Surveying & Geomatics
Intermediate

Relative Precision

Closure error expressed as a fraction of the traverse perimeter.

Formula

RP=EPRP = \frac{E}{P}

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Variables

RPRelative precision
EClosure error
PPerimeter length

Example

E=0.5 m, P=1000 m: RP = 1/2000

How it works

Relative precision compares the size of a traverse’s closure error to the total length of the traverse, so it tells you how large the misclosure is in proportion to the work done. It works because a longer traverse can tolerate a larger absolute error than a short one, so dividing the closure error by the perimeter gives a fair, scale-independent measure of quality. The smaller the value of RP, the better the traverse has closed.

When to use it

Use this when assessing the quality of a closed traverse in surveying, especially after field measurements are adjusted and you want to report the accuracy of the survey. It is also useful when comparing the reliability of different traverses that have different sizes.

Worked example, step by step

Given: closure error E = 0.24 m and perimeter length P = 600 m Step 1: Write the formula: RP = E / P Step 2: Substitute the values: RP = 0.24 / 600 Step 3: Calculate: RP = 0.0004 Step 4: Express as a ratio: 1 / 2500 Final answer: RP = 1/2500 (or 0.0004)

Common mistakes to avoid

  • Using the area of the traverse instead of the perimeter length
  • Forgetting that relative precision is a ratio, so the result should usually be written as 1 in N form
  • Mixing up closure error with an individual line error or applying the formula before the traverse is properly closed

Did You Know?

A precision of 1/5000 or better is typically demanded for boundary surveys.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026