Field guide
Read a direction before changing its format
An angle can be valid numerically and still point the wrong way if its notation is misread. Use the format selector as part of the calculation, and keep that choice with the result.
Start with the source convention
Find the angle format in the originating project, export specification, or field notes before pasting values. A decimal point alone does not identify the format. A value such as 30.1530 may have been written as decimal degrees or as a compact degrees, minutes and seconds entry. Both interpretations are plausible, but they describe different directions. This calculator defaults to decimal degrees and never switches modes based on how many digits follow the point.
The tool uses surveying azimuth: zero at coordinate north, increasing clockwise through east, south and west. It converts notation within that convention. It does not identify a coordinate system, determine magnetic declination, or turn a magnetic bearing into a grid bearing. If the source direction is relative to a different north reference, resolve that reference separately and record the adjustment in your project documentation.
Choose one format for the entire list
Enter one value for a quick calculation, or put one angle on each line for a batch. A UTF-8 TXT file can be read directly, without a header. Select decimal azimuth, DMS azimuth, decimal quadrant bearing, DMS quadrant bearing, compact DMS azimuth, or gon. Every nonblank line is interpreted using the selected mode. Mixed formats should be separated into distinct runs so that no record depends on an invisible guess.
In decimal mode, enter unsigned numbers with a decimal point when needed. Scientific notation, negative values, decimal commas and thousands separators are not accepted. Decimal inputs allow up to twelve fractional digits. In DMS mode, enter all three parts, such as 30 15 30.5 or 30°15′30.5″. Minutes are whole numbers; seconds may contain up to nine fractional digits. These limits keep the accepted grammar predictable for both pasted text and imported files.
Understand azimuth and quadrant bearing
An azimuth describes the full circle. A quadrant bearing describes an angle of no more than ninety degrees away from north or south, followed by east or west. The two letters are essential: N 30 E and S 30 E have the same internal angle but represent azimuths of 30 and 150 degrees. Removing the letters destroys that distinction. The result preview helps you see which part of the circle the selected record occupies.
For the northeast quadrant, the internal angle equals the azimuth. In the southeast, subtract the azimuth from 180 degrees. In the southwest, subtract 180 degrees from the azimuth. In the northwest, subtract the azimuth from 360 degrees. Exactly north, east, south and west are displayed using their single cardinal letters. The tool accepts those letters in either bearing input mode, avoiding an arbitrary choice between equivalent boundary expressions.
Keep compact DMS separate from decimal degrees
The compact mode follows DDD.MMSS: digits before the point are degrees, the next two are minutes, and the following two are seconds. Any additional digits are fractional seconds. Enter 30.1530 for thirty degrees, fifteen minutes and thirty seconds. Entering that same text in the default decimal mode instead produces 30 degrees, nine minutes and 10.800 seconds. Keeping the original text and parsing mode together is therefore as important as retaining the converted answer.
Compact entries require both minute digits and both second digits, even when they are zero. A short value such as 30.15 is rejected in this mode because it does not supply the full structure. The converter does not emulate every instrument vendor shortcut, direction suffix, mathematical expression or project preference. Use the plain syntax shown beside the selected mode, and verify a known direction before converting an unfamiliar export.
Review validation and rounding
Minutes and seconds must each be below sixty. The converter reports an error for 30 60 00 instead of quietly changing it to 31 degrees. A quadrant angle cannot exceed ninety degrees, and an azimuth cannot exceed a full turn. A full turn of 360 degrees, or 400 gon, is normalized to north. The DMS form of 360 degrees is valid only when its minutes and seconds are zero.
Choose between zero and six decimal places for output seconds. Rounding carries correctly across seconds, minutes and degrees, including back to north at the full circle. Decimal degrees and gon are displayed to at most ten decimal places. Different output formats can therefore reach a cardinal direction at different thresholds. This is a display precision effect, not evidence that the source angle had exactly that direction. Retain the original input if later work needs a different rounding choice.
Use gon only when it is the stated source unit
A full circle contains 400 gon, and a right angle contains 100 gon. Select the dedicated gon mode before entering those values. Do not assume that a number slightly above ninety is a badly formatted degree value; it may belong to a different angular unit. Conversely, a plausible value below ninety does not prove that degrees were intended. Check the instrument or project configuration first.
Gon input is a plain number without a unit suffix. The calculator provides gon output for every successful conversion, making it easy to compare formats while preserving the selected input mode. It does not accept radians, degrees with decimal minutes, south-based azimuths, or anticlockwise mathematical angles. Convert those conventions deliberately in an appropriate workflow instead of relabelling the values to make them fit.
Export a reviewable batch
The table shows twenty-five records per page so that large batches remain manageable. Select a source line to inspect its original value, conversion settings and direction preview. Invalid records remain visible with a reason and blank converted fields; they are not dropped from the exported report. Blank lines are counted separately, and physical source line numbers are retained even when blanks occur in the middle of a file.
Download CSV for a tabular review, or JSON to keep the complete structured result and settings. The CSV includes the original value, source filename, line, parsing mode, output precision, successful conversions and error reason. Text that could be treated as a spreadsheet formula is protected in this report. This is a calculation report rather than an instrument-ready observation file. Confirm the receiving software requirements before reusing any column as input.
Files are processed locally in the browser. Input is limited to ten MiB and one hundred thousand angles; CSV output also has a ten MiB limit. Large text is shown as a read-only preview while the full file is processed. Replace the file or clear the session to edit it. Changing the format or precision clears the previous result, which prevents a stale export from appearing to match new settings. Cancel a running conversion to retain the input without accepting a partial report.