Bearing & Distance

Status: Research brief below. Replace this entire body with finished MDX when research is complete. Update description in frontmatter.

Paired tool: /tools/calculators/bearing-distance

AI research prompt

You are writing a Learn article for Surveying Core, a professional surveying knowledge platform. Produce a single MDX-ready document (no wrapper frontmatter — only the article body with headings). The article will be published at /learn/tools/bearing-distance and must pair bidirectionally with the Bearing & Distance Calculator at /tools/calculators/bearing-distance.

Audience

• Field surveyors and engineering survey technicians who work in grid coordinates daily
• Civil engineering students learning coordinate geometry for the first time
• Office staff checking stakeout or traverse leg calculations

Assume the reader can use a calculator but may confuse bearing conventions, quadrant bearings vs azimuth, and which axis is which in Easting/Northing systems.

Platform conventions (must match the tool)

The paired calculator uses these rules — your article must not contradict them:

• Coordinates are Easting (E) and Northing (N) on a local or projected grid
• Azimuth is measured from grid north, clockwise, in decimal degrees (0°–360°)
• Polar → rectangular: ΔE = D × sin(θ), ΔN = D × cos(θ)
• Rectangular → polar: distance = hypot(ΔE, ΔN); azimuth from atan2(ΔE, ΔN) normalized to 0–360°
• No geodetic latitude/longitude in this article (out of scope)

Scope — must cover

1. Why bearing and distance matter in surveying (polar notation from total stations, traverse legs, stakeout offsets)
2. Azimuth vs quadrant bearing (DMS/quadrant notation): define both; show conversion examples; state that the tool uses azimuth
3. Grid axes and sign conventions (positive E = east, positive N = north); common mistakes (swapping E/N, using math angle from X-axis without rotating to north)
4. Polar to rectangular — formula, worked example with realistic coordinates (e.g. origin 500000.000 E, 150000.000 N; azimuth 127.5430°; distance 83.472 m) showing full intermediate steps
5. Rectangular to polar — same rigour; include a check-back verification step
6. Practical field notes: when to use grid azimuth vs magnetic (brief); importance of knowing your CRS/job datum (high level only)
7. Link to the tool in the intro and conclusion with clear CTA (“Try the Bearing & Distance Calculator”)

Out of scope

• Traverse adjustment, resection, or least-squares (other articles/tools)
• Full treatise on map projections or datum transformations
• Curved/ellipsoidal geodesy
• Generic “what is surveying” filler

Quality bar

• Cite primary sources where claims are technical (textbooks, FIG/ICS guidance, standard surveying texts such as Kavanagh, Uren & Price, or equivalent regional texts). Include a short References section.
• No filler paragraphs — every section must teach something actionable
• At least two fully worked numeric examples (one polar→rect, one rect→polar) with 3 decimal places on coordinates
• One “common errors” subsection (e.g. using anticlockwise angles, radian/degree mix-up, atan2 argument order)
• WCAG-friendly structure: one H1 worth of title is handled by the page shell — start article body at ##; use ### for subsections; no skipped heading levels; descriptive link text

Deliverable format

Return MDX body only, starting with ## Introduction. Suggested outline:

1. Introduction (with tool link)
2. Azimuth and bearing conventions
3. Easting and northing
4. Polar to rectangular conversion
5. Rectangular to polar conversion
6. Worked examples
7. Common errors
8. When to use this in the field
9. References
10. Next steps (link back to /tools/calculators/bearing-distance)

Target length: 1,200–1,800 words of substantive technical prose (excluding references).