Coordinates, Scale and Distance in OS Maps

Locating places with latitude and longitude

Coordinates describe a position using a pair of values. On atlas maps and globes, latitude and longitude let you locate places anywhere on Earth. Their network of lines is called a graticule.

Latitude measures angular position north or south of the Equator. The Equator is 0° latitude; values increase towards 90° N at the North Pole and 90° S at the South Pole. Lines of latitude run east–west, parallel to the Equator. Although the lines run across the Earth, their values tell you how far north or south a place lies.

Longitude measures angular position east or west of the prime meridian, the 0° line through Greenwich, England. Values extend to 180° E or 180° W. Lines of longitude, called meridians, run from pole to pole and meet at the poles. Their values tell you a place's east–west position.

Write latitude first, then longitude, including the directions. For example, the coordinate 25° N, 45° E describes a point north of the Equator and east of the prime meridian. Degrees can be subdivided into minutes and seconds: 60 minutes make one degree, and 60 seconds make one minute. Decimal degrees are another way of recording a more precise position.

To read a point's coordinates on an atlas map, first find the labelled latitude lines that bracket it. Read its latitude, estimating between those lines if necessary. Then do the same with the longitude lines. Check the labels carefully: latitude values increase away from the Equator, while longitude values increase eastwards or westwards away from 0°.

For a concrete illustration, imagine a rectangular, north-up graticule with latitude lines at 20° N and 30° N, and longitude lines at 40° E and 50° E. A point halfway between each pair has coordinates 25° N, 45° E. To locate that coordinate instead, find 25° N halfway between the two latitude lines and 45° E halfway between the two longitude lines; the point is where these positions intersect.

Transfer the method to an atlas by using its actual labels and line spacing. Graticule lines may be curved and their spacing may vary with the map projection, so follow the lines rather than assuming every atlas has a rectangular grid. An estimated coordinate is only as precise as the map allows.

Locating places with the OS map grid

Ordnance Survey (OS) maps represent the landscape from above. Their grid, scale, key and height information let you locate features and measure relationships between them. Start by checking the map's scale and key: the key explains its symbols, while the scale tells you how map distances relate to distances on the ground.

Unlike latitude and longitude, OS grid references use numbered eastings and northings rather than angles in degrees. The numbered vertical grid lines are eastings: their values increase towards the east. The numbered horizontal lines are northings: their values increase towards the north. A grid reference always gives the easting first and the northing second — across the map, then up it.

A four-figure grid reference identifies a whole grid square. Find the easting line forming the square's left-hand edge, then the northing line forming its bottom edge. In the grid below, the marked point lies in the square immediately east of easting 17 and north of northing 51. Its four-figure reference is 1751.

A six-figure grid reference locates a point more precisely within that square. Imagine dividing the square into ten equal parts across and ten equal parts upwards. The extra digit in each half of the reference shows how many tenths the point lies across or up the square.

The illustrated point is six-tenths across from easting 17 and three-tenths up from northing 51. Its easting becomes 176 and its northing becomes 513, giving 176513. Notice that the digits are grouped by coordinate: complete the easting before writing the northing.

On a real map, transfer this method to the numbered grid lines surrounding the requested feature. The diagram demonstrates the coordinate method; it does not represent a real location or reproduce OS feature symbols.

Understanding map scale

A ratio scale compares map distance with ground distance using the same units. At 1:25 000, one unit on the map represents 25 000 of those units on the ground. Therefore, 1 cm represents 25 000 cm, which is 250 m. At 1:50 000, 1 cm represents 500 m.

The 1:25 000 map is the larger-scale map: it shows a smaller area in greater detail. The same ground distance takes up twice as much space on it as on a 1:50 000 map.

For example, suppose two points are 4 cm apart on a 1:25 000 map. Their ground distance is $4 \times 250 = 1000\text{ m}$, or 1 km. If the same 4 cm measurement came from a 1:50 000 map, it would represent $4 \times 500 = 2000\text{ m}$, or 2 km. This is why checking the scale matters before measuring.

Other maps may use different scales. Apply the same ratio method, or use the scale bar printed on the map rather than memorising a conversion for every possible scale.

Measuring straight and curved distances

For a straight-line distance, place a ruler between the two points, measure their separation and convert it using the map scale. Alternatively, place the edge of a piece of paper against the points, mark both positions and compare the gap with the map's scale bar.

A curved route needs a different approach because a straight line between its endpoints misses the bends. Divide the road, river or path into short, nearly straight sections. Using a paper edge, mark the first section, pivot the paper at the end of that section and mark the next section. Continue along the route, accumulating the section lengths, then compare the total with the scale bar. Shorter sections follow tight bends more accurately.

These measurements give horizontal distance. They do not include the extra distance involved in climbing or descending a slope.

Giving direction from one place to another

Direction describes where a destination lies relative to a starting point. Use the map's north indication to orient yourself, then describe the destination using compass points such as north, north-east, east or south-west. A point above and to the right of the starting point on a north-up map is north-east of it.

A grid bearing gives direction more precisely as an angle measured clockwise from grid north. North is 0°, east is 90°, south is 180° and west is 270°. To measure a bearing, place the centre of a protractor on the starting point, align 0° with grid north and measure clockwise towards the destination.

Reading height and slope

Relief means the height and shape of the land. A spot height gives the height of a particular point. A contour line joins points at the same height above sea level, allowing you to trace the shape of the surrounding land rather than just read one height.

The contour interval is the vertical height difference between neighbouring contours. It is commonly 5 m or 10 m, but check the interval on the map you are using. For example, with a 10 m interval, consecutive contours above a labelled 100 m line represent 110 m, 120 m and so on.

Contour spacing tells you about steepness. Closely spaced contours show a large height change over a short horizontal distance, so the slope is steep. Widely spaced contours spread the same height change over a longer distance, showing a gentler slope.

On this hill, heights increase towards the centre. Its eastern slope is steeper than its western slope because the eastern contours are closer together. The 135 m spot height supplies information that the enclosing 130 m contour alone cannot give: the height of that particular point near the top.

On a real OS map, combine contour labels, spacing and spot heights. Contours do not show every small irregularity between their height intervals, so they cannot provide an exact height for every unmarked point.

Calculating an average gradient

A gradient compares vertical height change with horizontal distance. First subtract the lower height from the higher height. Then measure the horizontal separation using the map scale.

$$\text{gradient}=\frac{\text{vertical height change}}{\text{horizontal distance}}$$

To express the result as 1 in n, use the same units for both measurements and calculate:

$$n=\frac{\text{horizontal distance}}{\text{vertical height change}}$$

For example, suppose one point is 40 m above sea level and another is 100 m above sea level, with a horizontal separation of 1.2 km. The height change is $100-40=60\text{ m}$ and the horizontal distance is 1200 m. Dividing $1200\div60=20$ gives an average gradient of 1 in 20: the land changes height by 1 m for every 20 m horizontally.

This is an average between the two points. The contour spacing may reveal steeper and gentler sections along the way. A gradient of 1 in 10 is steeper than 1 in 20 because the same vertical change occurs over a shorter horizontal distance.

Latitude and longitude

• Latitude: 0° at the Equator to 90° N or S; lines run east–west.
• Longitude: 0° at the Greenwich prime meridian to 180° E or W; lines meet at the poles.
• Write latitude first, longitude second, with directions.
• Use labelled graticule lines; estimate between them where necessary.

Grid references

• Eastings first, second.