Surveying Calculator

Bearing to azimuth converter

Deeds and plats write directions as quadrant bearings — N 45°12'30" E — but traverse math, GIS, and most software need an azimuth: one angle measured clockwise from north, 0° to 360°. Use the converter below, or read on for the formulas so you can check any call by hand.

Quadrant bearing → azimuth

° ' "

Azimuth → quadrant bearing

° ' "

Bearing to azimuth formulas

A quadrant bearing starts facing north or south and turns toward east or west by an angle of 0° to 90°. Convert it with the rule for its quadrant:

Quadrant	Azimuth	Example
N … E	angle	N 30° E → 30°
S … E	180° − angle	S 30° E → 150°
S … W	180° + angle	S 30° W → 210°
N … W	360° − angle	N 30° W → 330°

Due north, east, south, and west are 0°, 90°, 180°, and 270°.

Working with degrees, minutes, and seconds

Convert DMS to decimal degrees with degrees + minutes/60 + seconds/3600. For subtraction, borrow just like hours and minutes:

S 12°03'15" E → 180°00'00" − 12°03'15" = 179°59'60" − 12°03'15" = 167°56'45"

Seconds of 60 or more carry into the minutes: 60°57'60" is a legal way of writing 60°58'00". Some software rejects it; the converter above handles it.

Convert a whole deed at once

The Polygon Closure Auditor reads every call in a deed, converts each bearing, runs the traverse, and tells you whether the description closes.

Try the auditor

Azimuth to bearing

0°–90°: N (azimuth) E
90°–180°: S (180° − azimuth) E
180°–270°: S (azimuth − 180°) W
270°–360°: N (360° − azimuth) W

Why it matters for closure

A flipped quadrant — SE entered as SW — is one of the most common reasons a deed fails to close, and it's easy to miss when you're reading 40 calls. Once every bearing is an azimuth, each course's latitude and departure are simply distance × cos(azimuth) and distance × sin(azimuth). See how to check metes and bounds closure for the full traverse.

Things to watch for in deed bearings

Basis of bearings. Every survey's bearings are relative to some reference line — true north, grid north, magnetic north at a given date, or simply "the north line of Section 12". Two deeds for adjoining parcels can describe the same line with different bearings.
Reversed calls. Walking a shared line in the other direction flips both letters: N 45° E becomes S 45° W, and the azimuth changes by exactly 180°.
Degree-only bearings. Older deeds often give whole or half degrees ("N 45½ E"). Treat ½ as 30 minutes and ¼ as 15 minutes.
Curve calls. A curve's chord bearing is the bearing to convert; the tangent bearings at each end are different directions.

Common questions

Is a bearing the same as an azimuth?

Both describe direction. A quadrant bearing is 0°–90° from north or south toward east or west; an azimuth is 0°–360° clockwise from north. Some fields (and older texts) measure azimuth from south — deeds and modern software almost always use north.

Do I need to correct for magnetic declination?

Only if the deed's bearings are magnetic. Old deeds often are; the conversion here is purely geometric and doesn't change the basis of bearings.