Traverse Misclosure Lat Departure Closure Calculator

Description

Calculate planar north/east traverse increments, perimeter and closure-vector magnitude.

Geodesy distinguishes a mathematical reference ellipsoid, a realized coordinate datum and the physical gravity field. Geodetic latitude follows the ellipsoid normal; geocentric latitude follows a radius from the center. Ellipsoidal height, orthometric height and geoid undulation are separate signed quantities. Keep the declared ellipsoid, coordinate axes, angular units and time scale with a result.

Calculate planar north/east traverse increments, perimeter and closure-vector magnitude.

When to use this tool

Use this tool when you need to calculate planar north/east traverse increments, perimeter and closure-vector magnitude.

How to use the tool and how it works

Enter lengthsMeters, azimuthsDegrees using the definitions below.
Run the operation. Resolve input-format errors before interpreting an output.
Read result.northMeters, result.eastMeters, result.closureNorthMeters, result.closureEastMeters, result.perimeterMeters, result.misclosureMeters, using the stated boundary, ordering, sign and absence conventions.

For every aligned positive length and azimuth, calculate north=L cos(azimuth) and east=L sin(azimuth), using clockwise-from-north degrees. Sum north and east components, sum lengths for perimeter, and return their closure-vector magnitude.^[1]

Input field	Meaning and units	Accepted input
lengthsMeters	Nonempty aligned leg lengths in meters, each strictly positive and at most 10⁶.	Dense list of at most 128 finite numbers, under the stated integer/range rules.
azimuthsDegrees	Clockwise-from-north leg azimuths in degrees, each in [0,360), aligned to lengthsMeters.	Dense list of at most 128 finite numbers, under the stated integer/range rules.

Output field	Interpretation
result	Object containing the fields below.
result.northMeters	North increments per leg, in input order, including adjustment when this operation applies one.
result.eastMeters	East increments per leg, in input order, including adjustment when this operation applies one.
result.closureNorthMeters	Sum of north increments before any adjustment, in meters.
result.closureEastMeters	Sum of east increments before any adjustment, in meters.
result.perimeterMeters	Sum of positive supplied leg lengths in meters.
result.misclosureMeters	Euclidean magnitude of the unadjusted closure vector, in meters.

json

{
  "input": {
    "lengthsMeters": [
      1,
      1
    ],
    "azimuthsDegrees": [
      0,
      90
    ]
  },
  "output": {
    "result": {
      "northMeters": [
        1,
        6.123233995736766e-17
      ],
      "eastMeters": [
        0,
        1
      ],
      "closureNorthMeters": 1,
      "closureEastMeters": 1,
      "perimeterMeters": 2,
      "misclosureMeters": 1.4142135623730951
    }
  }
}

Limitations and assumptions

At least one leg is required, each length at most 10⁶ m and each azimuth in [0,360). North/east are planar increments, not geodetic latitude/longitude; grid convergence, slope reduction and angular balancing are separate.
All quantities are finite and retain the units stated for this operation. Ellipsoid-parameter tools use semi-major axis 1–10⁸ m and dimensionless flattening 0–0.02; explicit-axis tools use 0.9a≤b≤a unless a tighter bound is stated. These tools do not fetch datums, geoid grids, satellite observations or Earth-orientation updates.
Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
Numeric results must be finite. Large physical magnitudes are allowed by the output evidence checks, while integer fields and source schemas retain their exactness rules. Source indexes are zero-based. Floating-point residues can remain even where an ideal formula gives an exact zero.

Alternative or Complementary methods

Use a coordinate transform for a change of representation and explicit datum parameters for a change of reference frame. Preserve model and convergence metadata, and use observation and datum information appropriate to a real survey before interpreting a computed tolerance as accuracy.

References

Tool behavior and example: Traverse Misclosure Lat Departure Closure Calculator — tool.io

Similar or alternative tools

Compass Rule Adjustment Distributor for Traverse
Distribute planar traverse closure by leg length using the Bowditch or compass rule.
Transit Rule Alternative Adjustment Distributor
Distribute planar traverse closure using the transit rule and return corrected coordinates.