Last reviewed 16 Sept 2026 · 8 min read
Definitions
| Term | Meaning |
|---|---|
| Contour | An imaginary line on the ground joining points of equal elevation; on a map, a contour line represents it |
| Contouring | The process of locating contours on the ground and plotting them |
| Contour interval (CI) | The constant vertical distance between two consecutive contours on a map |
| Horizontal equivalent (HE) | The horizontal distance between two consecutive contours — varies with the steepness of the ground |
| Contour gradient | A line on the ground along which the slope is constant (used for route alignment) |
Choice of contour interval
The contour interval is kept constant on a map and depends on:
- Nature of the ground — flat ground needs a small interval; steep hilly ground a larger interval.
- Scale of the map — large-scale maps use small intervals; small-scale maps larger intervals.
- Purpose and extent of the survey — detailed design (e.g. building sites, irrigation) needs small intervals; route location or reconnaissance can use larger intervals.
- Time and expense — smaller intervals need more field work.
Typical intervals range from about 0.5 m for detailed engineering plans on flat land to 10–20 m or more on small-scale topographic maps of hilly country.
Characteristics of contours
- All points on a contour have the same elevation.
- Two contours of different elevations cannot cross or meet each other — except for an overhanging cliff or cave, where they appear to cross.
- Contours merge into a single line where the ground is a vertical cliff.
- Closely spaced contours indicate steep slopes; widely spaced contours indicate gentle slopes; equally spaced contours indicate a uniform slope; straight, parallel, equally spaced contours indicate a plane surface.
- A series of closed contours with higher values inside represents a hill (summit); with lower values inside represents a depression (pond, lake).
- Contours crossing a ridge form U- or V-shapes with the convex side (apex) pointing towards lower ground; contours crossing a valley form V-shapes pointing towards higher ground (uphill).
- Contours are perpendicular to the line of steepest slope (and to ridge and valley lines).
- Every contour must close on itself, either within or beyond the limits of the map; a contour cannot end abruptly.
- A single contour cannot split into two.
- The same contour appears on both sides of a ridge or a valley.
Methods of locating contours
Direct method
Points on the contours themselves are located on the ground and then surveyed:
- Establish a benchmark and set up the level; the HI is known.
- For a contour of RL , the required staff reading .
- The staffman moves until the staff reading equals this value; the point is marked and its horizontal position fixed by plane table, tape/compass or total station.
- The procedure is repeated for other contours.
Most accurate but slow and tedious; suitable for small areas and where high accuracy is needed (e.g. reservoir sites, building layouts).
Indirect methods
Spot levels of selected guide points are observed, and contours are drawn by interpolation between them.
| Method | Description | Suitable for |
|---|---|---|
| Grid (squares) method | Area divided into a grid of squares (e.g. 5 m to 20 m sides); RLs observed at grid corners | Small, fairly flat areas |
| Cross-section method | Cross-sections at regular intervals perpendicular to a centre line; RLs at intervals along each section | Route surveys — roads, railways, canals |
| Tacheometric (radial lines) method | From a tacheometer/total station station, readings on radial lines at known angles | Hilly terrain, large areas |
Indirect methods are quicker, cheaper and adequate for most purposes.
Interpolation of contours
Assumes the slope between two guide points is uniform.
- Estimation — positions judged by eye (rough work, small scales).
- Arithmetic calculation — distance of a contour from a point:
- Graphical method — a tracing paper with equally spaced parallel lines representing contour values is placed over the two points and rotated until the points lie on lines of their RLs; intermediate crossings are pricked through.
Uses of contour maps
- Nature of the ground — assessing topography for planning.
- Drawing longitudinal sections and cross-sections along any line.
- Intervisibility between stations — by drawing the section between them.
- Locating route alignments (roads, railways, canals, pipelines) at a given gradient — by stepping off the horizontal equivalent (with dividers) from contour to contour.
- Catchment area — delineating the watershed (ridge line) of a drainage basin.
- Reservoir capacity — from areas enclosed by successive contours.
- Earthwork quantities — for cuts and fills, and choosing formation levels.
- Site selection — dams, bridges, buildings, drainage.
Volume from contour areas
Trapezoidal (average end area) formula:
Prismoidal (Simpson's) formula — odd number of contour areas (even number of intervals):
Cone formula for each interval:
Modern methods
Digital elevation models (DEM) and digital terrain models (DTM) are created from total station and GNSS points, LiDAR (airborne laser scanning), photogrammetry and satellite data. Software generates triangulated irregular networks (TIN) or grids and interpolates contours automatically, and computes slopes, sections, catchments and volumes.
Worked examples
Two points A and B, 55 m apart on a uniform slope, have RLs 102.3 m and 107.8 m. Locate contours at 1 m intervals.
Solution. Difference in RL = 5.5 m over 55 m → 10 m horizontal per metre rise. Contour 103 m: from A; 104 m: 17 m; 105 m: 27 m; 106 m: 37 m; 107 m: 47 m from A.
A road is to be aligned on a gradient of 1 in 25 on a map with a contour interval of 2 m. Find the horizontal equivalent to be stepped off between consecutive contours.
Solution. (to scale on the map)
Areas enclosed by contours at a reservoir site are: 100 m — 1000 m²; 102 m — 4000 m²; 104 m — 9000 m²; 106 m — 16 000 m²; 108 m — 25 000 m². Find the capacity between 100 m and 108 m by the trapezoidal and prismoidal formulas.
Solution. = 2 m. Trapezoidal: Prismoidal: (The prismoidal value is exact here because the areas vary as the square of height; the trapezoidal formula overestimates.)
The HI of a level is 105.45 m. What staff readings locate the 104 m and 102 m contours?
Solution. 104 m: ; 102 m:
Frequently tested points
- Contour: line of equal elevation; CI constant on a map; HE varies with slope.
- CI depends on nature of ground, scale, purpose, time and cost.
- Contours never cross except at overhanging cliffs; merge at vertical cliffs.
- Close spacing → steep slope; wide → gentle; equal → uniform slope.
- Closed contours: higher inside → hill; lower inside → depression.
- Valley contours point uphill (V towards higher ground); ridge contours point downhill.
- Contours are perpendicular to the steepest slope and close on themselves.
- Direct method — accurate but slow; indirect — grid (flat areas), cross-section (routes), radial lines/tacheometry (hilly areas).
- Interpolation assumes uniform slope; methods: estimation, arithmetic, graphical.
- Uses: sections, intervisibility, route at given gradient, catchment area, reservoir capacity, earthwork.
- Prismoidal formula needs an odd number of contour areas.
- Drawing valley V-shapes pointing downhill.
- Changing the contour interval within the same map.
- Using the prismoidal formula with an even number of areas.
- Contours join points of equal elevation; contour interval and horizontal equivalent describe relief and slope.
- The contour interval depends on terrain, scale, purpose and cost.
- Contour characteristics reveal hills, depressions, ridges, valleys, cliffs and uniform slopes.
- Contours are located directly or indirectly (grid, cross-sections, radial lines) and interpolated between spot levels.
- Contour maps are used for sections, intervisibility, route alignment, catchments, reservoir capacity and earthwork; DEMs and LiDAR now automate contouring.