One line, one elevation
A contour connects equal heights. Travel along a 1100 m contour and the modeled elevation stays 1100 m, even when the line curves. It is an imaginary line, not a path.
Explore the hill study ↗Field school / 01 · Topography
Read the shape
of the land.
A line on a map becomes a fold in the landscape. Follow the contours, turn the terrain, and learn to see what lies between.
The reading guide
Ten ways to see a contour.
Work in any order. These lessons and the field plates below are the complete static alternative.
Count the interval
The interval is a vertical difference, in metres here. At 20 m, successive lines can be 1080, 1100 and 1120 m. Our heavier index lines mark every fifth interval. A smaller interval adds lines without adding terrain detail.
Explore the slope study ↗Read the inside of a loop
On this hill, labels rise inward. Closed contours can also surround a depression; its elevations fall inward, often with short inward ticks called hachures. A loop alone does not prove a summit.
Explore the hill study ↗Spacing tells you steepness
Compare lines on the same map and at the same interval. Tight spacing means a steep slope; wide spacing means a gentle one. Grade = vertical rise ÷ horizontal run × 100%. A 20 m rise over 100 m is 20%, about 11.3°, not 20°.
Explore the slope study ↗A valley bends uphill
In the teaching valley, contours bend toward higher ground at the valley floor. The north–south profile confirms the direction. Water would tend downhill across the contours; this diagram maps no actual stream.
Explore the valley study ↗A ridge bends downhill
The ridge has high ground along its spine and lower flanks. Its contour nose points downhill. Similar-looking bends need elevation labels and surrounding context before you name the landform.
Explore the ridge study ↗A saddle has two readings
Pass a section through the same center in two perpendicular directions. One profile makes a hollow; the other makes a crest. At the exact saddle elevation, a level set can touch itself. Our fixed triangulation makes that special case explicit.
Explore the saddle study ↗Aspect is the downhill direction
Aspect is the direction of steepest descent: 0° north, 90° east, 180° south, 270° west. This kit uses grid north, not a magnetic compass bearing. Aspect at a perfectly flat or symmetric critical point is undefined.
Explore the slope study ↗A profile is a slice
A–B is a straight horizontal sampling line. The chart plots distance along it against elevation. Move the section and you sample different ground. It is not a hiking route; no path length or trail difficulty follows from the section.
Explore the bryce study ↗Stretch the view, keep the numbers
At 3× vertical exaggeration, a 20 m height difference is drawn three times as tall relative to horizontal distance. The stored heights, contour interval and calculated slope stay unchanged. Return to 1× before judging shape; even then, a sampled grid omits small and hidden features.
Explore the bryce study ↗The field plate library
Six forms. Two views each.
Twelve standalone vector diagrams, with both central profiles and sample tables. Open a plate at full size, or open the print edition for the complete guide.
01 / A rounded hill
ILLUSTRATIVE · original analytic shape
A circular hill rises from about 1001 m at the corners to 1180 m at its center. The central west–east profile rises and falls symmetrically.
Two sections through the center
Both charts use equal horizontal and vertical scale (1×). The plate’s dashed line shows west–east; north–south crosses it at the center.
| Distance from A | West–east | North–south |
|---|---|---|
| 0 m | 1012.5 | 1012.5 |
| 200 m | 1092.4 | 1092.4 |
| 400 m | 1180.0 | 1180.0 |
| 600 m | 1092.4 | 1092.4 |
| 800 m | 1012.5 | 1012.5 |
What do the nested rings tell you?
These labeled rings rise inward toward a summit. Closed rings alone are not enough: descending labels or inward hachures can identify a depression.
02 / An even slope
ILLUSTRATIVE · original analytic shape
Parallel, evenly spaced contours cross a tilted plane. Elevation increases eastward and southward. The west–east center profile rises from 1020 m to 1180 m.
Two sections through the center
Both charts use equal horizontal and vertical scale (1×). The plate’s dashed line shows west–east; north–south crosses it at the center.
| Distance from A | West–east | North–south |
|---|---|---|
| 0 m | 1020.0 | 1060.0 |
| 200 m | 1060.0 | 1080.0 |
| 400 m | 1100.0 | 1100.0 |
| 600 m | 1140.0 | 1120.0 |
| 800 m | 1180.0 | 1140.0 |
Does changing the interval change the slope?
The surface is unchanged. Here each 100 m east adds 20 m of elevation; each 100 m south adds 10 m. The steepest slope is about 12.6° (22.4%), down toward 297° from grid north.
03 / A valley
ILLUSTRATIVE · original analytic shape
Rounded V-shaped contours point north. Each side is higher than the valley floor. A north–south profile along the center falls from 1152 m to 1008 m.
Two sections through the center
Both charts use equal horizontal and vertical scale (1×). The plate’s dashed line shows west–east; north–south crosses it at the center.
| Distance from A | West–east | North–south |
|---|---|---|
| 0 m | 1192.0 | 1152.0 |
| 200 m | 1108.0 | 1116.0 |
| 400 m | 1080.0 | 1080.0 |
| 600 m | 1108.0 | 1044.0 |
| 800 m | 1192.0 | 1008.0 |
Which way does the contour bend point?
In this valley the contour bends point north, toward higher ground. A contour is not a stream: the valley floor descends southward across the contour lines.
04 / A ridge
ILLUSTRATIVE · original analytic shape
Contours bow south around a crest. The center is high compared with its east and west flanks. The central west–east profile rises to 1230 m and falls again.
Two sections through the center
Both charts use equal horizontal and vertical scale (1×). The plate’s dashed line shows west–east; north–south crosses it at the center.
| Distance from A | West–east | North–south |
|---|---|---|
| 0 m | 1118.0 | 1302.0 |
| 200 m | 1202.0 | 1266.0 |
| 400 m | 1230.0 | 1230.0 |
| 600 m | 1202.0 | 1194.0 |
| 800 m | 1118.0 | 1158.0 |
How is this bend different from the valley?
This ridge nose points south, downhill. The crest is higher than the land on either side. Read the labels to distinguish a ridge from a valley.
05 / A saddle
ILLUSTRATIVE · original analytic shape
The center is a low point on a west–east section and a high point on a north–south section. The saddle has no single downhill aspect exactly at its center.
Two sections through the center
Both charts use equal horizontal and vertical scale (1×). The plate’s dashed line shows west–east; north–south crosses it at the center.
| Distance from A | West–east | North–south |
|---|---|---|
| 0 m | 1272.0 | 1048.0 |
| 200 m | 1188.0 | 1132.0 |
| 400 m | 1160.0 | 1160.0 |
| 600 m | 1188.0 | 1132.0 |
| 800 m | 1272.0 | 1048.0 |
Can one point be high and low at the same time?
At 1160 m the center is lower than its east and west shoulders, but higher than the north and south approaches. The exact critical-level contour touches here; real map generalization can hide this special case.
06 / Below Sunset Point
DERIVED · USGS terrain, 8 m sampling
An irregular plateau edge gives way to steep, closely spaced contours and lower branching terrain. Heights in this crop range from 2286.5 m to 2468.1 m NAVD88. The cut boundary is editorial.
Two sections through the center
Both charts use equal horizontal and vertical scale (1×). The plate’s dashed line shows west–east; north–south crosses it at the center.
| Distance from A | West–east | North–south |
|---|---|---|
| 0 m | 2456.7 | 2430.7 |
| 192 m | 2442.7 | 2385.2 |
| 384 m | 2413.5 | 2413.5 |
| 576 m | 2334.4 | 2357.0 |
| 768 m | 2292.5 | 2309.0 |
What can this Bryce grid actually show?
This 768 m square comes from an existing USGS bare-earth terrain derivative, sampled every 8 m. Thin fins and steep breaks can be simplified. It cannot recover hidden rock faces, establish a route or replace a ground-level scan.
Read the evidence, too
A teaching model has a scale—and a limit.
The first five surfaces are mathematical illustrations. The Bryce study is derived from a copied USGS bare-earth terrain grid: a 768 m square sampled every 8 m, with heights retained in NAVD88 metres. The original DEM was recorded as 1 m resolution; the copied regional record does not identify an individual source tile or acquisition date. These lines do not establish trails, rock stability, survey positions or present-day conditions.
Map services and data available from U.S. Geological Survey, National Geospatial Program. Contour School’s diagrams, lighting, code and explanations are original. No source photographs or third-party map images are included. The terrain is not a ground-level scan of Thor’s Hammer.
- USGS · US Topo Map Symbol Guide — Contour and index-line symbols; reference only.
- USGS · Finding your way with map and compass — Equal-elevation lines, contour intervals and close spacing on steep slopes; factual reference only.
- LANDFIRE · Aspect — Downslope aspect definition; reference only.
- USGS · Depression contour symbols — Depression hachures; reference only.
- USGS · Vertical Exaggeration — Vertical versus horizontal display scale; reference only.
- USGS · National Map data terms — Public-domain elevation data and requested attribution.
- NPS · Sunset Point — Place context only; no page photograph copied.
- Original analytic teaching surfaces — Equations, triangulation, units and calculation limits.
References checked October 2, 2026. Read equations, data lineage & limitations · Structured lesson & asset catalogue