targas-edu.de
DE ☾ A+

Gradians (gon)

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

There is a third angle measure: the gradian, also called gon (das Neugrad). You learn how many gon a circle has and how to convert between gon, degrees and radians.
📄 Open worksheet (PDF, German)

The video

In the video you see the circle with \(100\), \(200\), \(300\) and \(400\) gon. Then you compare all three measures in a table.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction: a third measure
  2. 0:14 The circle in gon
  3. 0:28 Converting
  4. 0:52 Three measures compared
  5. 1:18 Careful, mistake!
  6. 1:36 Try it yourself

The most important points

The circle in gon

Full circle: \(400\) gon. Half circle: \(200\) gon. Right angle: exactly \(100\) gon. Four right angles make \(400\) gon.

The circle in gon: 100, 200, 300, 400.
The circle in gon: \(100\), \(200\), \(300\), \(400\).

Converting

\(400\) gon \(= 360^\circ\), so \(1\) gon \(= 0{,}9^\circ\). Degrees \(=\) gon \(\cdot\, 0{,}9\). Gon \(=\) degrees \(\cdot \frac{10}{9}\). Example: \(45^\circ \cdot \frac{10}{9} = 50\) gon.

Converting between gon and degrees.
Converting between gon and degrees.

Three measures compared

\(90^\circ = 100\) gon \(= \frac{\pi}{2}\). \(180^\circ = 200\) gon \(= \pi\). \(270^\circ = 300\) gon \(= \frac{3\pi}{2}\). \(360^\circ = 400\) gon \(= 2\pi\).

Degrees, gon and radians in one table.
Degrees, gon and radians in one table.

Careful: \(100\) gon is not \(100^\circ\). A right angle has \(90^\circ\), but \(100\) gon. GeoGebra does not know gon: first convert to degrees, then write the degree sign.

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
Page 1/4
The worksheet – Page 2
Page 2/4
The worksheet – Page 3
Page 3/4
Show the worksheet solutions
The worksheet – Page 4
Page 4/4

Try it yourself

Task

Convert \(60\) gon to degrees. Then convert \(30^\circ\) to gon.

Show solution

\(60 \cdot 0{,}9 = 54^\circ\). \(30 \cdot \frac{10}{9} \approx 33{,}3\) gon.

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Neugrad (Gon, Umrechnen zwischen Gon, Grad und Bogenmaß). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.