Degrees to Gradians (° → gon)

Degrees to Gradians Conversion

Gradians divide a right angle into 100 units, so a full circle has 400 gradians. The conversion uses a scale factor of 10/9 (since 360 degrees correspond to 400 gradians). Surveying and civil engineering use gradians for metric-friendly angle measurements.

Sources: NIST Guide for the Use of the SI

Degrees → Gradians

Converting Degrees (°) to Gradians (gon) is a common angle conversion. 1 ° equals 1.111111 gon. For example, 100 ° is equal to 111.111111 gon.

Quick Mental Math: Degrees to Gradians

Multiply degrees by 1.111 (10/9) to estimate gradians.

Why is converting Degrees to Gradians tricky?

Confusion arises because gradians are less common and have a different base circle division than degrees.

Quick Reference Values

1 ° = 1.111111 gon. 5 ° = 5.555556 gon. 10 ° = 11.111111 gon. 25 ° = 27.777778 gon. 50 ° = 55.555556 gon. 100 ° = 111.111111 gon.

What is Degrees?

Degrees (°) is a unit of angle. A degree is a unit of angular measurement defined as 1/360 of a full rotation or circle. One degree equals exactly π/180 radians, aligning with the International System of Units (SI) conventions for angles. It is commonly used in geometry, navigation, and geospatial coordinates to measure angles and directions [iso-80000]. The degree originated with the ancient Babylonians around 3000 BCE, who divided a circle into 360 parts likely based on their sexagesimal numeral system. This system was formalized over centuries and incorporated into modern angle measurement standards. The consistent division into 360 degrees became globally accepted due to its mathematical convenience and historical use [iso-80000]. Degrees are used worldwide in navigation, astronomy, cartography, and engineering. Countries including the United States, Canada, and members of the European Union employ degrees for geographic coordinates. Scientific organizations such as ISO and BIPM recognize degrees as a standard unit for angles [bipm-si-brochure].

What is Gradians?

Gradians (gon) is a unit of angle. A gradian, also called a gon, is an angular unit where one full circle equals 400 gradians. Each gradian equals 0.9 degrees or π/200 radians. This unit facilitates decimal subdivision of right angles and is defined by international standards for angular measurement [bipm-si-brochure]. Gradians were introduced in the late 18th century during the French Revolution to simplify angle calculations using a decimal system. The unit was later adopted by the ISO and BIPM as part of supplementary units to the SI [bipm-si-brochure]. Gradians are used in surveying, geodesy, and cartography, particularly in Europe, including France and Germany. They provide a convenient decimal-based alternative to degrees for precise angular measurements [nist-si-guide].

Common Misspellings

People often search for this conversion using these alternate spellings: degres, degreess, degreees, degre, degr, gradian, graden, gradian. All of these refer to the Degrees to Gradians conversion.

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