Revolution to Gradian Converter
Angle · unit-converter
Convert Revolution to Gradian 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 Revolution
One revolution (turn) is a full circle: 2π radians or 360°. Used in rotation rates, motors, and astronomy (e.g. revolutions per minute).
About Gradian
Gradians (gon) divide a right angle into 100 parts; 400 gradians make a full turn. Used in some surveying and European contexts.
How to convert revolutions to gradians
1 revolution equals 399.99999999999994 gradian in this tool (via radian):
1 turn = (6.283185307179586 rad ÷ 0.015707963267948967 rad) grad = 399.99999999999994 grad
Each revolution carries 6.283185307179586 rad and each gradian 0.015707963267948967 rad, so one turn equals 6.283185307179586 ÷ 0.015707963267948967 grad.
Let θ(turn) be the angle in Revolution (turn), and θ(grad) in Gradian (grad). Then:
θ(grad) = θ(turn) × (6.283185307179586 / 0.015707963267948967)
Equivalently, divide by how many turn fit into one grad (rad per grad divided by rad per turn):
θ(grad) = θ(turn) ÷ 0.0025
Examples
Example #1: Convert 1 turn to gradian
1 turn = 1 turn × (6.283185307179586/0.015707963267948967) grad = 400 grad
1 turn = 1 turn ÷ 0.0025 = 400 grad
1 turn × (6.283185307179586/0.015707963267948967) = 400.000000 grad
Example #2: Convert 10 turn to gradian
10 turn = 10 turn × (6.283185307179586/0.015707963267948967) grad = 4000 grad
10 turn = 10 turn ÷ 0.0025 = 4000 grad
10 turn × (6.283185307179586/0.015707963267948967) = 4,000.000000 grad
Summary
To convert Revolution to Gradian, multiply the value in turn by (6.283185307179586 rad per turn) / (0.015707963267948967 rad per grad). Equivalently: value_grad = value_turn × (6.283185307179586 / 0.015707963267948967). Numerically, 1 turn equals 399.99999999999994 grad.
Relationship context
Both Revolution and Gradian are converted by fixed multiples of the radian. Multiplying by (rad per turn) ÷ (rad per grad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Revolution (turn) | Gradian (grad) |
|---|---|
| 0.1 | 40 |
| 1 | 400 |
| 2 | 800 |
| 3 | 1,200 |
| 4 | 1,600 |
| 5 | 2,000 |
| 6 | 2,400 |
| 7 | 2,800 |
| 8 | 3,200 |
| 9 | 3,600 |
| Revolution (turn) | Gradian (grad) |
|---|---|
| 10 | 4,000 |
| 20 | 8,000 |
| 30 | 12,000 |
| 40 | 16,000 |
| 50 | 20,000 |
| 60 | 24,000 |
| 70 | 28,000 |
| 80 | 32,000 |
| 90 | 36,000 |
| 100 | 40,000 |