Calculate azimuth bearing (degrees, minutes, seconds) and horizontal distance between two survey coordinate pairs. Enter Northing/Easting for both points.
Total stations and GPS rovers automate inverse calculations in the field. Browse survey equipment at Express Tools.
Shop Express Tools →Azimuth = atan2(ΔE, ΔN) converted to 0–360° clockwise from north. Distance = √((ΔN)² + (ΔE)²). Enter two Northing/Easting pairs in any plane coordinate system. Quadrant bearing (e.g., N 45° E) is derived from the azimuth.
Bearing and distance (inverse) calculations are fundamental to survey layout. Given two control points in a plane coordinate system, the inverse calculation yields the direction (azimuth) and distance needed to stake the line in the field. This is the inverse of a traverse — instead of computing coordinates from bearing and distance, you compute bearing and distance from coordinates. Use this tool for property line staking, traverse leg checks, offset line setup, and layout verification. All calculations are performed in plane geometry; no geodetic corrections are applied.
| Azimuth Range | Quadrant | Quadrant Bearing Formula |
|---|---|---|
| 0° – 90° | NE | N (azimuth)° E |
| 90° – 180° | SE | S (180° − azimuth)° E |
| 180° – 270° | SW | S (azimuth − 180°)° W |
| 270° – 360° | NW | N (360° − azimuth)° W |
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Start free trialBearing (azimuth) is calculated using the inverse tangent of the difference in Easting over the difference in Northing: azimuth = atan2(ΔE, ΔN). The result is converted to a clockwise angle from north (0-360°).
An azimuth is measured 0-360° clockwise from north. A quadrant bearing expresses the same direction as an angle from north or south toward east or west - for example, N 45° E or S 30° W. Both describe the same line direction.
Horizontal distance between two plane coordinate pairs is the Pythagorean formula: distance = √((N2-N1)2 + (E2-E1)2). This gives the straight-line horizontal distance in the same units as the coordinates.
This calculator works with any plane coordinate system - State Plane, local assumed coordinates, or project grid. Enter Northing and Easting in feet. The tool does not account for geodetic curvature or scale factors.
Yes - calculate bearing and distance for each leg of your traverse. Compare computed bearings to field measurements to check closure and angular error.
Enter two coordinate pairs to calculate azimuth bearing and horizontal distance between points.
Point 1
Point 2