Convert Gradians to Degrees

To convert gradians (gon) to degrees (°), use the fact that a full circle equals 400 gradians and 360 degrees.

• Conversion formula:
  degrees = gradians × 0.9
  (Because 360 ÷ 400 = 0.9)

• Exact fraction form:
  degrees = gradians × (9/10)

• Quick examples (gradian to degree conversion):

  • 100 gradians = 90°
  • 200 gradians = 180°
  • 50 gradians = 45°
  • 400 gradians = 360°

Tip: If you need a fast mental method, take 10% off the gradians value. The result is the angle in degrees.

What is a gradian (gon) in angle measure?

A gradian, also called a gon, is a unit used to measure angles. It splits a full circle into 400 equal parts. This makes right angles easy to work with, since a right angle is 100 gradians.

How many degrees are in one gradian?

One gradian equals 0.9 degrees. Degrees split a full circle into 360 parts, while gradians split it into 400 parts. Since 360/400 = 0.9, each gradian is slightly smaller than one degree.

What is the formula to convert gradians to degrees?

Use this conversion formula:

degrees = gradians × 0.9

You can also write it as:

degrees = gradians × (9/10)

Both forms give the same result.

How do you convert degrees to gradians?

To convert the other way, use:

gradians = degrees × (10/9)

This works because 1 degree equals 1.111... gradians.

Why are gradians used instead of degrees?

Gradians make some angle values cleaner in base-10 form. A right angle is 100 gradians, a straight angle is 200 gradians, and a full turn is 400 gradians. This can help in some surveying and mapping work.

What are common angle values in gradians and degrees?

Here are a few helpful matches:

• 0 g = 0°
• 50 g = 45°
• 100 g = 90°
• 150 g = 135°
• 200 g = 180°
• 300 g = 270°
• 400 g = 360°

These are common reference angles in geometry and trigonometry.

Is a gradian the same as a radian?

No, they are different units. A radian is based on a circle’s radius, while degrees and gradians are based on splitting a full turn into equal parts. A full circle is 2π radians, 360 degrees, or 400 gradians.

How do you convert gradians to radians?

Convert gradians to radians with:

radians = gradians × (π/200)

This works because 200 gradians equals π radians (half a circle).

What does 1 gradian equal in minutes and seconds?

Angle minutes and seconds are based on degrees, not gradians. Still, you can convert:

1 gradian = 0.9 degrees
0.9 degrees = 54 minutes
So 1 gradian = 54′ (arcminutes)

In arcseconds, that’s 54 × 60 = 3,240″ (arcseconds).

How do you convert gradians to degrees-minutes-seconds (DMS)?

First convert gradians to degrees:

degrees = gradians × 0.9

Then change the decimal part of the degrees into minutes and seconds:

• minutes = decimal degrees × 60
• seconds = decimal minutes × 60

Example: 25 g
25 g × 0.9 = 22.5°
0.5 × 60 = 30′
So 25 g = 22°30′00″

Are gradians and grads the same thing?

In many contexts, yes. People may say grad, gradian, or gon to mean the same unit. In math and surveying, gon is common. In general use, gradian is clear and widely understood.

What’s a quick way to estimate degrees from gradians?

A fast estimate is to take 10% off the gradian value. That works because degrees are 90% of gradians.

Example: 120 g
10% of 120 is 12
120 − 12 = 108°
So 120 g ≈ 108° (exact in this case).