One complete circle.
Circles to Gradians Converter — circle to gon
Convert Circle (circle) to Gradian (gon) using the exact conversion factor (1 circle = 400 gradian). See the formula, worked examples, and conversion table.
Circles to Gradians converter
Converter
Angle Converter
Convert radians, degrees, gradians, turns, arcminutes, arcseconds, and milliradians.
Context values
Some unit families need one extra value for a physically accurate result.
A gradian is 1/400 of a turn.
Result = input x 6.283185307 / 0.01570796327.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Circles to Gradians
Circle and Gradian are the two standard ways to measure angles — degrees for everyday and navigational use, radians for calculus and physics — so converting between them comes up constantly in math, engineering, and programming. Specifically: One complete circle, and a gradian is 1/400 of a turn.
Formula
gradians = circles × 400
This factor comes from each unit's defined relationship to the category's base unit: 1 circle equals 6.28318530718 base units, and 1 gradian equals 0.0157079632679 base units, so dividing one by the other gives the direct circle-to-gradian factor of 400.
Simple example
1 circle × 400 = 400 gon
1 circle = 400 gradians.
Real-world example
90 circle × 400 = 36,000 gon
90 circles = 36,000 gradians.
Conversion table
| Circle (circle) | Gradian (gon) |
|---|---|
| 0 circle | 0 gon |
| 30 circle | 12,000 gon |
| 45 circle | 18,000 gon |
| 90 circle | 36,000 gon |
| 180 circle | 72,000 gon |
| 360 circle | 144,000 gon |
Reverse conversion: Gradian to Circle
400 gon × 0.0025 = 1 circle
400 gradians = 1 circles.
circles = gradians × 0.0025
For a page dedicated to this direction, see Gradian to Circle.
Understanding the Circle (circle)
One complete circle.
Understanding the Gradian (gon)
A gradian is 1/400 of a turn.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many gradians are in 1 circle?
1 circle equals 400 gradians, using the exact defined conversion factor rather than an estimate.
How do I convert circle to gradian?
Multiply the circle value by 400. The converter above does this instantly to whatever precision you set.
How do I convert gradian back to circle?
Use the reverse factor: 1 gradian equals 0.0025 circles. You can also use the swap control in the converter above to flip the direction instantly.
What is a circle?
Circle (circle) is a unit of angle.
What is a gradian?
Gradian (gon) is a unit of angle.
Is the circle to gradian conversion exact?
Yes. Both circle and gradian are defined by fixed standards rather than physical artifacts, so the factor of 400 used above is exact to as many digits as you choose to display.