Direction, north and bearings
A topographic map can carry three different norths, and a compass needle follows only one of them, magnetic north.
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Which way is north?
Most maps are drawn with north at the top, and they show it with a north arrow. But surveyors distinguish three norths, and the NGII explains all three. True north points along the meridian to the geographic North Pole. Grid north is the direction of the vertical grid lines printed on the map, which follow the map projection and so can lean slightly away from true north. Magnetic north is the direction a compass needle settles in. The small angles between them have their own names: between true and grid north, between grid and magnetic north, and between true and magnetic north.
Magnetic declination
The angle between magnetic north and true north is called magnetic declination, or magnetic variation. NOAA’s National Centers for Environmental Information, which publishes the World Magnetic Model with the British Geological Survey, gives the rule: declination is positive when magnetic north is east of true north and negative when it is west. It changes from place to place and from year to year, because Earth’s magnetic field slowly changes. The North Magnetic Pole was found in northern Canada by James Clark Ross in 1831 and has been moving toward Russia ever since, at about 55 kilometres a year in 2007. In the latest annual report on the World Magnetic Model (2025), its average speed over the past year was about 36 kilometres.
Because declination changes, the declination diagram on an old map can be out of date. NOAA offers a calculator that gives the current value for any place and date. The correction itself is simple addition. To turn a compass reading into a true bearing, add the declination, counting west as negative. With a declination of 8 degrees west, a magnetic bearing of 100 degrees becomes a true bearing of 92 degrees.
Bearings: directions as numbers
Words like northeast are fine for conversation, but they are vague. A bearing turns a direction into a number: the angle measured clockwise from north, from 0 to 360 degrees. North is 0, east 90, south 180 and west 270. Northeast sits halfway between north and east at 45 degrees, and southwest at 225. To go back the way you came, add 180 degrees to your bearing, or subtract 180 if the number is already more than 180. A walker heading out on a bearing of 60 degrees returns on 240.
In the scene, the readout calculates the bearing from A to B with map north at the top. Try to predict it before you click. Put B straight above A and you should see a bearing near 0 degrees. Put B to the lower left and the number should land between 180 and 270. The grid lines in the scene are exactly north-south and east-west, so here grid north and true north are the same.
N 0°, NE 45°, E 90°, SE 135°, S 180°, SW 225°, W 270°, NW 315°.
- True north points to the North Pole, grid north follows the map grid, magnetic north follows the compass.
- Declination is east positive, west negative, and it changes over time.
- True bearing = magnetic bearing + declination.
- A back bearing is the bearing plus or minus 180°.
- What is the bearing of due south?
- What is the bearing of southwest?
- You walk out on a bearing of 60°. What bearing takes you straight back?
- You walk out on 300°. What is the back bearing?
- Declination is 8° west. A compass reads 100°. What is the true bearing?
- Declination is 12° east. A compass reads 30°. What is the true bearing?
- Which north follows the vertical grid lines of the map?
- True north
- Grid north
- Magnetic north
- Why can the declination printed on an old map be wrong today?
- Earth’s magnetic field changes over time
- Paper shrinks
- True north moves
- You walk 1 km with a 5° error in direction. About how far off target do you end up, in metres? (Use 1000 × sin 5°.)
- Who first located the North Magnetic Pole, in 1831?
- James Clark Ross
- Roald Amundsen
- Robert Peary
- Put these directions in order of bearing, smallest first.
Sources for this course (14)
- USGS, Topographic Map Symbols (pubs.usgs.gov/gip/TopographicMapSymbols/topomapsymbols.pdf: colours, contours never cross, index contours wider, close contours = steep, interval 10 ft or less in flat areas, 100 ft or more in mountains, interval printed in the margin)
- USGS FAQ Why are USGS topographic maps called quadrangles? (usgs.gov/faqs: 7.5-minute maps at 1:24,000, one inch = 24,000 inches = 2,000 feet; Alaska 1:25,000)
- USGS Topographic Mapping (usgs.gov/educational-resources/topographic-mapping: 1:63,360 = 1 inch to 1 mile, accuracy 1/50 inch = 40 ft, half the contour interval)
- USGS Map Scales fact sheet (pubs.usgs.gov/fs/2002/0015, 1:100,000 about 1.6 miles, 1:250,000 about 4 miles per inch)
- USGS US Topo specifications, Elevation (index contour = every fifth contour)
- 국토지리정보원(NGII): 지도의 구성 (ngii.go.kr/kor/content.do?sq=272: 진북·도북·자북, 도편각·도자각·자편각, 수치지형도 분류 교통·건물·시설·식생·수계·지형·경계·주기 8가지, 주곡선·계곡선·간곡선·조곡선, 경위도 원점과 수준원점 26.6871 m)
- 「1/25000 및 1/50000 지형도도식규정」 국토지리정보원고시 제2009-584호 제129조 (law.go.kr: 주곡선 1/25,000 10 m, 1/50,000 20 m)
- 「소축척지형도 도식적용규정」 (law.go.kr: 계곡선은 주곡선 다섯 개마다)
- NOAA NCEI, Magnetic Declination (ncei.noaa.gov/products/magnetic-declination: angle between magnetic north and true north, east positive, changes with time and place; true bearing = magnetic bearing + declination)
- NOAA NCEI Tracking Changes in Earth's Magnetic Poles (2018, updated: Ross 1831; pole moving about 55 km/yr in 2007, about 45 km/yr in the IGRF of that time)
- NCEI news, 2025 WMM Annual Report is Released (9 Jan 2026: north magnetic pole average drift about 36 km/yr over the past year)
- IOF ISOM 2017-2, symbol 601 Magnetic north line (magnetic north lines printed on the map, 20 mm = 300 m at 1:15,000, map rotated so the lines run parallel to the paper edges)
- UK House of Commons Standing Orders (Private Business) 55: deposited railway section
- The National Archives catalogue, King's Lynn to Spalding railway plan deposited 30 Nov 1850 (horizontal 6 chains = 132 yards to 1 inch, vertical 60 feet to 1 inch, VE 396/60 = 6.6).
Checked: 2026-10-18