How To Calculate Bearings | Get Accurate Direction Angles

A bearing is direction written as an angle. Get the angle right and you can plot a line on a map, set a compass bezel, check a GPS course, or confirm a line in field notes. Most errors come from mixing formats: whole-circle vs quadrant, true vs magnetic north, forward vs back.

Below you’ll learn the core rules, then apply them to map lines and coordinate points. Each section ends with a fast check so you can catch mistakes before they cost you distance on the ground or points on an assignment.

How To Calculate Bearings For Maps And GPS

In everyday navigation, a bearing is often shown as a single number from 0° to 360°, measured clockwise from north. In surveying classes, you may see a quadrant style like N 35° E, which stays tied to north/south and east/west. Both describe the same direction, just with different notation.

Pick The Bearing Style First

Whole-circle bearing: one number, 0° to 360° (east 90°, south 180°, west 270°).

Quadrant bearing: N/S then an angle (0°–90°) then E/W, like S 20° W.

Quick check: quadrant angles never exceed 90°. If your math gives 120° in quadrant form, switch to whole-circle or re-check the steps.

Keep The North Reference Clear

Maps and coordinate math usually give a true (or grid) direction. A compass needle follows magnetic north, which can sit east or west of true north. If you’re converting between true and magnetic, you need local declination for the date you’re working with.

For a current declination value by place and date, you can use NOAA’s Magnetic Declination Calculator. Write the declination next to your work and label your final bearing as true, grid, or magnetic so the reader knows what the number means.

Read A Whole-Circle Bearing From A Map Line

If you have a line from point A to point B on a north-up map, you can get its bearing with a protractor or baseplate compass. The math view is the same measurement:

1. Draw the line A→B.
2. Draw a north line through A (straight up the page).
3. Measure the clockwise angle from north to the A→B line.
4. Write it as a three-digit degree value (045°, 312°).

Fast check: if the line points southeast on the page, your bearing must land between 90° and 180°.

Convert Whole-Circle To Quadrant And Back

Use these four ranges to move from whole-circle to quadrant:

• 0° to 90°: N θ E, θ = bearing
• 90° to 180°: S θ E, θ = 180° − bearing
• 180° to 270°: S θ W, θ = bearing − 180°
• 270° to 360°: N θ W, θ = 360° − bearing

To move from quadrant to whole-circle, use the letters as your map. N θ E stays θ. S θ E becomes 180° − θ. S θ W becomes 180° + θ. N θ W becomes 360° − θ.

One Worked Conversion

GPS bearing 238° sits between 180° and 270°, so it’s SW. θ = 238° − 180° = 58°. Quadrant form: S 58° W. Going back: 180° + 58° = 238°.

If your class wants three digits every time, Ordnance Survey lays out that writing convention and the clockwise-from-north rule in Ordnance Survey’s bearing format notes.

Find The Back Bearing

A back bearing points along the same line in the opposite direction.

• Whole-circle: add 180° if the bearing is below 180°. Subtract 180° if it’s 180° or above.
• Quadrant: swap N↔S and E↔W, keep the angle the same.

Examples: 052° becomes 232°. 244° becomes 064°. N 35° E becomes S 35° W.

Get A Bearing From Two Coordinate Points

This shows up in GIS, surveying homework, and coding. Use a flat coordinate system where +y is north and +x is east. For point A (x₁, y₁) and point B (x₂, y₂):

• ΔE = x₂ − x₁
• ΔN = y₂ − y₁

Compute the angle from north with the two-argument arctangent:

Bearing = atan2(ΔE, ΔN) in degrees, shifted into 0–360°.

If your calculator returns a negative angle, add 360°. If it returns 360°, write 0°.

Worked Coordinate Example

A(200, 100) to B(260, 220): ΔE = 60, ΔN = 120. atan2(60, 120) gives 26.565°, so the bearing is about 26.6° (027° if rounding to the nearest degree). Fast check: both ΔE and ΔN are positive, so the direction must be in the NE quadrant (0°–90°).

Common Bearing Tasks And The Right Formula

Use this table to match the task to the clean rule. It’s built to cover the questions that show up most in classes and field exercises.

Task	What You Compute	Fast Check
Map line to whole-circle bearing	Clockwise angle from map north to A→B	Angle matches the line’s quadrant
Whole-circle to quadrant	Use the 4-range rules (0–90, 90–180, 180–270, 270–360)	Quadrant angle stays 0–90
Quadrant to whole-circle	Compute from 0, 180, or 360 based on letters	NE lands 0–90; SE lands 90–180
Back bearing (whole-circle)	Add 180° or subtract 180°	Result differs by 180°
Back bearing (quadrant)	Swap N↔S and E↔W	Angle stays the same
Coordinates (x, y) to bearing	atan2(ΔE, ΔN) → degrees → shift into 0–360	Signs of ΔE and ΔN set the quadrant
Turn update from a starting bearing	Right turn: (B + α) mod 360; left turn: (B − α) mod 360	Right turns raise the number in most cases
Convert true ↔ magnetic	Add or subtract declination using your class convention	Sketch two north arrows to verify the rotation
Fix a negative output angle	Add 360°	Angle lands near 360° when close to north

Turn Updates Without Losing The 360° Wrap

Turn problems are simple until the number crosses 0° or 360°. Treat every update as “wrap into range.”

• Start at 350°. Turn right 20°. New bearing: 370°. Wrap: 10°.
• Start at 10°. Turn left 35°. New bearing: −25°. Wrap: 335°.

Spot The Mistakes That Cost The Most Points

• Wrong atan2 order: bearings start from north, so use atan2(ΔE, ΔN), not atan2(ΔN, ΔE).
• North mismatch: don’t mix a map’s true direction with a compass’s magnetic direction unless you correct with declination.
• Early rounding: keep decimals until the last step, then round once.

Bearing Conversion Cheat Sheet

Use this as a quick final check after you show your working. It’s built around the four quadrant cases that cover most conversions.

If You Have	You Want	Do This
Whole-circle 0–90	Quadrant	N θ E (θ = bearing)
Whole-circle 90–180	Quadrant	S θ E (θ = 180 − bearing)
Whole-circle 180–270	Quadrant	S θ W (θ = bearing − 180)
Whole-circle 270–360	Quadrant	N θ W (θ = 360 − bearing)
Quadrant N θ E	Whole-circle	bearing = θ
Quadrant S θ E	Whole-circle	bearing = 180 − θ
Quadrant S θ W	Whole-circle	bearing = 180 + θ
Quadrant N θ W	Whole-circle	bearing = 360 − θ

Write Bearings Cleanly In Notes And Assignments

Clear notation keeps your reader from guessing what your numbers mean. These habits help in class reports and real field logs:

• Use the degree symbol (°) and keep it consistent.
• For whole-circle bearings, write three digits: 005°, 090°, 275°.
• Label the north reference: true, grid, or magnetic.
• When you apply declination, write the value and direction (E or W) on the same line as the correction step.
• State your rounding rule once: nearest degree, nearest tenth, or nearest minute.