Convert Angle from gradians (grad) to other units

gradian Conversion Formulas

gradian to radian Conversion Formula

gradian to degree Conversion Formula

gradian to arcminute Conversion Formula

gradian to arcsecond Conversion Formula

What is a Gradian?

While most of us learn about measuring angles in degrees, there's another unit of angle measurement called the gradian.

A gradian (often abbreviated as grad) is a unit of angle equal to 0.9 (or 9/10) of a degree. It's an alternative to degrees and radians, designed to make some calculations simpler.

How Many Gradians Are in a Circle?

Unlike the familiar 360-degree system, a full circle is divided into 400 gradians.

This base-100 system simplifies many geometric calculations:

• A right angle is exactly 100 gradians.
• A straight angle is 200 gradians.
• A three-quarter turn is 300 gradians.

This makes it an intuitive framework for certain types of angular math.

How Do You Convert Gradians to Degrees?

The conversion between gradians and degrees is straightforward.

Here is the simple gradians to degrees formula:

• Gradians to Degrees: Multiply the gradian value by 0.9.
• Degrees to Gradians: Multiply the degree value by 10/9 (approximately 1.11).

For example, to convert 200 gradians to degrees, you would calculate: 200 grad × 0.9 = 180 deg.

What is the Relationship Between Gradians and Radians?

When comparing radians vs. gradians, the relationship is key for trigonometry and higher math.

A full circle is 400 gradians or 2π radians.

This means that 200 gradians are equal to π radians. The conversion factor, π/200, is fundamental for calculations that bridge these two systems.

Why Use Gradians?

So, why use this system at all?

Gradians are primarily used in specific professional fields like surveying and some branches of engineering, especially in Europe.

The decimal-based nature of the 400-gradian circle simplifies calculations involving right angles, making fieldwork and topographical analysis more efficient.

Where Gradians Survive Today

The gradian is the rarest of the three common angle units, but it has not disappeared — it has retreated into a few specific places.

• Continental European surveying. French, Swiss, Austrian and some German cadastral practice still works in gradians, where the unit is often called the gon. A quadrant is exactly 100 gon, so a bearing can be read and written without ever leaving decimal arithmetic.
• Total stations and survey instruments. Many instruments ship with a unit selector offering degrees, gradians and mils, precisely because a crew may have to match whatever the existing site records use.
• Calculators. The DEG / RAD / GRAD switch on nearly every scientific calculator is the unit's most widely seen trace — and the most common way people encounter it by accident.

That last point is worth a warning. A calculator left in GRAD mode returns answers that look reasonable but are wrong by a factor of 0.9 against degrees. If a trigonometric result is off by roughly ten percent and nothing else explains it, check the mode before checking the formula.

The quick conversions are:

• 1 gradian = 0.9 degrees; 1 degree = 1.111… gradians
• A right angle is 100 gradians, a full turn is 400
• 1 gradian ≈ 0.015708 radians