Skip to main content
Geosciences LibreTexts

3.4: Contour Lines

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)

    Contour lines allow a vertical dimension to be added to a map and represent elevations above sea level. Since each individual contour line connects points of equal elevation, then following that line in the real world means that you are staying at the same elevation while walking along that imaginary line. If you were to move off that line, you are either walking up or down in elevation. Imagine if you are on a small circular island in the ocean, and you walk from the shore up to 10 feet above the shoreline. If you were to walk around the island and stay exactly 10 feet above shore, you would be walking a contour line that represents 10ft of elevation above sea level. If you move off that line, you are either moving uphill or downhill. If you could walk uphill another 10ft and again stay at that elevation (now 20ft above sea level) while circling the island, then you are now walking the 20ft contour line. The vertical change in elevation between these two adjacent contour lines is called the contour interval, which in this case is 10 feet. If you were to transfer these imaginary lines onto a map, you would see three lines forming concentric circles that represent 0 ft (the seashore or sea level), 10ft and 20ft, and your map would look like a bull’s eye pattern. Congratulations, you’ve made your first topographic map!


    A topographic map will have contour lines shown as brown lines, and all maps will have a contour interval that is specific for that map. However, the elevations represented by the contour lines are not always labeled on each line (see Figure 3.2). Instead, every 5th contour line is labeled with an elevation, and is darkened; such a contour line is called an index contour. The use of index contours allows a map to be visually more appealing, especially when the contour lines are numerous and closely spaced to one another.


    To determine the elevation of each contour line you must first know the contour interval for the map. By using the values of two adjacent index contours, one can easily calculate the contour interval between each line. For example, there are 4 contour lines between the 5200ft and 5400ft index contours (see Figure 3.2), which means that there are 4 contour lines separating the 200ft of elevation between the index contours into 5 sections. Dividing this 200ft elevation change between the index contours by 5 gives a contour interval of 40 ft (just as cutting a ruler in half creates two 6 inch pieces, or dividing the ruler into 3 evenly spaced cuts yields four 3 inch pieces). To verify this, locate the 5200ft index contour on the western side of the map in Figure 3.2, and increase the elevation by 40ft each time you cross a contour line while traveling east (to the right) towards the 5400ft contour line. Luckily there is no need to do this calculation to find the contour interval on a complete topographic map, as all topographic maps give the contour interval at the bottom of the map near the bar and fractional scales (see Figure 3.3). The contour interval must be obeyed for each contour line on a map; for example, if the contour interval is 50 ft, then an example of possible contour lines on such a map could be 50ft, 100ft, 150ft, 200ft, etc.


    You may be wondering why some contour lines are closely spaced in some areas of a map (such as the central portion of the map in Figure 3.2) and why they are farther apart in other areas of a map (such as the western part of the map in Figure 3.2). Imagine yourself again on the circular island in the ocean, and you are standing 10ft above sea level (on the 10ft contour line). If you want to walk up the hill to reach the 20ft elevation, how far did you have to walk? It depends on how steep the hill is; if it is a gentle slope you may have to walk a long time before you reach a higher elevation of 20ft. On a topographic map, the contour lines for this hill would be spaced far apart. However, if the hill’s slope is very steep, you do not need to walk as far up the hill to reach a 20ft elevation, and the contour lines representing such a steep slope will be closely spaced on a topographic map. Recall that a slope (gradient) is the change in elevation divided by the distance; you can easily calculate the slope of your hill or any region on a topographic map if you know the change in elevation between two points, and if you know the distance between those same two points. Gradients are usually reported in feet per mile (\(\frac{ft}{mile}\)), but other units are also used. Remember to use the contour lines to determine the elevations, and the bar scale on your map to measure the distance.


    In addition to contour lines, topographic maps will also have benchmarks (actual surveyed points) in various locations on your map. These surveyed points are exact elevations above sea level and are commonly used to mark the elevations of mountains, hilltops, road intersections, and airport runways. These benchmarks are rarely located on a contour line and instead are usually identified by a black “x” or identified with the letters “BM” and with the elevations included in black numbers (as opposed to the brown numbers on index contours). Benchmark locations will normally be found in the area between contour lines. For example, a benchmark of 236ft will be found somewhere between the 230ft and 240ft contour line (if the contour interval is 10ft), or between the 235ft and 240ft contour line (if the contour interval is 5ft).


    In addition to obeying the set contour interval for a map, contour lines should never branch (split) or simply end inside of the mapped region. Instead, these lines are continuous, although they can continue off the edge of the map. Contour lines also never touch or overlap, unless certain rare instances occur, such as if there is a vertical or overhanging cliff. In the case of a vertical cliff, the contour lines will appear to merge.


    The entire third dimension (elevation) represented by the contour lines on a topographic map is called the relief and is easily determined if you can find the highest and lowest contour line elevations and subtract the two values to determine the vertical relief represented in the map. The hardest part is finding these highest and lowest elevations on the map. Start by finding the highest index contour line and continue counting lines until you reach the lowest contour line. In Figure 3.2, the highest contour line is the line that runs through the letter “r” in Fort (of Fort Garrett Point). This same contour line circles back and goes through the letter “o” in Fort. The elevation of this line is 6360ft (based on the contour interval of 40ft). Recall that this is only a small portion of a 7.5-minute map (or quadrangle) and, because of this, some of the index contours appear to be missing the identifying elevation numbers. Nonetheless, it is still easy to identify the index contours because all index contours are in bold (darkened lines). To find the lowest elevation on the map, find the lowest index contour line and continue counting lines in the downhill direction. An easy way to determine which way is downhill is to find a water feature on the map; water is colored blue on topographic maps and flowing water such as a river or stream is a blue line. A dashed blue line such as in Figure 3.2 implies that the stream is dry part of the year (this is called an intermittent stream). Since water collects in low spots, such as a basin (where ponds, lakes, or oceans are found) or a valley (such as a stream or river valley), then the contour lines should represent decreasing elevation as you move towards a water feature on a map.


    Referring back to Figure 3.2, it is apparent that the highest portion of the map is the central portion where Fort Garrett Point is located, and that any point west, south and east of this is a downhill direction. Note that all of the streams are flowing away from this Fort Garrett Point region. The lowest elevation will be a contour line that is crossing the stream just before leaving the map area. Close examination of the contour lines reveals that the lowest contour line is in the lower right corner of the map; the contour line that is crossing the stream in this portion of the map represents an elevation of 4560ft. So for this small portion of the 7.5-minute map shown in Figure 3.2, the relief of the map region is 6360ft (highest contour) – 4560ft (lowest contour) = 1800ft.


    An interesting feature regarding flowing water such as streams and rivers is that they erode the landscape and, as a result, the topography of the land is affected; we see this as a deflection of the contour lines on a map as they cross flowing water. Notice in Figure 3.2 that the contour lines form a “v” shape as they cross the water and that the pointed end of this “v” is pointing in the upstream direction. We can use this to easily determine which way water is flowing without even paying attention to the elevation of the contour lines. Notice in Figure 3.2 that the contour lines that cross the streams are pointing toward the central hill (Fort Garrett Point), which means that the streams are all flowing away from the central portion of this map and towards the edges of the map region.

    This page titled 3.4: Contour Lines is shared under a CC BY-SA license and was authored, remixed, and/or curated by Deline, Harris & Tefend (GALILEO Open Learning Materials) .

    • Was this article helpful?