90
°
1.57079633
rad
0.25
rev
1,570.796327
mrad
90
°
1.57079633
rad
0.25
rev
1,570.796327
mrad
The Gradians to Degrees Converter converts angular measurements from gradians (also known as gons or grades) to degrees and radians. The gradian is a unit where a full circle is divided into 400 equal parts, making a right angle exactly 100 gradians. This clean decimal relationship is why gradians are popular in surveying, civil engineering, and geodesy.
The gradian was introduced during the French Revolution as part of the broader metrication effort. The goal was to create a decimal-based angle system that would complement the metric system of lengths and masses. While gradians never achieved the universal adoption of degrees or radians, they remain the standard angle unit in many surveying instruments manufactured in Europe, especially in France, Germany, and Scandinavia.
The conversion is straightforward: 1 gradian = 0.9 degrees, because 360°/400 = 0.9. So 100 gon = 90°, 200 gon = 180°, and 400 gon = 360°. The advantage of gradians is that compass directions fall on clean numbers: North = 0/400 gon, East = 100 gon, South = 200 gon, West = 300 gon.
Our converter also provides the equivalent in radians, which is useful when transitioning from survey data to scientific computations or programming environments that use radian-based trigonometry.
The formulas: degrees = gradians × 0.9 and radians = gradians × 0.9 × pi/180, or equivalently radians = gradians × pi/200. These factors come from: 360° = 400 gon, so 1 gon = 360/400 = 0.9°.
Key conversions: 100 gon = 90° (right angle), 200 gon = 180° (straight line), 400 gon = 360° (full rotation). When reading European survey data, angles are commonly in gradians. North American surveys typically use degrees or DMS.
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100 gon = 90°
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400 gon = 360°
A gradian (gon or grade) is 1/400 of a full rotation. A right angle = 100 gradians, a straight angle = 200 gradians, a full circle = 400 gradians.
Multiply by 0.9. Since a full circle = 400 gon = 360°, each gradian equals 360/400 = 0.9 degrees.
Gradians were created during the French Revolution (1790s) to decimalize angle measurement, complementing the metric system. The goal was a base-10 system where a right angle = 100 units.
Surveyors in France, Germany, and several European countries routinely use gradians. Many survey-grade total stations and theodolites have a gradian mode.
Full circle: 400 gradians = 360 degrees = 2pi radians. Right angle: 100 gon = 90° = pi/2 rad. Each system has its strengths for different applications.
45° = 50 gradians. Divide degrees by 0.9 (or multiply by 400/360) to convert degrees to gradians.
Most languages don't have built-in gradian support, but conversion is simple: radians = gradians × pi/200. Some scientific calculators have a 'GRAD' mode.
Right angles and compass directions are clean decimal numbers (0, 100, 200, 300, 400). Percentage of slope corresponds directly to gradians near small angles. Easy mental arithmetic for perpendicular angles.
50 gradians = 45 degrees. This is half a right angle.
No, you must convert to a single unit first. Mixing units will produce incorrect results. Our converter helps you standardize to whichever unit your application requires.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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