A gradian is 1/400 of a turn.
Gradians to Turns Converter — gon to turn
Convert Gradian (gon) to Turn (turn) using the exact conversion factor (1 gradian = 0.0025 turn). See the formula, worked examples, and conversion table.
Gradians to Turns 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 full revolution.
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 Turns
Gradian and Turn 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 full revolution.
Formula
turns = 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 turn equals 6.28318530718 base units, so dividing one by the other gives the direct gradian-to-turn factor of 0.0025.
Simple example
1 gon × 0.0025 = 0.0025 turn
1 gradian = 0.0025 turns.
Real-world example
90 gon × 0.0025 = 0.225 turn
90 gradians = 0.225 turns.
Conversion table
| Gradian (gon) | Turn (turn) |
|---|---|
| 0 gon | 0 turn |
| 30 gon | 0.075 turn |
| 45 gon | 0.1125 turn |
| 90 gon | 0.225 turn |
| 180 gon | 0.45 turn |
| 360 gon | 0.9 turn |
Reverse conversion: Turn to Gradian
0.0025 turn × 400 = 1 gon
0.0025 turns = 1 gradian.
gradians = turns × 400
For a page dedicated to this direction, see Turn to Gradian.
Understanding the Gradian (gon)
A gradian is 1/400 of a turn.
Understanding the Turn (turn)
One full revolution.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many turns are in 1 gradian?
1 gradian equals 0.0025 turns, using the exact defined conversion factor rather than an estimate.
How do I convert gradian to turn?
Multiply the gradian value by 0.0025. The converter above does this instantly to whatever precision you set.
How do I convert turn back to gradian?
Use the reverse factor: 1 turn 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 turn?
Turn (turn) is a unit of angle.
Is the gradian to turn conversion exact?
Yes. Both gradian and turn 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.