Three independent tolerance gauges for sides, angle mean, and angular closureUpdates with every input
Math & Statistics
Polygon Verification Calculator
Audit whether measured side lengths and interior angles are consistent with a claimed regular polygon, keeping side spread, angle closure, tolerance compliance, and pass/fail evidence separate.
Regularity verdict -
Ideal interior angle -
Worst side deviation -
Mean-angle error -
Angle-sum closure error -
Side gate -
Angle gate -
Closure gate -
REGULARITY CONFORMANCE
Three independent tolerance gauges for sides, angle mean, and angular closure
Each gauge compares measured error with its own allowed limit, preventing one good metric from hiding another failed condition.
CONFORMANCE RECORD
Claimed geometry tested against explicit acceptance gates
The audit distinguishes dimensional equality from angular equality and total closure.
| Check | Observed | Ideal | Absolute error | Allowed error | Status |
|---|
INSPECTION SETUP
Use measurements from the same physical polygon
- Record the claimed whole side count.
- Compute the mean, minimum, and maximum from all sides.
- Enter the mean of all measured interior angles.
- Enter their measured total independently.
- Set tolerances from the applicable drawing or inspection plan.
WHY THREE GATES
Equal-looking sides do not prove correct angular closure
A polygon can have nearly equal sides but distorted angles. It can also have a plausible mean angle while individual or accumulated measurement errors create poor closure.
This summary cannot replace point-by-point metrology, but it makes the acceptance logic explicit and prevents averaging from silently erasing the largest side deviation.
Subject fundamentals
Five ideas that control this calculation
Regularity needs both sides and angles
Near-equal sides alone cannot show that vertices follow the intended angular pattern or that the boundary closes correctly.
Worst deviation is intentionally retained
The side gate uses the largest departure from the entered mean so opposite high and low measurements cannot cancel in an average.
Ideal angle depends on n
A regular n-gon has interior angle 180(n-2)/n degrees and total interior-angle sum 180(n-2) degrees.
Per-angle and closure tolerances differ
The entered angular tolerance governs the mean-angle gate; multiplying it by n creates the separate accumulated closure allowance.
A pass is conditional evidence
The verdict means the supplied summaries meet the entered gates. It does not prove unmeasured sides, corners, planarity, or datum quality.
REGULARITY AUDIT
A regular polygon must pass both equality and closure tests
The ideal interior angle and angle sum come from n. Side extremes are compared with the measured mean; angular measurements are checked against the ideal mean and total.
Detailed calculation process and general formulas
beta = 180(n - 2) / nS_beta = 180(n - 2)e_s = max(|s_min-s_bar|, |s_max-s_bar|) / s_bare_beta = |beta_bar-beta|e_sum = |S_measured-S_beta|Symbols, meanings, and units
- n
- claimed side countcount
- s_bar
- mean measured sidelength
- e_s
- worst relative side deviationpercent
- beta
- ideal regular interior angledegrees
- e_beta
- mean-angle deviationdegrees
- e_sum
- angle-sum closure errordegrees
AUDIT INTERPRETATION
Read a failed gate as a diagnostic direction
The three tests point toward different follow-up work.
Side gate
-A failure suggests unequal edges, scale error, or an incorrect mean.
Mean-angle gate
-A failure suggests systematic angular distortion.
Closure gate
-A failure suggests cumulative angular error or inconsistent observations.
Decision takeaway: A regularity claim passes only when all selected acceptance gates pass.
MEASUREMENT RECORD
Retain these items with the verdict
- Instrument and calibration
- Measurement temperature
- Individual side readings
- Individual angle readings
- Datum convention
- Specified tolerances
Applied decisions
How the audit distinguishes failure modes
Fabricated hexagonal frame
Side lengths are consistent but the angle total is high.
What the result clarifies: The closure gauge flags assembly distortion that a perimeter check would miss.
Surveyed parcel sketch
Angles close well but one side differs materially from the mean.
What the result clarifies: The side gate prevents the figure from being called regular.
Worked default scenario
Current-input substitution and reconciliation
Key terms
Glossary for interpreting the result
- Regularity gate
- A stated acceptance test for one required aspect of regular geometry.
- Side deviation
- The largest side departure from the entered mean, expressed as a percentage.
- Ideal interior angle
- The common angle required by a regular polygon with n sides.
- Closure error
- The absolute difference between measured and theoretical interior-angle sums.
- Tolerance
- The maximum allowed deviation chosen from a specification or measurement plan.
- Datum convention
- The reference orientation or baseline from which measurements are taken.
Method references
References for this calculator's specific method
Scope and limitations
This is a summary-level tolerance audit. It does not test every individual angle, diagonal, vertex coordinate, flatness, or uncertainty correlation. Use the governing drawing and metrology procedure for acceptance.
Polygon Verification Calculator | Regularity Tolerance Audit FAQ
Does passing prove the polygon is perfectly regular?
No. It shows the entered summary measurements satisfy the entered tolerances.
Why check both mean angle and angle sum?
They reveal systematic deviation and cumulative closure using different summaries.
What tolerance should I use?
Use the project specification, drawing, survey standard, or inspection plan rather than an arbitrary default.
Can side units differ?
No. Mean, minimum, and maximum side values must use the same unit.