Survey angular closure calculator

Calculate angular misclosure and adjusted interior angles with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use angular misclosure and adjusted interior angles to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Closed polygon interior angles (degrees)
90.01,89.98,90.02,90
Relative observation weights
1,1,1,1
Angular misclosure (degrees)
0.01
Adjusted interior angles (degrees)
[90.0075,89.9775,90.0175,89.9975]
Per-angle corrections (degrees)
[-0.0025,-0.0025,-0.0025,-0.0025]

Try another scenario

Closed polygon interior angles (degrees)
91.01,89.98,90.02,90.0
Relative observation weights
1,1,1,1
Angular misclosure (degrees)
1.01
Adjusted interior angles (degrees)
[90.7575,89.7275,89.7675,89.7475]
Per-angle corrections (degrees)
[-0.2525,-0.2525,-0.2525,-0.2525]
Calculation method

Calculation method

Angular misclosure (degrees)

Expected sum=(n-2)180; minimize weighted correction squares gives correction∝1/weight.

Adjusted interior angles (degrees)

Expected sum=(n-2)180; minimize weighted correction squares gives correction∝1/weight.

Per-angle corrections (degrees)

Expected sum=(n-2)180; minimize weighted correction squares gives correction∝1/weight.

Symbols and units
a
Closed polygon interior angles (degrees)
b
Relative observation weights

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Assumptions & limits

Assumptions & limits

  • Simple planar closed polygon; observation weights interpreted as inverse variance. Supported limits: All required fields must be finite values of the exact declared type and within displayed bounds. Lists contain1–1000 finite numbers. JSON tables are numeric rectangular rows, at most100 rows and30 columns; individual tools have stricter shape/domain constraints. Simple planar closed polygon; observation weights interpreted as inverse variance.
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