Gradian to Revolution Converter
Angle · unit-converter
Convert Gradian to Revolution with a fixed input and output unit, step-by-step formula line, and reference tables. All calculations bridge through radians with fixed definitions (360° per turn, 400 grad per turn, 60′ per degree, 60″ per minute, plus practical units like MOA, urad, and NATO 6400 mils per turn).
About Gradian
Gradians (gon) divide a right angle into 100 parts; 400 gradians make a full turn. Used in some surveying and European contexts.
About Revolution
One revolution (turn) is a full circle: 2π radians or 360°. Used in rotation rates, motors, and astronomy (e.g. revolutions per minute).
How to convert gradians to revolutions
1 gradian equals 0.0025 revolution in this tool (via radian):
1 grad = (0.015707963267948967 rad ÷ 6.283185307179586 rad) turn = 0.0025 turn
Each gradian carries 0.015707963267948967 rad and each revolution 6.283185307179586 rad, so one grad equals 0.015707963267948967 ÷ 6.283185307179586 turn.
Let θ(grad) be the angle in Gradian (grad), and θ(turn) in Revolution (turn). Then:
θ(turn) = θ(grad) × (0.015707963267948967 / 6.283185307179586)
Equivalently, divide by how many grad fit into one turn (rad per turn divided by rad per grad):
θ(turn) = θ(grad) ÷ 399.99999999999994
Examples
Example #1: Convert 1 grad to revolution
1 grad = 1 grad × (0.015707963267948967/6.283185307179586) turn = 0.0025 turn
1 grad = 1 grad ÷ 399.99999999999994 = 0.0025 turn
1 grad × (0.015707963267948967/6.283185307179586) = 0.002500 turn
Example #2: Convert 10 grad to revolution
10 grad = 10 grad × (0.015707963267948967/6.283185307179586) turn = 0.025 turn
10 grad = 10 grad ÷ 399.99999999999994 = 0.025 turn
10 grad × (0.015707963267948967/6.283185307179586) = 0.025000 turn
Summary
To convert Gradian to Revolution, multiply the value in grad by (0.015707963267948967 rad per grad) / (6.283185307179586 rad per turn). Equivalently: value_turn = value_grad × (0.015707963267948967 / 6.283185307179586). Numerically, 1 grad equals 0.0025 turn.
Relationship context
Both Gradian and Revolution are converted by fixed multiples of the radian. Multiplying by (rad per grad) ÷ (rad per turn) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Gradian (grad) | Revolution (turn) |
|---|---|
| 0.1 | 0.00025 |
| 1 | 0.0025 |
| 2 | 0.005 |
| 3 | 0.0075 |
| 4 | 0.01 |
| 5 | 0.0125 |
| 6 | 0.015 |
| 7 | 0.0175 |
| 8 | 0.02 |
| 9 | 0.0225 |
| Gradian (grad) | Revolution (turn) |
|---|---|
| 10 | 0.025 |
| 20 | 0.05 |
| 30 | 0.075 |
| 40 | 0.1 |
| 50 | 0.125 |
| 60 | 0.15 |
| 70 | 0.175 |
| 80 | 0.2 |
| 90 | 0.225 |
| 100 | 0.25 |