Convert Bearing and Distance to Coordinates

Every metes and bounds description is a series of bearing-distance pairs. To plot them — or to compute areas, check closure, or import into GIS — you need to convert those pairs into coordinates. This guide covers the math, walks through examples, and shows you how to skip the manual calculation entirely.

The Core Formula

Given a starting point (X₀, Y₀), a bearing, and a distance, the next point (X₁, Y₁) is:

The key is converting the bearing to an azimuth — a single angle measured clockwise from North (0° to 360°).

Bearing to Azimuth Conversion

Surveying bearings use quadrant notation (N/S angle E/W). Convert to azimuth like this:

Where θ is the angle from the bearing. Remember to convert degrees-minutes-seconds to decimal degrees before doing trig.

DMS to Decimal Degrees

Example: 45° 30' 15" = 45 + (30/60) + (15/3600) = 45.504167°

Worked Example

Starting at point (1000.00, 2000.00), travel N 45° 30' 00" E a distance of 200.00 feet.

Step 1: Convert bearing angle to decimal degrees.

Step 2: Determine azimuth. Bearing is NE quadrant, so azimuth = θ = 45.5°

Step 3: Calculate deltas.

Step 4: New coordinates.

Repeat for each call in the description, using the previous endpoint as the starting point for the next call.

Multiple Calls: Building the Traverse

A full parcel traverse looks like this in a coordinate table:

When the last point matches the POB, you've achieved closure.

Skip the Calculator

If you're doing this more than once a week, manual conversion is a waste of time. CADastral does all of this automatically — including parsing the bearing notation, handling curves, computing closure, and plotting the result. Upload the deed document and the coordinates are calculated in seconds.