The pins are color coded to the average drop at 100m from the summit. There are four arms extending which represent the minimum (purple lines) and maximum (orange lines) drops on a logarithmic scale on their respective bearings.

Three tables are presented below. The first is a summary table showing the Max/Min/Avg drops at 100m/800m. The next table provides detailed information at 100m while the final table provides detailed information at 800m.


This table presents summary steepness information:
Max 100 – maximum drop in feet at 100m
Min 100 – highest minimal drop in feet at 100m
Avg 100 – average drop in feet at 100m
Max 800 – maximum drop in feet at 800m
Min 800 – highest minimal drop in feet at 800m
Avg 800 – average drop in feet at 800m

Only admnistrator owned posts can execute the [includeme] shortcode. This message is shown only to administrators.

* – Note that Connecticut is measured from Mount Frissell, MA (the summit) versus the contour line on the CT/MA border.
* – Note that Northern Marianas Islands has no spot elevations


In this section we present detailed steepness information at 100m. The following graphic shows the maximum, average and minimum drops for the 50+6 summits.

This table presents detailed steepness information at 100m:
Max Drop – maximum drop in feet
Max Angle – maximum angle [atan(max drop/100m)] in degrees
Max Brng – the true compass bearing of the max drop line
Min Drop – highest minimal drop in feet
Min Angle – highest minimal angle [atan(min drop/100m)] in degrees
Min Brng – the true compass bearing of the min drop line
Avg Drop – average drop in fee
Avg Angle – average angle [atan(avg drop/100m)] in degrees

Only admnistrator owned posts can execute the [includeme] shortcode. This message is shown only to administrators.

* – Note that Connecticut is measured from Mount Frissell, MA (the summit) versus the contour line on the CT/MA border.
* – Note that Northern Marianas Islands has no spot elevations


In this section we present detailed steepness information at 800m. The following graphic shows the maximum, average and minimum drops for the 50+6 summits.

This table presents detailed steepness information at 800m:
Max Drop – maximum drop in feet
Max Angle – maximum angle [atan(max drop/800m)] in degrees
Max Brng – the true compass bearing of the max drop line
Min Drop – highest minimal drop in feet
Min Angle – highest minimal angle [atan(min drop/800m)] in degrees
Min Brng – the true compass bearing of the min drop line
Avg Drop – average drop in fee
Avg Angle – average angle [atan(avg drop/800m)] in degrees

Only admnistrator owned posts can execute the [includeme] shortcode. This message is shown only to administrators.

* – Note that Connecticut is measured from Mount Frissell, MA (the summit) versus the contour line on the CT/MA border.
* – Note that Northern Marianas Islands has no spot elevations

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