Compass bearings
Read and write compass bearings in N/S–angle–E/W notation, convert between compass bearings and true bearings, and identify the quadrant of a direction.
Worked examples
Stating a compass bearing
Straightforward
Problem
A direction is measured from north toward the east. Write this direction as a compass bearing.
1
Identify the reference pole.
The direction is measured from north, so the first letter is N.
2
Identify the angle.
The angle is .
3
Identify which side the direction moves toward.
The direction moves toward the east, so the last letter is E.
4
Write the compass bearing in N/S–angle–E/W notation.
Combining these: the compass bearing is NE.
Answer
The compass bearing is NE.
Converting a compass bearing to a true bearing
Moderate
Problem
Convert the compass bearing SE to a true bearing.
1
Identify the reference pole and determine its true bearing.
The reference pole is south, which is on the true bearing scale.
2
Determine the direction of the angle from the reference pole.
S[x]°E means the direction is x° measured from south toward the east. Moving toward east from south means moving anti-clockwise, so the true bearing will be less than .
3
Calculate the true bearing.
4
Check the answer is in the correct quadrant.
lies between (east) and (south), which is the SE quadrant. A direction east of south should be in the SE quadrant — this is consistent.
Answer
The true bearing is .
Converting a compass bearing and identifying the quadrant
Challenging
Problem
A compass bearing of NW is given. Convert it to a true bearing and state the quadrant in which the direction lies.
1
Identify the reference pole and its true bearing value.
The reference pole is north, which is (equivalently ) on the true bearing scale.
2
Determine the direction of the angle from north.
N[x]°W means x° measured from north toward the west. Moving from north toward the west is anti-clockwise, so the true bearing will be less than but greater than . Equivalently, subtract x° from .
3
Calculate the true bearing.
4
Identify the quadrant.
lies between (west) and (north). This places the direction in the NW quadrant, which is consistent with a compass bearing that starts with N and ends with W.
Answer
The true bearing is . The direction lies in the NW quadrant.
Practise
Q1·Straightforward
A direction makes an angle of measured from north toward the east. Which compass bearing describes this direction?
Explanation
Compass bearings start with the nearest pole: here, north (N). The angle is and the direction moves toward the east (E). The compass bearing is NE.
Q2·Straightforward
A direction is west of south. Which compass bearing describes this direction?
Explanation
The reference pole is south (S), the angle is , and the side is west (W). The compass bearing is SW.
Q3·Straightforward
A direction is measured from north toward the west. Which compass bearing describes it?
Explanation
Starting from north (N) and measuring toward the west (W) gives the compass bearing NW.
Q4·Straightforward
A ship heads in a direction that is from south toward the east. Which compass bearing describes its heading?
Explanation
Starting from south (S) and measuring toward the east (E) gives the compass bearing SE.
Q5·Moderate
Convert the compass bearing NE to a true bearing.
Explanation
NE means measured from north toward the east. True bearings are measured clockwise from north, and east is clockwise from north, so the true bearing is .
Q6·Moderate
Convert the compass bearing SW to a true bearing.
Explanation
South is at on the true bearing scale. SW means past south continuing clockwise toward the west. True bearing .
Q7·Moderate
A direction has a true bearing of . Which compass bearing is equivalent?
Explanation
is between west () and north (), so it lies in the NW quadrant. The angle from north is . The direction is west of north, so the compass bearing is NW.
Q8·Moderate
Convert the compass bearing SE to a true bearing.
Explanation
SE means measured from south toward the east. East of south corresponds to true bearings less than , so the true bearing .
Q9·Challenging
A surveyor records a compass bearing of SW. What is the equivalent true bearing, and in which quadrant does this direction lie?
Explanation
SW: south is and the direction continues past south toward the west (clockwise). True bearing . This lies between south () and west (), which is the SW quadrant.
Q10·Challenging
A trail heads on a compass bearing of NW. What is the equivalent true bearing, and in which quadrant does this direction lie?
Explanation
NW: north is at and the direction is back toward the west (anti-clockwise from north). True bearing . This lies between west () and north (), which is the NW quadrant.
Q11·Challenging
Convert the compass bearing SE to a true bearing.
Explanation
SE means measured from south toward the east. East of south corresponds to true bearings between and , so the true bearing . This lies in the SE quadrant, consistent with a direction east of south.
Q12·Challenging
A true bearing of is given. Which compass bearing is equivalent, and in which quadrant does this direction lie?
Explanation
lies between south () and west (), so it is in the SW quadrant. Angle past south . The direction moves from south toward the west, giving the compass bearing SW.