Two notations for the same horizontal direction
An azimuth is measured clockwise from north in [0°, 360°). A quadrant bearing starts with N or S, turns by θ from 0° through 90°, and ends with E or W. The bearing to azimuth converter applies those references instead of treating a bearing as an ordinary math angle measured counterclockwise from east.
Use the bearing to azimuth converter builder so N/S and E/W order stays visible, or apply text such as N45°E or a DMS value. The reverse tab accepts an azimuth in decimal degrees or DMS. Exact N, E, S, and W are shown as cardinal directions, never redundant forms such as N 0° E.
Convert a direction and check its reverse
- For a bearing, select N or S, enter θ no greater than 90°, and select E or W. The first letter sets the reference axis; the last sets the turning side.
- For text, include both quadrant letters around the decimal or DMS angle. Cardinal N, E, S, or W can be entered alone.
- For azimuth, enter clockwise degrees from north. Decimal 360° becomes 0°; negative and multi-turn decimal values are accepted and normalization is disclosed.
- Choose decimal or DMS display, then read normalized azimuth, quadrant bearing, reverse azimuth, and reverse bearing from the same ray.
- Optionally compare another azimuth for smallest, clockwise, and counterclockwise turns. Confirm the intended north reference before sharing.
Quadrant formulas and direction conventions
- N θ E → A = θ; S θ E → A = 180° − θ; S θ W → A = 180° + θ; N θ W → A = 360° − θ, normalized if needed.
- Azimuths in the four open quadrants become N A E, S (180° − A) E, S (A − 180°) W, or N (360° − A) W.
- Exact 0°, 90°, 180°, and 270° are N, E, S, and W. Separate axis handling removes ambiguity at θ = 0° or 90°.
- Reverse azimuth = (A + 180°) mod 360°. Reverse bearing comes from converting that direction, not editing text.
- Smallest angle = min(|A − B|, 360° − |A − B|); clockwise = (B − A + 360°) mod 360°; counterclockwise reverses A and B.
Worked bearing and azimuth examples
- N 45° E is 45° azimuth. Its reverse is 225° or S 45° W.
- S 45° E is 180° − 45° = 135° azimuth, in the southeast quadrant.
- S 45° W is 225°, while N 45° W is 315°, covering southwest and northwest.
- Cardinals convert directly: N = 0°, E = 90°, S = 180°, W = 270°. Azimuth 360° normalizes to N at 0°.
- From 350° to 10°, clockwise is 20°, counterclockwise is 340°, and the smallest separation is 20°.
Decimal degrees and DMS
DMS divides one degree into 60 minutes and one minute into 60 seconds. The parser accepts DMS quadrant bearings, and azimuth mode has separate DMS fields. Output performs carry, so rounded 59.9999 seconds becomes the next minute rather than an invalid 60 seconds.
More decimals do not guarantee a more accurate field direction. Preserve source precision and record whether it referenced true, magnetic, or grid north.
Why bearing order matters
The first letter is always N or S and the last is E or W. N 30° E starts from north and corresponds to azimuth 30°. A string such as E 30° N is outside this convention and is rejected rather than guessed.
Notation conversion is not a navigation solution
This page converts notation only. True north follows a geographic meridian, magnetic north follows the local field, and grid north follows a projection; they can differ. The tool does not request location, read a compass, calculate declination, transform coordinates, account for convergence, or validate a survey. Do not use it as safety-critical navigation, aviation, marine, emergency, or surveying instruction. Confirm reference north, datum, instrument, and professional procedure independently.
Conversions run in the browser. Share state contains only quadrant choices, numeric values, tab, and display options; the page neither requests nor stores location.