Skip to content
  • Home
  • About
    • Privacy Policy
    • Disclaimer
    • Terms and Conditions
  • Contact Us
Geoscience.blogYour Compass for Earth's Wonders & Outdoor Adventures
  • Home
  • About
    • Privacy Policy
    • Disclaimer
    • Terms and Conditions
  • Contact Us
Posted on April 26, 2022 (Updated on July 23, 2025)

How do you find the sides of an octagon with diameter?

Space & Navigation

Okay, so you want to figure out the side length of an octagon when all you know is its diameter? Sounds simple, right? Well, it can be, but there are a few twists depending on the type of octagon and what you actually mean by “diameter.” Let’s break it down, shall we? Think of this as your friendly guide to octagon side-sleuthing.

First things first: what is an octagon? It’s just a shape with eight sides. Now, if all those sides and angles are equal, we’ve got ourselves a regular octagon – nice and symmetrical. But if they’re all wonky and different lengths, that’s an irregular octagon. And that’s where things can get a bit hairy.

Then there’s the “diameter” question. It’s not as straightforward as you might think. We’re not just talking about circles here! When it comes to octagons, “diameter” could mean a few different things:

  • The Inscribed Circle’s Diameter (Apothem Connection): Imagine the biggest circle you could squeeze inside the octagon, just touching each side. That circle’s diameter is one option. Its radius is called the apothem, which will be useful later.

  • The Circumscribed Circle’s Diameter: Now picture a circle that goes around the octagon, hitting all eight corners. Its diameter is another possibility.

  • Width (Across the Flats): For a regular octagon, this is just the distance between two opposite, parallel sides. Think of it as measuring the octagon at its widest point. This is also the same as the diameter of the inscribed circle.

  • Vertex-to-Vertex Distance: This could be the longest diagonal or some other distance between corners.

  • Cracking the Code: Regular Octagons

    Let’s stick with the regular octagons for now – they’re much easier to deal with.

    1. Circumscribed Circle Diameter (D) is Known:

    • Here’s the magic formula: s = D * sin(π/8) or s = D * sin(22.5°). Basically, the side length (s) is related to the diameter (D) by a sine function. Who knew trigonometry could be so useful?

    • Quick cheat: sin(22.5°) is roughly 0.3827, so you can use s ≈ 0.3827 * D.

    • Example Time: Let’s say that outer circle has a diameter of 10 cm. Then, the side length is about 0.3827 * 10 cm = 3.827 cm. Not bad, eh?

    2. Inscribed Circle Diameter (d) or Width (Across Flats) is Known:

    • Different diameter, different formula: s = d * tan(π/8) or s = d * tan(22.5°). Now we’re using the tangent function.

    • Another shortcut: tan(22.5°) is about 0.4142, giving us s ≈ 0.4142 * d.

    • Example: If that inner circle has a diameter of 10 cm, then the side length is roughly 0.4142 * 10 cm = 4.142 cm.

    3. Got the Apothem (a)?

    • Remember the apothem? It’s half the diameter of the inscribed circle (a = d/2). So, if you know the apothem:

    You may also like

    What is an aurora called when viewed from space?

    Asymmetric Solar Activity Patterns Across Hemispheres

    Unlocking the Secrets of Seismic Tilt: Insights into Earth’s Rotation and Dynamics

    Categories

    • Climate & Climate Zones
    • Data & Analysis
    • Earth Science
    • Energy & Resources
    • General Knowledge & Education
    • Geology & Landform
    • Hiking & Activities
    • Historical Aspects
    • Human Impact
    • Modeling & Prediction
    • Natural Environments
    • Outdoor Gear
    • Polar & Ice Regions
    • Regional Specifics
    • Safety & Hazards
    • Software & Programming
    • Space & Navigation
    • Storage
    • Water Bodies
    • Weather & Forecasts
    • Wildlife & Biology

    New Posts

    • Field Gear Repair: Your Ultimate Guide to Fixing Tears On The Go
    • Outdoor Knife Sharpening: Your Ultimate Guide to a Razor-Sharp Edge
    • Don’t Get Lost: How to Care for Your Compass & Test its Accuracy
    • Your Complete Guide to Cleaning Hiking Poles After a Rainy Hike
    • Headlamp Battery Life: Pro Guide to Extending Your Rechargeable Lumens
    • Post-Trip Protocol: Your Guide to Drying Camping Gear & Preventing Mold
    • Backcountry Repair Kit: Your Essential Guide to On-Trail Gear Fixes
    • Dehydrated Food Storage: Pro Guide for Long-Term Adventure Meals
    • Hiking Water Filter Care: Pro Guide to Cleaning & Maintenance
    • Protecting Your Treasures: Safely Transporting Delicate Geological Samples
    • How to Clean Binoculars Professionally: A Scratch-Free Guide
    • Adventure Gear Organization: Tame Your Closet for Fast Access
    • No More Rust: Pro Guide to Protecting Your Outdoor Metal Tools
    • How to Fix a Leaky Tent: Your Guide to Re-Waterproofing & Tent Repair

    Categories

    • Home
    • About
    • Privacy Policy
    • Disclaimer
    • Terms and Conditions
    • Contact Us
    • English
    • Deutsch
    • Français

    Copyright (с) geoscience.blog 2025

    We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. By clicking “Accept”, you consent to the use of ALL the cookies.
    Do not sell my personal information.
    Cookie SettingsAccept
    Manage consent

    Privacy Overview

    This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.
    Necessary
    Always Enabled
    Necessary cookies are absolutely essential for the website to function properly. These cookies ensure basic functionalities and security features of the website, anonymously.
    CookieDurationDescription
    cookielawinfo-checkbox-analytics11 monthsThis cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Analytics".
    cookielawinfo-checkbox-functional11 monthsThe cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional".
    cookielawinfo-checkbox-necessary11 monthsThis cookie is set by GDPR Cookie Consent plugin. The cookies is used to store the user consent for the cookies in the category "Necessary".
    cookielawinfo-checkbox-others11 monthsThis cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Other.
    cookielawinfo-checkbox-performance11 monthsThis cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Performance".
    viewed_cookie_policy11 monthsThe cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. It does not store any personal data.
    Functional
    Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features.
    Performance
    Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors.
    Analytics
    Analytical cookies are used to understand how visitors interact with the website. These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc.
    Advertisement
    Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. These cookies track visitors across websites and collect information to provide customized ads.
    Others
    Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet.
    SAVE & ACCEPT