Team Physics -
Created by: Team Physics -, Last Updated: April 25, 2024


What is Gradian?

Gradian is a unit of angular measurement equal to 1/400th of a circle, commonly used in surveying, mapping, and some European educational contexts. Each gradian subdivides into 100 centesimal minutes.

Gradians = Degrees × (200/180)

Additional Formula

From Radians to Gradians

Gradians = Radians×(200/π)

From Gradians to Degrees

Degrees = Gradians×(180/200)

From Gradians to Radians

Radians = Gradians×(π/200)

Examples of Gradian


A land surveyor measures a field boundary angle as 100 gradians to ensure accurate mapping.

2. Civil Engineering

Engineers design a road curve that subtends an angle of 50 gradians for safe and efficient traffic flow.

3. Mathematics Education

A math teacher uses an angle of 25 gradians in a geometry problem to teach students about angular measurements.

4. Mapping

Cartographers might denote a 150-gradian angle on a new map to represent specific landmark orientations.

5. Construction

In constructing a pentagon, each internal angle might be set to approximately 158.4 gradians for precision.

6. Artillery

Military uses, such as calculating the firing angle for an artillery piece, often involve measurements like 75 gradians.

7. Astronomy

Astronomers might use a small angular measurement of 1 gradian to track the movement of a star across the sky.

8. Robotics

A robotic arm might rotate 80 gradians to position itself to pick up an object correctly.

9. Navigation

Navigators might use gradians to measure the bearing between two points in a navigation chart.

10. 0 grad

This represents a zero angle, where no rotation from the reference line is observed.

Conversion of Gradian into Other Units

Arcsecond36 gradian
Degree0.9 gradian
Milliradian15.708 gradian
Minutes of arc54 gradian
Radian0.0157 gradian

Gradian(grad) to Arcsecond(arc)

1 Gradian(grad) = 36 Arcsecond(arc)

One gradian equals 3600 arcseconds, a unit used in precise angular measurements in astronomy and geodesy.

Gradian(grad) to degrees(°)

1 Gradian(grad) = 9⁰/10 (0.9 degrees)

One gradian equals 0.9 degree, a unit used for measuring angles, especially in surveying and certain educational contexts.

Gradian(grad) to Milliradian

1 Gradian(grad) = 15.708 Milliradian

One gradian is equivalent to approximately 15.708 milliradians, used in ballistics, optics, and other precision scientific calculations.

Gradian(grad) to Minutes of arc

1 Gradian(grad) = 54 Minutes of arc

One gradian is equal to 54 minutes of arc, a measurement unit commonly used in astronomy and navigation.

Gradian(grad) to Radians(rad)

1 Gradian(grad) = π/200​ radians

One gradian is equivalent to π/200 radian, a measurement used in angles, particularly beneficial in surveying and geometry.

Uses of Gradian

  1. Angular Measurement: Gradians, also known as grads or gon, are a unit of angular measurement that divides a circle into 400 equal parts. This makes calculations involving angles more convenient in certain applications.
  2. Surveying: Gradians are commonly used in surveying, particularly in European countries, for measuring angles in land surveying and construction projects. They offer a straightforward alternative to degrees and radians.
  3. Military and Navigation: Gradians are also used in military and navigation applications. In some contexts, such as artillery targeting or compass bearings, gradians provide a simple and precise way to communicate directions and angles.
  4. Trigonometric Calculations: While degrees and radians are more prevalent in mathematics and physics, gradians can be useful in trigonometric calculations, especially when dealing with regular polygons or circular measurements that are multiples of 100.
  5. Engineering and Architecture: In engineering and architecture, gradians are occasionally used for specific calculations and drawings, especially in regions where the metric system is predominant.
  6. Educational Purposes: Gradians are sometimes introduced in educational settings as an alternative angle measurement unit. They can help students understand the concept of angles and provide a different perspective on angular measurement.


Where are Gradians commonly used?

Gradians are commonly used in fields like surveying, navigation, military, and certain trigonometric calculations.

What is the relationship between Gradians and Radians?

One full rotation in radians is equal to 2π radians, while in gradians it is equal to 400 gradians.

Can Gradians be used for precise measurements?

Yes, in certain applications like artillery targeting or compass bearings, gradians offer a simple and precise way to communicate directions and angles.

What is the abbreviation for Gradians?

The abbreviation for Gradians is “grad” or sometimes “gon”.

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