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Traverse Closure Error

Also known as misclosure · closure error

Ec=(ΣLat)2+(ΣDep)2E_c = \sqrt{\left(\Sigma\text{Lat}\right)^{2} + \left(\Sigma\text{Dep}\right)^{2}}
sig figs

Worked example: 10 cm misclosure with 8 cm of departure → 0.06 m of latitude. Press Try an example to run it live, then adjust anything.

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Where Traverse Closure Error fits

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Traverse Precision Ratio
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See also

Departure of a Traverse Leg: Both use sum of the departures.Latitude of a Traverse Leg: Both use sum of the latitudes.Traverse Precision Ratio: Both use linear closure error.
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Traverse Closure Error explained

EcΣDepΣLat

Walk a closed traverse and you finish where you started, so in a perfect world the latitudes sum to zero and so do the departures. They never do. Whatever is left over is the misclosure, and because the two residuals are perpendicular the total error is their hypotenuse. The direction of that closing line is informative too: a misclosure that lies consistently along one bearing usually means a systematic problem such as an uncalibrated tape or a mis-set instrument height, while a randomly oriented one is ordinary measurement noise.

A worked example: a five-sided boundary traverse closes with ΣLat = +0.24 ft and ΣDep = −0.32 ft. The linear misclosure is √(0.24² + 0.32²) = 0.40 ft: a tidy 3-4-5 triangle. Whether 0.40 ft is acceptable depends entirely on the perimeter, which is why the closure error is almost always quoted as a precision ratio rather than a raw length. Before adjusting anything by the compass rule or least squares, check the angular closure first: an angle blunder shows up as a misclosure that no distance adjustment can absorb.

Traverse Closure Error formula

Ec=(ΣLat)2+(ΣDep)2E_c = \sqrt{\left(\Sigma\text{Lat}\right)^{2} + \left(\Sigma\text{Dep}\right)^{2}}
Where
  • EcE_c= Linear closure error (m)
  • ΣLat\Sigma\text{Lat}= Sum of the latitudes (m)
  • ΣDep\Sigma\text{Dep}= Sum of the departures (m)
In this toolkit

Survey traverse closure

6 formulasClosing a traverse: latitudes and departures per leg, the misclosure they expose, and the precision ratio that decides whether it passes.

Revised 16 October 2026
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formula.expert. (2026, October 16). Traverse Closure Error Formula & Calculator. https://formula.expert/solvers/traverse-closure-error

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