Degree to Gradian Converter
Convert degree to gradian instantly. 1 degree = 1.111111 gradian.
Degree to Gradian Table
| Degree | Gradian |
|---|---|
| 1 ° | 1.111111 grad |
| 5 ° | 5.555556 grad |
| 10 ° | 11.111111 grad |
| 30 ° | 33.333333 grad |
| 45 ° | 50.0 grad |
| 90 ° | 100.0 grad |
| 180 ° | 200.0 grad |
| 360 ° | 400.0 grad |
Related Conversions
Quick Answer
Formula: Gradian = Degree × 1.111
Multiply any degree value by 1.111 to get gradian.
Reverse: Degree = Gradian × 0.9
Worked Examples
Degree to Gradian Conversion Table
Common degree values — factor: 1 ° = 1.111 grad
| Degree (°) | Gradian (grad) | Context |
|---|---|---|
| 1 ° | 1.111 grad | 1° |
| 5 ° | 5.556 grad | 5° |
| 10 ° | 11.11 grad | 10° |
| 15 ° | 16.67 grad | Clock hour |
| 30 ° | 33.33 grad | Clock half-hour |
| 45 ° | 50 grad | Half right angle |
| 60 ° | 66.67 grad | Equilateral triangle |
| 90 ° | 100 grad | Right angle |
| 120 ° | 133.3 grad | Obtuse |
| 135 ° | 150 grad | 3/8 turn |
| 180 ° | 200 grad | Straight line |
| 270 ° | 300 grad | 3/4 turn |
| 360 ° | 400 grad | Full circle |
| 720 ° | 800 grad | Two rotations |
| 1080 ° | 1200 grad | Three rotations |
Mental Math Tricks
Degrees × 10/9 = gradians. Right angle: 90° = 100 grad.
Multiply degrees by 10, divide by 9. Or: 1° = 1.111 grad.
Gradians × 9/10 = degrees.
Who Uses This Conversion?
Measures horizontal and vertical angles in degrees for land surveys and boundary marking.
Specifies roof pitches, staircase angles, and geometric building features in degrees.
Uses compass bearings and course headings expressed in degrees for maritime and aviation.
Learns sine, cosine, and tangent functions using degree inputs on a calculator.
Specifies shaft rotation, cam profiles, and gear engagement angles in degrees.
Reports wind direction in degrees from north (0°–360°) for weather forecasts.
Related Conversions
Frequently Asked Questions
About Degree and Gradian
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.
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 Degree to Gradian Conversion
Converting degree 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 = 0.9 °. Exact factor: 1 ° = 1.111 grad.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.