Contour Lines and Intervals

Contour lines are the classic topographic-map representation of terrain shape — a 19th- and 20th-century cartographic solution that remains in use because nothing has displaced it. This article covers the convention, the history, the reading skills, and the modern algorithmic generation.

Companion to /learn/digital-elevation-models-explained (the data) and /learn/mean-sea-level-explained (the reference).

What a contour is

A contour line is a line on a topographic map that follows a single elevation value as it winds through the terrain. Every point on the “500 m” contour is at exactly 500 m above the reference datum (typically mean sea level — see /learn/mean-sea-level-explained).

Properties:

• Contours never cross in normal terrain. A point has exactly one elevation; it can't be on two different contours simultaneously. Exception: overhangs and cliffs (rare in practice; treated with special symbols).
• Contours are closed curves at large enough scope. Inside a country's topographic map, contours may extend off the edge, but on the whole globe every contour is a closed loop.
• Each contour represents one elevation, labeled on the map (usually only every fifth — the index contours).

The contour interval

The contour interval is the vertical distance between adjacent contour lines on a map. The interval is chosen to balance:

• Detail: smaller interval = more contour lines = more precise elevation reading.
• Legibility: smaller interval = more crowded lines = harder to read in steep terrain.

Standard intervals vary by:

Map scale

| Scale (USGS / Ordnance Survey example) | Typical contour interval | | -------- | ------------------------ | | 1:5,000 (urban detail) | 1–2 m | | 1:10,000 | 2 m | | 1:24,000 (USGS US Topo) | 10, 20, or 40 ft | | 1:25,000 (OS Explorer) | 5 m | | 1:50,000 (OS Landranger) | 10 m | | 1:100,000 | 50 m / 100 ft | | 1:250,000 | 100 m / 200 ft | | 1:1,000,000 | 200–500 m |

Terrain

Within a single scale, intervals adapt to terrain roughness:

• Flat areas: smaller interval (5 m, 10 ft) — fine detail visible without crowding.
• Hills: medium interval (10 m, 20 ft).
• Mountains: larger interval (20 m, 40 ft, or more) — contours stay legible.

USGS 1:24,000 maps use 10, 20, or 40 ft depending on terrain; some Alaska maps use even larger intervals.

National conventions

• United States (USGS): feet typically (with metric versions on US Topo modern maps).
• United Kingdom (OS): meters.
• Europe (most national agencies): meters.
• Japan (GSI): meters.

Index contours

Every fifth contour is drawn as an index contour:

• Thicker line (typically 2–3× the normal contour width).
• Slightly darker color or with explicit color emphasis.
• Elevation labeled with the numeric value (e.g., “1,200”).

The pattern: four regular contours, then an index contour, four regular contours, another index. On a map with 10 m intervals, index contours appear every 50 m.

Index contours let the reader quickly identify the elevation of any spot without counting every contour line.

Reading contours

Several visual cues translate contour patterns into terrain understanding:

V-shapes

When a contour line crosses a valley (a stream or drainage), it forms a V-shape:

   500 ▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲ (uphill ridge)
   500    ─────── ↑
   490   ───╲     ↑ stream
   490     V      ↑ flows
   480       \    ↑ downhill
   480       │    ↑
   470  ─────│───

The V points uphill (toward higher elevation). Water flows from the open end of the V toward the point. Recognizing V-patterns is the fastest way to identify drainages in unfamiliar terrain.

A ridge produces the opposite pattern: contours form a rounded ridge with the bulge pointing downhill.

Closed rings

Concentric closed contour lines indicate either:

• A peak: innermost ring is the smallest and highest. The summit elevation is between the innermost contour and the next interval above.
• A pit (depression): same shape but with tick marks (hachures) pointing inward, indicating the ring encloses lower ground.

Without depression markings, a closed ring is assumed to be a peak.

Spacing

The horizontal spacing of contours indicates slope steepness:

• Closely spaced contours = steep slope.
• Widely spaced contours = gentle slope.
• Cliff: extremely closely spaced or merging contours (often shown with a special cliff symbol).

Saddles

A saddle (the low point of a ridge between two peaks) appears as a figure-eight pattern: two sets of closed contours adjacent to each other, with a “waist” between them.

Slope from contours

The slope between two adjacent contours is:

slope = contour_interval / horizontal_distance

Worked example: USGS 1:24,000 map with 20 ft contour interval. Two adjacent contours are 0.05 inches apart on the map. At 1:24,000 scale, 0.05 inches = 100 ft on the ground. Slope:

20 ft / 100 ft = 0.20 = 20% grade (~11.3°)

A common hiking-grade reference:

| Slope | Grade | Description | | ----- | ----- | ----------- | | 5° | 8.7% | Gentle | | 10° | 17.6% | Moderate | | 20° | 36.4% | Steep | | 30° | 57.7% | Very steep | | 45° | 100% | Extreme | | Vertical | ∞ | Cliff |

Slope steeper than ~30° generally requires scrambling; ~40°+ is technical climbing.

Historical origin

Isobaths (depth contours)

Contour lines for depth (called isobaths) predate land contours by nearly two centuries.

Pieter Bruinsz, a Dutch surveyor, drew a chart of the Spaarne River in the Netherlands in 1584 showing depth contours. The chart is the earliest known example of isobaths and predates land contours by 190 years.

Dutch nautical charts continued using isobaths through the 17th and 18th centuries, supporting Dutch maritime trade. The technique was adopted by other European nautical charting traditions.

Land contours

The first widely-cited land contour map was drawn by Charles Hutton, an English mathematician and astronomer, in 1774. The context:

The Schiehallion experiment was an attempt to measure Earth's density by observing the gravitational deflection of a pendulum caused by the mass of a nearby mountain. Schiehallion (a Scottish mountain) was chosen because of its regular, symmetric shape. Nevil Maskelyne (then Astronomer Royal — the same one we encounter in /learn/the-longitude-problem as opponent to John Harrison) conducted the field measurements.

To compute the mountain's mass from its volume required estimating its three-dimensional shape. Hutton developed contour lines as a technique for representing the shape, then computed the volume as a series of contour-bounded slabs. The 1774 Schiehallion contour map is preserved in the Royal Society's archives.

The technique spread through 19th-century European military cartography. The first national topographic map series with contours: France's Carte de Cassini (mid-18th century, hachured rather than contoured) and Britain's Ordnance Survey (early 19th c., adopting contours by mid-century).

The US Geological Survey introduced contours in its topographic map series in the 1880s. The 7.5-minute quadrangle 1:24,000 series (the iconic US topo) began in 1947 and reached completion of the contiguous US in the 1990s.

Special contour types

Depression contours

Closed contours enclosing lower ground (pits, sinkholes, dry lake beds) are marked with tick marks (hachures) pointing inward — toward the depression center.

Without depression markings, a closed ring is assumed to be a peak. The tick-mark convention disambiguates.

Auxiliary / intermediate contours

When the main interval would miss important terrain features (a small but significant feature between two main contours), an auxiliary contour is drawn at half the main interval, typically with a dashed line. This adds detail in critical areas without forcing a smaller main interval globally.

Common on USGS maps in nearly-flat terrain: the main 20 ft contours plus dashed 10 ft auxiliary contours in low-relief areas.

Color conventions

• Brown: land contours (USGS, OS, most national agencies).
• Blue: bathymetric (water-depth) contours.
• Black or red: index contours (when emphasized beyond just thicker).
• Other colors: specific products may use distinct colors (e.g., aviation charts have specific contour schemes).

Digital contour generation

Modern contour maps are typically derived from Digital Elevation Models (see /learn/digital-elevation-models-explained) rather than drafted by hand.

The standard algorithm is Marching Squares:

1. For each elevation interval (each “500 m, 510 m, 520 m, ...” level), determine where the contour crosses the DEM grid.
2. Process each 2×2 cell of the DEM, comparing each corner's elevation against the contour level.
3. Each cell has one of 16 cases based on which corners are above/below the level.
4. Generate line segments through the cell based on the case.
5. String the segments together to form contour polylines.

The algorithm is O(n²) in DEM resolution and O(k) in number of contour intervals. Modern implementations (GDAL gdaldem, ArcGIS, QGIS, MATLAB's contourf) generate contours from typical DEMs in seconds.

Variations and refinements:

• Smoothing: raw marching-squares output is blocky (segments along grid cells). Post-processing smooths the contours with splines or polyline simplification.
• Coupled contours: ensure successive contour levels don't cross each other (a numerical precision issue near saddles).
• Hierarchical contouring: skip detail in nearly-flat areas; add detail in steep areas.

Hypsometric tinting and hillshading

Two related visualizations derived from contours and DEMs:

Hypsometric tinting

Color bands by elevation. Each elevation range gets a color:

• Green for low elevations (forests, valleys).
• Yellow for mid elevations (plains).
• Orange/brown for high elevations (mountains).
• White or purple for the highest.

Hypsometric tinting is intuitive but conventional; different national agencies use different palettes.

Hillshading

Computed light direction (typically NW-from-above) illuminates the terrain in a grayscale rendering. The result mimics what you'd see if a low sun illuminated the terrain from the northwest.

Hillshading is a visualization, not a quantitative representation — but it's the fastest way to convey terrain shape on a map without contour lines. Most modern topographic maps combine hillshading with contours; the contours give quantitative elevation values; the hillshading provides intuitive shape.

Common misconceptions

“Contours show terrain in 3D.” They encode 3D information in 2D. Reading them requires practice. A contour map shows terrain shape, but interpreting it is a learnable skill, not a direct 3D perception.

“Contour intervals are standardized globally.” They're standardized by national agency and scale, not globally. USGS, Ordnance Survey, IGN (France), BKG (Germany), GSI (Japan) all have their own intervals. Cross-agency comparison requires noting the interval.

“V-shapes always point uphill.” V-shapes in valleys point uphill. V-shapes on ridges point downhill (with the V's open end facing the higher ground beyond the ridge). The shape is the same; the orientation distinguishes.

“Contour lines mean exact elevations.” Between contours, elevation is interpolated — your actual elevation can be anywhere between the two surrounding contour values. A point between the 500 m and 510 m contours could be at 504.7 m or 508.2 m — only the bracketing values are guaranteed.

“Closer contours always mean steeper slope.” Yes — closely spaced contours indicate steeper slope. The specific spacing-to-slope conversion depends on the contour interval; tighter intervals (say 5 m) at the same spacing as wider intervals (say 20 m) indicate a much gentler slope.

“Contour maps are obsolete.” They're still widely used: hiking and topo maps, USGS US Topo series, OS Explorer/Landranger, aviation charts, construction site plans. Digital 3D visualizations supplement but don't replace contour representations.

“Contour lines mark cliffs distinctly.” A true cliff is shown with a special cliff symbol (a row of black triangles or hachures) — not just closely-spaced contours. The cliff symbol indicates that contour interpolation can't represent the vertical drop.

“Contour-derived slope is exact.” It's an estimate based on the contour interval and spacing. Real slopes vary continuously; contour slope is averaged over the inter-contour distance. For precise slope analysis, use the underlying DEM directly.

“All countries use index-every-fifth.” Most do, but exceptions exist. Some Russian maps use every fourth; some specialized maps use every tenth. The general convention is every fifth, with the index frequency typically labeled in the map legend.

“Contour lines are easy to compute from a DEM.” Marching squares is fast and well-understood, but edge cases (handling saddles correctly, smoothing without distortion, ensuring levels don't cross numerically) require careful implementation. Modern GIS tools handle this correctly; rolling your own contour generator is non-trivial.

“Contour maps are only for outdoors.” Engineers use contours on construction site plans (showing the existing ground surface) and excavation designs (proposed ground surface). Geologists use contours for subsurface strata. Meteorologists use contours (isobars for pressure, isotherms for temperature). The technique generalizes well beyond land elevation.