Convert Degrees to Gradians

To convert degrees to gradians (gons), use this base fact: a full circle is 360 degrees and 400 gradians. That means 1 degree = 400/360 gradians, which simplifies to 10/9 gradians (about 1.111... gradians).

Formula (degrees to gradians):

• gradians = degrees × (10/9)
• gradians = degrees × 1.111111...

Quick examples:

• 45° × 10/9 = 50 gradians
• 90° × 10/9 = 100 gradians
• 180° × 10/9 = 200 gradians

Tip: For a fast estimate, multiply degrees by 1.11, then adjust if you need more accuracy.

What are gradians?

Gradians (also called grads or gon) are a unit for measuring angles. A full circle is 400 gradians. This makes a right angle equal to 100 gradians.

How do you convert degrees to gradians?

To convert degrees to gradians, multiply the degree value by 10/9.
Formula: gradians = degrees × 10/9

Why is the degrees-to-gradians conversion factor 10/9?

Degrees divide a full circle into 360 parts. Gradians divide a full circle into 400 parts.
So 1 degree equals 400/360 gradians, which simplifies to 10/9.

What is 1 degree in gradians?

1° = 1.111111... gradians
(That’s 10/9 gradians.)

What is 90 degrees in gradians?

A right angle is 90 degrees.
90° = 100 gradians

What is 180 degrees in gradians?

A straight angle is 180 degrees.
180° = 200 gradians

What is 360 degrees in gradians?

A full turn is 360 degrees.
360° = 400 gradians

What is 45 degrees in gradians?

45° = 50 gradians
This is half of a right angle in both systems.

What is 30 degrees in gradians?

30° = 33.333333... gradians
(Exact value: 100/3 gradians.)

How do you convert gradians back to degrees?

To convert gradians to degrees, multiply the gradian value by 0.9.
Formula: degrees = gradians × 9/10

Are gradians the same as radians?

No. Gradians and radians are different angle units.

• 400 gradians = full circle
• 2π radians = full circle
• 360 degrees = full circle

Where are gradians used?

Gradians show up in some surveying, mapping, and civil engineering work. They can make right angles and quarter turns easy to read and divide.

Do gradians appear on scientific calculators?

Some calculators include a gradian mode labeled GRA, GRAD, or GON. If yours does, check the angle mode before you calculate trig values.

Does converting degrees to gradians change the angle size?

No. The angle stays the same. Only the unit changes, like inches to centimeters.

How should you round degrees-to-gradians results?

Rounding depends on your use. For quick checks, 2 to 4 decimal places often works well. For survey or layout work, keep more decimals to match your needed accuracy.