Gradian to Degree Converter
Convert gradian to degree instantly. 1 gradian = 0.9 degree.
Gradian to Degree Table
| Gradian | Degree |
|---|---|
| 1 grad | 0.9 ° |
| 5 grad | 4.5 ° |
| 10 grad | 9.0 ° |
| 30 grad | 27.0 ° |
| 45 grad | 40.5 ° |
| 90 grad | 81.0 ° |
| 180 grad | 162.0 ° |
| 360 grad | 324.0 ° |
Related Conversions
Quick Answer
Formula: Degree = Gradian × 0.9
Multiply any gradian value by 0.9 to get degree.
Reverse: Gradian = Degree × 1.111
Worked Examples
Gradian to Degree Conversion Table
Common gradian values — factor: 1 grad = 0.9 °
| Gradian (grad) | Degree (°) | Context |
|---|---|---|
| 1 grad | 0.9 ° | 1 grad |
| 5 grad | 4.5 ° | 5 grad |
| 10 grad | 9 ° | 10 grad |
| 25 grad | 22.5 ° | 22.5° |
| 50 grad | 45 ° | 45° |
| 100 grad | 90 ° | 90° right angle |
| 150 grad | 135 ° | 135° |
| 200 grad | 180 ° | 180° half circle |
| 250 grad | 225 ° | 225° |
| 300 grad | 270 ° | 270° |
| 400 grad | 360 ° | 360° full circle |
| 800 grad | 720 ° | Two circles |
| 1200 grad | 1080 ° | Three circles |
| 2000 grad | 1800 ° | Five circles |
| 4000 grad | 3600 ° | Ten circles |
Mental Math Tricks
Gradians × 0.9 = degrees. Exact.
100 grad = 90°. Quarter of 400 grad = 90°.
Degrees × 10/9 = gradians.
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 Degree
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.
Degree (°)
The degree (°) divides a full circle into 360 equal parts. This system traces back to ancient Babylonian astronomy, which used a base-60 (sexagesimal) number system. The choice of 360 is practical: it is divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, and 120.
Degrees remain the dominant angle unit in everyday life, navigation, surveying, and most engineering disciplines. Compass bearings, latitude and longitude, and architectural drawings all use degrees.
Interesting fact: The Babylonians may have chosen 360 because they approximated the solar year as 360 days, making each day of travel correspond to one degree of the Sun's apparent annual motion around the sky.
About Gradian to Degree Conversion
Converting gradian to degree 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°) = 90 °. A full circle (360°) = 360 °. Reverse: 1 ° = 1.111 grad. Exact factor: 1 grad = 0.9 °.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.