Polygon Diagonals from Sides

Calculate the number of diagonals in a polygon from the number of sides.

Author

Prof. Mei-Ling Wu

Math editorial contributor

Taiwanese genomics researcher at National Taiwan University, leading studies on pharmacogenomics in East Asian populations

Reviewed by

Prof. Kenji Tanaka

Math content reviewer

Japanese materials scientist at Kyoto University, known for breakthroughs in sustainable polymer research

Last updatedFebruary 22, 2026

PublishedFebruary 22, 2026

Table of Contents

  1. Reference values
  2. Calculator
  3. Reference table
  4. FAQs
  5. Methodology and review
  6. Related conversions

20 Number of Sides =

170 Diagonal Count

Representative value from the Polygon Diagonals from Sides reference table.

Reference Values

Browse 20 reference values with individual detail pages for quick lookup.

Browse all reference values

Polygon Diagonals from Sides

Calculate the number of diagonals in a polygon from the number of sides.

Calculated Result

Reference Table

Use this complete table for quick lookup and internal linking to specific value pages.

Polygon Diagonals from Sides Reference
Number of SidesDiagonals
3 Number of Sides0 Diagonal Count
4 Number of Sides2 Diagonal Count
5 Number of Sides5 Diagonal Count
6 Number of Sides9 Diagonal Count
7 Number of Sides14 Diagonal Count
8 Number of Sides20 Diagonal Count
9 Number of Sides27 Diagonal Count
10 Number of Sides35 Diagonal Count
12 Number of Sides54 Diagonal Count
15 Number of Sides90 Diagonal Count
20 Number of Sides170 Diagonal Count
24 Number of Sides252 Diagonal Count
30 Number of Sides405 Diagonal Count
40 Number of Sides740 Diagonal Count
50 Number of Sides1,175 Diagonal Count
60 Number of Sides1,710 Diagonal Count
100 Number of Sides4,850 Diagonal Count
180 Number of Sides15,930 Diagonal Count
360 Number of Sides64,260 Diagonal Count
720 Number of Sides258,120 Diagonal Count

Frequently Asked Questions

Common questions about Polygon Diagonals from Sides, formulas, and typical use cases.

What does the Polygon Diagonals from Sides calculator do?

It helps with counting diagonals in polygon geometry and combinatorics-style shape problems.

What formula does the Polygon Diagonals from Sides calculator use?

Polygon diagonals = n × (n - 3) / 2.

What inputs are valid?

The number of sides must be an integer greater than or equal to 3.

When would I use this?

counting diagonals in polygon geometry and combinatorics-style shape problems

Methodology and Review

This page combines a live calculator, precomputed reference values, and FAQ content from the same conversion definition to reduce mismatch between calculator output and lookup tables.

Editorial metadata (author, reviewer, and update date) is rendered on the page and in structured data. See our editorial policy, review process, and corrections policy.

For compliance-sensitive work, verify final values against project requirements, governing standards, and manufacturer documentation.