Bearing from Coordinates / Offsets
Enter the position of point B relative to point A (positive = north/east, negative = south/west)
Back Bearing (Reciprocal) Calculator
Enter a bearing to find its back bearing (opposite direction)
Bearing to Compass Direction
Convert a 3-figure bearing to a named compass point (N, NE, SSW, etc.)
What is a Compass Bearing?
A compass bearing is a direction expressed as an angle measured clockwise from north. In the UK navigation system, bearings are always written as 3-figure bearings — a number from 000° to 359° with exactly three digits.
Cardinal and Intercardinal Points
| Direction | 3-Figure Bearing | Compass Point |
|---|---|---|
| North | 000° | N |
| North-East | 045° | NE |
| East | 090° | E |
| South-East | 135° | SE |
| South | 180° | S |
| South-West | 225° | SW |
| West | 270° | W |
| North-West | 315° | NW |
How to Measure a Bearing on a Map
To measure a bearing from point A to point B on an OS map:
- Draw a line from A to B (or place a ruler/compass edge along this path)
- Place a protractor at point A with the centre hole exactly on A
- Align the 000°/180° baseline with a vertical grid line (north–south line)
- Read off the angle clockwise from the top (north) to the line to B
- Write as a 3-figure number — add leading zero if needed (e.g. 37° → 037°)
True North, Magnetic North, and Grid North
True north is the direction of the geographic North Pole — the axis around which Earth rotates. Magnetic north is the direction a compass needle points, which varies from true north due to Earth's magnetic field. Grid north is the direction of the vertical grid lines on an OS map, which aligns with true north only along the central meridian of each map zone.
In the UK in 2026, magnetic declination is approximately 0° to 2° West depending on location. In much of England, the difference between magnetic north and grid north is less than 1°, which is negligible for most navigation. OS maps always print the declination value for that sheet in the margin, alongside the date it was measured.
Back Bearing (Reciprocal Bearing)
The back bearing is the exact opposite direction — the bearing from B back to A. To calculate it:
- If the bearing is less than 180°, add 180° to get the back bearing
- If the bearing is 180° or more, subtract 180°
Examples:
Bearing of 053° → back bearing = 053 + 180 = 233°
Bearing of 247° → back bearing = 247 − 180 = 067°
Back bearings are used in navigation to check your position by resection, and in GCSE geography questions.
Calculating Bearing from Coordinates — Worked Example
If point B is 3 km north and 4 km east of point A, what is the bearing from A to B?
Step 1: tan(angle from north) = east ÷ north = 4 ÷ 3 = 1.333
Step 2: angle = arctan(1.333) = 53.1°
Step 3: Because B is north and east of A, bearing = 053°
If B were south and east: bearing = 180 − 53.1 = 126.9° → 127°
If B were south and west: bearing = 180 + 53.1 = 233.1° → 233°
If B were north and west: bearing = 360 − 53.1 = 306.9° → 307°
Navigation Applications
Orienteering uses bearings constantly — competitors navigate from control to control using compass and map. The bearing is set on the compass, which is then held level and used to walk in the correct direction.
Hillwalking in poor visibility relies on bearings. Walkers take a bearing from the map, set it on their compass, and use the compass to maintain direction even in cloud or darkness.
Sailing uses bearings to plot courses. A True bearing is adjusted for magnetic variation and compass deviation to give the course to steer.
Aviation uses bearings in VOR navigation — beacons broadcast radials (bearings from the beacon) which aircraft receivers display for route guidance.
GCSE Geography — Bearing Questions
UK GCSE geography papers regularly ask students to measure or calculate bearings. Common question types:
- Measure the bearing from town A to town B on a map extract
- A ship sails on a bearing of 125° for 40 km — how far south and east has it gone?
- Back bearing questions: "What is the bearing from B back to A?"
- Three-point problems: find a location using two or more bearings
Frequently Asked Questions
What is a 3-figure bearing?
A 3-figure bearing is a compass direction expressed as a number between 000° and 359°, always written with exactly three digits. It is measured clockwise from north. North = 000°, East = 090°, South = 180°, West = 270°. Using three digits avoids ambiguity — 037° cannot be confused with 37 (which might mean 37° west).
What is the back bearing of 053°?
The back bearing (reciprocal bearing) is found by adding or subtracting 180°. For 053°: 053 + 180 = 233°. The rule is: if bearing is less than 180°, add 180°; if 180° or more, subtract 180°. Back bearings are used for resection navigation and GCSE geography questions.
What is magnetic declination in the UK?
In the UK in 2026, magnetic declination is approximately 0° to 2° West depending on location and year. In central England it is very close to 0°. Scotland has slightly higher westerly declination (around 1–2°). OS maps print the current declination value for each sheet. Historically, UK declination was much larger (around 10° W in 1900) and it is slowly decreasing.
How do I calculate a bearing from coordinates?
Use the formula: bearing = atan2(east difference, north difference) converted to degrees, then adjusted to 0–360°. If point B is 4 km east and 3 km north of A: angle = atan2(4, 3) = 53.1°, bearing = 053°. If values are negative (south or west), the quadrant adjustments apply automatically if using atan2. Our calculator above handles this automatically.
What is the difference between true north and magnetic north?
True north points to the geographic North Pole. Magnetic north points to the magnetic pole, which wanders over time and is currently near the Canadian Arctic. In the UK the difference is small (under 2°) so it rarely matters for walking navigation. Grid north aligns with the vertical grid lines on OS maps and differs slightly from true north except at the central meridian of each zone.
How do I measure a bearing on a map?
Place a protractor at your starting point with the centre hole on that point and the baseline aligned with a north–south grid line (vertical line on an OS map). Read off the angle clockwise to the direction of travel. Always read clockwise from north (top of map). A compass can also be used — place it on the map and rotate the dial until the orienteering lines align with the grid, then read the bearing from the index mark.
Compass Points Reference
| Point | Bearing |
|---|---|
| N | 000° |
| NNE | 022.5° |
| NE | 045° |
| ENE | 067.5° |
| E | 090° |
| ESE | 112.5° |
| SE | 135° |
| SSE | 157.5° |
| S | 180° |
| SSW | 202.5° |
| SW | 225° |
| WSW | 247.5° |
| W | 270° |
| WNW | 292.5° |
| NW | 315° |
| NNW | 337.5° |