Gradian to Radian Converter
Convert gradian to radian instantly. 1 gradian = 0.015708 radian.
Gradian to Radian Table
| Gradian | Radian |
|---|---|
| 1 grad | 0.015708 rad |
| 5 grad | 0.07854 rad |
| 10 grad | 0.15708 rad |
| 30 grad | 0.471239 rad |
| 45 grad | 0.706858 rad |
| 90 grad | 1.413717 rad |
| 180 grad | 2.827433 rad |
| 360 grad | 5.654867 rad |
Related Conversions
Quick Answer
Formula: Radian = Gradian × 0.01571
Multiply any gradian value by 0.01571 to get radian.
Reverse: Gradian = Radian × 63.66
Worked Examples
Gradian to Radian Conversion Table
Common gradian values — factor: 1 grad = 0.01571 rad
| Gradian (grad) | Radian (rad) | Context |
|---|---|---|
| 1 grad | 0.01571 rad | 1 grad |
| 5 grad | 0.07854 rad | 5 grad |
| 10 grad | 0.1571 rad | 10 grad |
| 25 grad | 0.3927 rad | 22.5° |
| 50 grad | 0.7854 rad | 45° |
| 100 grad | 1.571 rad | 90° right angle |
| 150 grad | 2.356 rad | 135° |
| 200 grad | 3.142 rad | 180° half circle |
| 250 grad | 3.927 rad | 225° |
| 300 grad | 4.712 rad | 270° |
| 400 grad | 6.283 rad | 360° full circle |
| 800 grad | 12.57 rad | Two circles |
| 1200 grad | 18.85 rad | Three circles |
| 2000 grad | 31.42 rad | Five circles |
| 4000 grad | 62.83 rad | Ten circles |
Mental Math Tricks
1 grad = 0.01571 rad. Memorize for instant estimates.
Right angle: 90° = 1.571 rad.
Multiply result by 63.66 to recover the original grad value.
Who Uses This Conversion?
Uses gradians for land surveying in France, Sweden, and other European countries.
Applies gradians in road gradient calculations where 100 grad = right angle is convenient.
Works with national coordinate systems in countries that standardized on gradians.
Uses gradians in French topographic mapping traditions.
Applies gradians for dip and strike measurements in some European mining standards.
Uses gradians in some European military targeting and range calculation systems.
Related Conversions
Frequently Asked Questions
About Gradian and Radian
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.
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.
About Gradian to Radian Conversion
Converting gradian to radian 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°) = 1.571 rad. A full circle (360°) = 6.283 rad. Reverse: 1 rad = 63.66 grad. Exact factor: 1 grad = 0.01571 rad.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.