Zerdly

Angular Misclose Calculator

Compares summed interior angles against the theoretical total and reports the angular misclose and correction.

100% FreeRuns in your browserIntermediate
How to use this calculator

Inputs

Expected sum, signed misclose and the equal correction for a closed polygon's interior angles.

A closed polygon has at least 3. Reflex (concave) angles are allowed.

The sum of your observed interior angles, unadjusted.

More options
″

Your project's own c in c × √n seconds. No standard is assumed.

Enter the values and press Calculate.

Or load an example to see a worked result.

Your closure
Schematic
Your closureSchematic closed polygon.n = 5Expected (n − 2) × 180°Observed ΣMisclose = Σ − expectedCorrection = −misclose ÷ nSchematic polygon
Calculate to show your expected sum, misclose and correction.

Angle table

Enter each interior angle to see every correction and adjusted angle. Reflex angles over 180° are fine.

How the method works

Interior-angle closure
Illustrative method
Interior-angle closureA five-sided closed polygon with its interior angles marked, beside the expected sum, the misclose and the equal correction.n = 5Expected (n − 2) × 180° = 540°Observed Σ = 540° 03′ 00″Misclose = +180″Correction = −180″ ÷ 5 = −36″Schematic polygon
Five interior angles should sum to (5 − 2) × 180° = 540°. Observed 540° 03′ 00″ gives a misclose of +180″; the equal correction is −180″ ÷ 5 = −36″ per angle, and the corrected angles sum to exactly 540°. Signs stay with the misclose: correction = −misclose.

Fixed example values for illustration — not your result.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Enter the number of interior angles and their measured sum (DD, DMS or DDM).
  2. Optionally enter your project's tolerance constant c to compare the misclose with c × √n seconds.
  3. Read the misclose and the equal correction per angle, with the working.
  4. The angle sum can be typed in decimal degrees, DMS, DDM or gon. The closure diagram and the result update together; Keep as A compares two cases, and the angle table below takes each angle and an optional weight.

How it works

The interior angles of a closed n-sided polygon sum to (n − 2) × 180°. Misclose = measured sum − expected sum, and an equal correction gives each angle −misclose ÷ n.

Equal distribution suits angles of similar quality. With observation weights (inverse variance) each correction is −misclose × (1/wᵢ) ÷ Σ(1/w), so a less-trusted angle (smaller weight) takes the larger share — weights of 1 and 4 split it 80% / 20%.

Concave polygons have reflex interior angles over 180°; those are fine. Exterior, deflection and direction-set traverses follow other closure rules.

Worked example

5 angles summing to 540.05°. Expected 540°, misclose +0.05° = +180″, so −36″ per angle; the corrected angles sum to exactly 540°.

Common mistakes

  • Using exterior angles with the interior formula — exterior angles of a closed figure sum to (n + 2) × 180°.
  • Forcing every angle below 180° in a concave figure.
  • Rounding each correction and not redistributing the leftover seconds.

Frequently asked questions

Interior or exterior angles?

This uses interior angles. Exterior angles of a closed figure sum to (n + 2) × 180°.

What tolerance should I use?

Your project's. Enter its constant c and the tool compares the misclose with c × √n seconds; no default standard is applied.

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Cite this tool

Zerdly. (2026). Angular Misclose Calculator. Retrieved from https://www.zerdly.com/tools/angular-misclose-calculator/

Tip: Enter any known values to calculate the remaining results.

Designed to run locally in your browser. Tool inputs are not intentionally stored by Zerdly unless stated otherwise.