Turn to Gradian Converter

Convert turn to gradian instantly. 1 turn = 400.0 gradian.

1 Turn =
Gradian
From
To

Turn to Gradian Table

TurnGradian
1 turn400.0 grad
5 turn2000.0 grad
10 turn4000.0 grad
30 turn12000.0 grad
45 turn18000.0 grad
90 turn36000.0 grad
180 turn72000.0 grad
360 turn144000.0 grad

Quick Answer

Formula: Gradian = Turn × 400

Multiply any turn value by 400 to get gradian.

Reverse: Turn = Gradian × 0.0025

Worked Examples

1 turn
1 turn × 400 = 400 grad
Single unit reference.
45 turn
45 turn × 400 = 1.8e+04 grad
45° — half a right angle.
90 turn
90 turn × 400 = 3.6e+04 grad
90° — one right angle.
180 turn
180 turn × 400 = 7.2e+04 grad
180° — a straight line / half circle.

Turn to Gradian Conversion Table

Common turn values — factor: 1 turn = 400 grad

Turn (turn)Gradian (grad)Context
0.001 turn0.4 grad~0.36°
0.01 turn4 grad3.6°
0.0833 turn33.32 grad30°
0.1 turn40 grad36°
0.125 turn50 grad45°
0.25 turn100 grad90° right angle
0.333 turn133.2 grad120°
0.5 turn200 grad180° half turn
0.75 turn300 grad270°
1 turn400 grad360° full circle
2 turn800 gradTwo rotations
5 turn2000 gradFive rotations
10 turn4000 gradTen rotations
100 turn4e+04 grad100 turns
1000 turn4e+05 grad1,000 turns

Mental Math Tricks

Exact factor

1 turn = 400 grad. Memorize for instant estimates.

Key anchors

Right angle: 90° = 100 grad.

Reverse

Multiply result by 0.0025 to recover the original turn value.

Who Uses This Conversion?

Mechanical Engineer

Specifies gear ratios and shaft rotation counts in turns or revolutions.

Motor Designer

Rates motor speed in RPM (turns per minute) and total shaft rotation.

Screw Manufacturer

Defines thread pitch as advance per turn for screws, bolts, and lead screws.

Watchmaker

Measures mainspring tension and escapement timing in turns of the crown.

Mathematician

Uses turns (τ = 2π) for clean representation of periodic functions and complex numbers.

Dancer / Choreographer

Counts spins and rotations in full turns for choreography notation.

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.