A closed traverse walks around a parcel and returns — or is supposed to return — to where it started. It never quite does, and the distance by which it misses is the closure error. That single number decides whether a set of measurements is good enough to use, and it is computed from two quantities that do all the work in traverse mathematics: latitudes and departures. This guide covers the computation, the precision it implies, and the adjustment that follows.
Each leg of a traverse has a length and an azimuth. Resolve every leg into a north-south component and an east-west component:
The latitude is positive north and negative south; the departure is positive east and negative west. In a perfect closed traverse, the latitudes sum to zero and the departures sum to zero, because the path has gone exactly as far north as it went south. Those two sums are the residual misclosures in each axis:
The two axis residuals combine into one distance, the linear misclosure:
A linear misclosure on its own tells you nothing, because 50 mm is excellent on a ten-kilometre traverse and poor on a hundred-metre one. What makes it interpretable is the ratio of the total traverse length to the misclosure, called the relative precision:
Take a closed loop with a perimeter of 521.02 m whose latitudes sum to +0.038 m and whose departures sum to +0.021 m.
| Step | Working | Result |
|---|---|---|
| Linear misclosure | √(0.038² + 0.021²) = √(0.001444 + 0.000441) | 0.0434 m |
| Relative precision | 521.02 ÷ 0.0434 | 1 : 12,000 |
| Latitude correction, 130.00 m leg | −0.038 × 130.00 ÷ 521.02 | −0.0095 m |
| Departure correction, same leg | −0.021 × 130.00 ÷ 521.02 | −0.0052 m |
A relative precision of 1:12,000 means that after walking 12,000 metres the traverse could miss its starting point by one metre. For a loop measured with a total station over ordinary ground, that is a good result.
| Relative precision | Typical measurement class | Reading |
|---|---|---|
| 1 : 2,000 | Compass and tape, rough terrain | Usable for reconnaissance only |
| 1 : 5,000 | Ordinary total station work | Acceptable for many boundary and topographic jobs |
| 1 : 10,000 | Careful total station work | Comfortably within most cadastral requirements |
| 1 : 20,000 | High-order control, good geometry | Control networks and precise traverses |
| 1 : 50,000 and better | GNSS-assisted or specialist | Geodetic-grade work |
These bands are indicative only. The acceptable precision is whatever the governing standard for the jurisdiction and the class of survey states, and it varies — some cadastral rules are expressed as an allowable misclosure in metres rather than as a ratio, and some specify different values for urban and rural work. Check the standard, not the table.
Once the misclosure is judged acceptable, it is distributed across the legs so that the traverse closes exactly. The compass rule, also called the Bowditch rule, distributes in proportion to leg length:
The corrections carry the opposite sign to the residuals, so that applying them cancels the error rather than doubling it. The assumption behind the compass rule is that the angular and linear errors are of comparable magnitude and are distributed evenly along the traverse — which is a reasonable model for a measured traverse and a poor one for a traverse whose error is concentrated in a single suspected leg.
Where the error is known to be concentrated, or where the geometry is high-value, a least squares adjustment is used instead: it minimises the sum of the squares of the corrections, weighting each observation by its expected precision, and it returns an assessment of the residuals and their uncertainty rather than a single set of adjusted coordinates.
Check the angular closure first. A traverse that closes in distance still has to close in angle, and a systematic angular error will distribute itself into a neat-looking displacement that hides its cause. Check the sum of the interior angles against the expected total for the number of sides before you look at the linear misclosure at all. A well-closing traverse built on a misread bearing is a trap: it can look excellent in the ratio and still be metres from the truth.
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