Geodetic Calculation

Azimuth & Traverse Calculator

Compute azimuth and horizontal distance from two points (inverse calculation), or a new point's coordinates from point + azimuth + distance (polar calculation). Gon/grad and degrees (D-M-S) shown together.

P1 — Station Point

P2 — Target Point

All calculations run in your browser — your data is never uploaded to any server. Convention: Y = easting, X = northing; the azimuth is measured clockwise from north.

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Online Azimuth (Bearing) and Traverse Calculation

Inverse: Azimuth + Distance from Two Points

A fundamental surveying computation: given the coordinates of two points, find the azimuth and horizontal distance between them. Following the Turkish convention where Y is the easting and X the northing, the azimuth is computed as t = atan2(ΔY, ΔX), measured clockwise from north and normalized to 0-400 gon. The distance is S = √(ΔY² + ΔX²).

  • Gon (g): the standard surveying unit; results shown with 4 decimals
  • Degrees: decimal degrees and D-M-S notation shown together
  • Quadrant-safe: atan2 gives correct results in all four quadrants
  • Millimetre precision: coordinate results with 3 decimals (mm)

Polar: Point + Azimuth + Distance → New Point

The reverse of stake-out and detail surveys: from a known point, a measured (or given) azimuth and distance yield the new point's coordinates: Y2 = Y1 + S·sin(t), X2 = X1 + S·cos(t). You can enter the angle in gon/grad or degrees; the tool displays both.

Other Tools

Use the Area & Parcel Division Calculator for parcel areas and subdivision, or the Coordinate Converter for conversions between coordinate systems.

Frequently Asked Questions

What is an azimuth (bearing)?

An azimuth is the angle of a direction measured clockwise from north. In surveying it is computed as t = atan2(ΔY, ΔX) and normalized to 0-400 gon (or 0-360 degrees), where ΔY is the easting difference and ΔX the northing difference.

What is the difference between gon (grad) and degrees?

A full circle is 360° in degrees and 400g in gon (grad); 1 gon = 0.9 degrees. Gon is the standard angular unit in Turkish and many European surveying practices, while degrees are used in decimal or D-M-S (degree-minute-second) notation. Conversion: gon = degrees × 400/360.

Which axis is the easting, Y or X?

This tool follows the Turkish surveying convention: Y is the easting (rightward) and X is the northing (upward) — the opposite of the mathematical axis convention. The azimuth is therefore computed as t = atan2(ΔY, ΔX), measured clockwise from north.