A gradian is 1/400 of a turn.
Gradians to Circles Converter — gon to circle
Convert Gradian (gon) to Circle (circle) using the exact conversion factor (1 gradian = 0.0025 circle). See the formula, worked examples, and conversion table.
Gradians to Circles 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.
One complete circle.
Result = input x 0.01570796327 / 6.283185307.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Gradians to Circles
Gradian and Circle 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: A gradian is 1/400 of a turn, and one complete circle.
Formula
circles = gradians × 0.0025
This factor comes from each unit's defined relationship to the category's base unit: 1 gradian equals 0.0157079632679 base units, and 1 circle equals 6.28318530718 base units, so dividing one by the other gives the direct gradian-to-circle factor of 0.0025.
Simple example
1 gon × 0.0025 = 0.0025 circle
1 gradian = 0.0025 circles.
Real-world example
90 gon × 0.0025 = 0.225 circle
90 gradians = 0.225 circles.
Conversion table
| Gradian (gon) | Circle (circle) |
|---|---|
| 0 gon | 0 circle |
| 30 gon | 0.075 circle |
| 45 gon | 0.1125 circle |
| 90 gon | 0.225 circle |
| 180 gon | 0.45 circle |
| 360 gon | 0.9 circle |
Reverse conversion: Circle to Gradian
0.0025 circle × 400 = 1 gon
0.0025 circles = 1 gradian.
gradians = circles × 400
For a page dedicated to this direction, see Circle to Gradian.
Understanding the Gradian (gon)
A gradian is 1/400 of a turn.
Understanding the Circle (circle)
One complete circle.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many circles are in 1 gradian?
1 gradian equals 0.0025 circles, using the exact defined conversion factor rather than an estimate.
How do I convert gradian to circle?
Multiply the gradian value by 0.0025. The converter above does this instantly to whatever precision you set.
How do I convert circle back to gradian?
Use the reverse factor: 1 circle equals 400 gradians. You can also use the swap control in the converter above to flip the direction instantly.
What is a gradian?
Gradian (gon) is a unit of angle.
What is a circle?
Circle (circle) is a unit of angle.
Is the gradian to circle conversion exact?
Yes. Both gradian and circle are defined by fixed standards rather than physical artifacts, so the factor of 0.0025 used above is exact to as many digits as you choose to display.