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Calcimator

Bearing & Distance Calculator

Calculate bearing (azimuth and quadrant) and horizontal distance between two survey coordinate points.

About this calculator

This is the classic surveying "inverse" problem: given the northing/easting coordinates of two points, work backward to the bearing and distance between them. The engine takes the coordinate difference (ΔN and ΔE), runs it through the Pythagorean theorem for distance and an arctangent for azimuth, then rewrites that azimuth as a quadrant bearing — the N/S-degrees-E/W notation (e.g. N 34° 59' 31" E) that appears on deeds and plats instead of a raw 0-360° compass heading. At the default points, moving from (1000, 1000) to (1500, 1350), the difference is 500 feet north and 350 feet east, giving a horizontal distance of about 610.3 feet — every downstream distance figure (meters, chains, rods) is that same number converted by a fixed factor, not recomputed independently.

Elevation Difference is the one input that does nothing to the horizontal figures: it only feeds Slope Distance, Slope percentage, and Slope Angle, computed as a second right triangle laid over the first. Leave it at its default of zero and those three outputs simply mirror the horizontal distance with a 0% grade. This calculator has no knowledge of coordinate system, datum, or convergence angle — the northings and eastings it accepts are assumed to already be in a single consistent plane (state plane, local grid, or similar), and it will not warn you if the two points come from different systems.

Inputs

ft
ft
ft
ft

Results

Horizontal Distance

610.33 ft

≈ 8 tennis courts

Quadrant Bearing

N 34° 59' 31.27" E

Azimuth34.99°
ΔN (Latitude)500 ft
ΔE (Departure)350 ft
Distance (metric)186.03 m
Distance (chains)9.25 ch
Slope Distance610.33 ft
Slope0%
Distance Rods36.99
How to Use This Calculator
  1. Enter Point 1 Northing/Easting and Point 2 Northing/Easting — the coordinates of your two survey points.
  2. Optionally enter Elevation Difference to also compute slope distance and slope angle; leave it at 0 for a horizontal-only inverse.
  3. Read Horizontal Distance and Quadrant Bearing (e.g. N 34° 59' 31" E) for deed and plat notation.
  4. Use Azimuth, ΔN, and ΔE if you need the raw compass heading or coordinate differences instead.
  5. Check Distance (metric), Distance (chains), and Distance Rods for the same length in other survey units.

How the result changes with Point 2 Northing

Point 2 NorthingHorizontal DistanceQuadrant Bearing
750430.12 ftS 54° 27' 44.36" E
1,125371.65 ftN 70° 20' 46.23" E
2,2501,298.08 ftN 15° 38' 32.09" E
3,7502,772.18 ftN 7° 15' 11.5" E

What each input means

Point 1 Northing
Northing (Y) coordinate of the starting point.
Point 1 Easting
Easting (X) coordinate of the starting point.
Point 2 Northing
Northing (Y) coordinate of the ending point.
Point 2 Easting
Easting (X) coordinate of the ending point.
Elevation Difference
Difference in elevation between points (optional, for slope calculations).

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Point 1 Northing = 1000, Point 1 Easting = 1000, Point 2 Northing = 1500, Point 2 Easting = 1350 = 5 input(s) provided
  2. Calculate Horizontal Distance
    Horizontal Distance
    610.328 = 610.328
  3. Calculate Quadrant Bearing
    Quadrant Bearing
    N 34° 59' 31.27" E = N 34° 59' 31.27" E
  4. Calculate Azimuth
    Azimuth
    34.992 = 34.992
  5. Calculate ΔN
    ΔN
    500 = 500

Engine last updated . Checked against 4 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

What is the difference between Azimuth and Quadrant Bearing?

Azimuth is the angle measured clockwise from due north, from 0° to 360°. Quadrant Bearing is the same direction expressed relative to the nearest north or south line, such as N 34° 59' 31" E, which is the format most deeds, plats, and legal descriptions use. The calculator computes azimuth first with an arctangent, then converts it into whichever of the four NE/SE/SW/NW quadrants the angle falls in.

Why doesn't Elevation Difference change the Horizontal Distance?

Horizontal Distance is computed purely from the northing and easting difference — it represents the flat-plane distance you'd measure on a map. Elevation Difference only feeds a second calculation, Slope Distance, which lays a vertical leg over that same horizontal distance and solves a new hypotenuse. Leave it at zero and Slope Distance simply equals Horizontal Distance.

Why does the calculator need coordinates instead of a bearing and distance?

This is the "inverse" direction of survey math — going from known point locations to the bearing and distance between them, the reverse of a "traverse" calculation that starts from a bearing/distance and solves for the next point's coordinates. Field crews typically collect coordinates first, so the inverse calculation is what turns raw GPS or total-station data into a written bearing.

What units does Distance Rods use, and why would I need it?

A rod is a historical survey unit equal to 16.5 feet, still referenced in some older deeds and rural land descriptions in the U.S. The calculator divides the horizontal distance in feet by 16.5 to produce it, alongside chains (66 feet) and meters, so you can match whichever unit an older recorded document used.

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