Radian to Gradian Converter
Convert radian to gradian instantly. 1 radian = 63.661977 gradian.
Radian to Gradian Table
| Radian | Gradian |
|---|---|
| 1 rad | 63.661977 grad |
| 5 rad | 318.309886 grad |
| 10 rad | 636.619772 grad |
| 30 rad | 1909.859317 grad |
| 45 rad | 2864.788976 grad |
| 90 rad | 5729.577951 grad |
| 180 rad | 11459.155903 grad |
| 360 rad | 22918.311805 grad |
Related Conversions
Quick Answer
Formula: Gradian = Radian × 63.66
Multiply any radian value by 63.66 to get gradian.
Reverse: Radian = Gradian × 0.01571
Worked Examples
Radian to Gradian Conversion Table
Common radian values — factor: 1 rad = 63.66 grad
| Radian (rad) | Gradian (grad) | Context |
|---|---|---|
| 0.001 rad | 0.06366 grad | ~0.057° |
| 0.01 rad | 0.6366 grad | ~0.573° |
| 0.1 rad | 6.366 grad | ~5.73° |
| 0.5236 rad | 33.33 grad | 30° |
| 0.7854 rad | 50 grad | 45° |
| 1 rad | 63.66 grad | ~57.3° |
| 1.571 rad | 100 grad | 90° right angle |
| 2 rad | 127.3 grad | ~114.6° |
| 3.142 rad | 200 grad | 180° π |
| 4 rad | 254.6 grad | ~229° |
| 4.712 rad | 300 grad | 270° 3π/2 |
| 6.283 rad | 400 grad | 360° 2π |
| 10 rad | 636.6 grad | ~573° |
| 20 rad | 1273 grad | ~1,146° |
| 100 rad | 6366 grad | ~5,730° |
Mental Math Tricks
1 rad = 63.66 grad. Memorize for instant estimates.
Right angle: 90° = 100 grad.
Multiply result by 0.01571 to recover the original rad value.
Who Uses This Conversion?
Uses radians for calculus — derivatives of sin/cos are clean only in radians.
Applies radians in wave equations, angular momentum, and rotational dynamics.
Uses Math.sin(), Math.cos() which require radians in virtually all languages.
Describes phase angles, frequency in rad/s, and Fourier transforms in radians.
Models angular velocity in rad/s and phase margins in radians.
Programs joint angles and end-effector orientation using radians in ROS and MATLAB.
Related Conversions
Frequently Asked Questions
About Radian and Gradian
Radian (rad)
The radian is the SI unit of angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. It was formally adopted by the SI system in 1995, though it had been used in mathematics since the 18th century.
Radians simplify calculus and physics: derivatives of trigonometric functions, wave equations, and angular velocity formulas are all cleaner in radians. One full circle = 2π radians ≈ 6.2832 rad.
Interesting fact: The name 'radian' was coined by physicist James Thomson in 1873. At exactly 1 radian, the arc length equals the radius — the elegant geometric relationship that makes radians so mathematically natural.
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 Radian to Gradian Conversion
Converting radian 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 = 0.01571 rad. Exact factor: 1 rad = 63.66 grad.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.