Turn to Gradian Converter
Convert turn to gradian instantly. 1 turn = 400.0 gradian.
Turn to Gradian Table
| Turn | Gradian |
|---|---|
| 1 turn | 400.0 grad |
| 5 turn | 2000.0 grad |
| 10 turn | 4000.0 grad |
| 30 turn | 12000.0 grad |
| 45 turn | 18000.0 grad |
| 90 turn | 36000.0 grad |
| 180 turn | 72000.0 grad |
| 360 turn | 144000.0 grad |
Related Conversions
Quick Answer
Formula: Gradian = Turn × 400
Multiply any turn value by 400 to get gradian.
Reverse: Turn = Gradian × 0.0025
Worked Examples
Turn to Gradian Conversion Table
Common turn values — factor: 1 turn = 400 grad
| Turn (turn) | Gradian (grad) | Context |
|---|---|---|
| 0.001 turn | 0.4 grad | ~0.36° |
| 0.01 turn | 4 grad | 3.6° |
| 0.0833 turn | 33.32 grad | 30° |
| 0.1 turn | 40 grad | 36° |
| 0.125 turn | 50 grad | 45° |
| 0.25 turn | 100 grad | 90° right angle |
| 0.333 turn | 133.2 grad | 120° |
| 0.5 turn | 200 grad | 180° half turn |
| 0.75 turn | 300 grad | 270° |
| 1 turn | 400 grad | 360° full circle |
| 2 turn | 800 grad | Two rotations |
| 5 turn | 2000 grad | Five rotations |
| 10 turn | 4000 grad | Ten rotations |
| 100 turn | 4e+04 grad | 100 turns |
| 1000 turn | 4e+05 grad | 1,000 turns |
Mental Math Tricks
1 turn = 400 grad. Memorize for instant estimates.
Right angle: 90° = 100 grad.
Multiply result by 0.0025 to recover the original turn value.
Who Uses This Conversion?
Specifies gear ratios and shaft rotation counts in turns or revolutions.
Rates motor speed in RPM (turns per minute) and total shaft rotation.
Defines thread pitch as advance per turn for screws, bolts, and lead screws.
Measures mainspring tension and escapement timing in turns of the crown.
Uses turns (τ = 2π) for clean representation of periodic functions and complex numbers.
Counts spins and rotations in full turns for choreography notation.
Related Conversions
Frequently Asked Questions
About Turn and Gradian
Turn (turn)
A turn (also called revolution or cycle) represents one complete 360° rotation. It is the most intuitive angle unit — zero ambiguity about what constitutes 'one full rotation.'
Turns are used in mechanics (RPM = revolutions per minute), engineering (screw thread pitch expressed in turns per inch), and signal processing. The number τ (tau = 2π ≈ 6.2832) represents one turn in radians — some mathematicians advocate using τ instead of π for clarity.
Interesting fact: The tau movement in mathematics argues that using τ = 2π = one full turn would make formulas like Euler's identity and Fourier transforms more intuitive than using π = half-turn.
Gradian (grad)
The gradian (also called gon or grade) divides a full circle into 400 equal parts, so a right angle equals exactly 100 gradians. It was introduced during the French Revolution as part of the decimal metric system reform in the 1790s.
Gradians are used primarily in surveying, civil engineering, and some European geodetic systems. The advantage: since a right angle = 100 grad, slope percentages and bearing calculations involve simple arithmetic.
Interesting fact: France briefly mandated decimal angles (gradians) in the 1790s alongside the metric system, but the gradian never achieved the same global adoption as the meter and kilogram.
About Turn to Gradian Conversion
Converting turn to gradian is essential in mathematics, physics, engineering, and surveying. Degrees are used in everyday contexts and navigation; radians are the standard in calculus and physics; gradians are common in European surveying. Having accurate conversions ensures correct results across disciplines.
Key reference: a right angle (90°) = 100 grad. A full circle (360°) = 400 grad. Reverse: 1 grad = 0.0025 turn. Exact factor: 1 turn = 400 grad.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.