Convert Degree (°) to Gradian (grad) instantly. Enter any value and get the result immediately.
° → grad Converter
| Degree (°) | Gradian (grad) |
|---|---|
| 0.1 ° | 0.11111111 grad |
| 0.5 ° | 0.55555556 grad |
| 1 ° | 1.11111111 grad |
| 2 ° | 2.22222222 grad |
| 5 ° | 5.55555556 grad |
| 10 ° | 11.11111111 grad |
| 20 ° | 22.22222222 grad |
| 50 ° | 55.55555556 grad |
| 100 ° | 111.11111111 grad |
| 200 ° | 222.22222222 grad |
| 500 ° | 555.55555556 grad |
| 1000 ° | 1111.11111111 grad |
| 5000 ° | 5555.55555556 grad |
| 10000 ° | 11,111.1111 grad |
Converting degrees to gradians moves between the two most commonly used angular measurement systems in science and engineering. While degrees divide a full circle into 360 equal parts, gradians divide it into 400 — making gradians especially convenient for right-angle calculations. To convert, multiply the degree value by 10/9 (approximately 1.11111). Use the converter above for instant results, or follow the formula and examples below.
Step-by-step example — Convert 90° to gradians:
Step-by-step example — Convert 45° to gradians:
Step-by-step example — Convert 270° to gradians:
Degree (°) is the most widely recognized unit of angular measurement in the world. A full circle is divided into 360 degrees, a convention inherited from ancient Babylonian mathematics which used a base-60 (sexagesimal) numeral system. One degree is further subdivided into 60 arc-minutes, and each arc-minute into 60 arc-seconds — giving degrees a fine-grained precision system. Degrees are used universally in navigation, geography (latitude and longitude), astronomy, everyday geometry, and most general-purpose engineering. A right angle equals exactly 90°, a straight angle is 180°, and a full rotation is 360°.
Gradian (grad), also called a gon or grade, is a metric unit of angular measurement in which a full circle is divided into exactly 400 gradians. This means a right angle equals exactly 100 grad — a clean, base-10 value that makes gradians particularly useful in surveying, civil engineering, and artillery calculations where right angles are fundamental. The gradian was introduced during the French Revolution as part of the broader metrication effort to bring angular measurement in line with the decimal system. Although gradians never replaced degrees in everyday use, they remain the standard unit on most modern surveying instruments (theodolites and total stations) and in European civil engineering practice, where the clean decimal relationship to right angles simplifies calculations significantly.
| Degrees (°) | Gradians (grad) | Common Reference |
|---|---|---|
| 0° | 0 grad | No rotation |
| 45° | 50 grad | Half a right angle (diagonal) |
| 90° | 100 grad | Right angle — quarter circle |
| 135° | 150 grad | Interior angle of a regular octagon |
| 180° | 200 grad | Straight angle — half circle |
| 270° | 300 grad | Three-quarter rotation |
| 360° | 400 grad | Full circle — one complete rotation |
| 1° | 1.1111 grad | Fine angular increment |
| 60° | 66.6667 grad | Interior angle of equilateral triangle |
| 120° | 133.3333 grad | Interior angle of regular hexagon |
There are exactly 10/9 gradians (approximately 1.11111111 grad) in one degree. So 1° = 1.11111 grad.
The formula is: grad = ° × (10 ÷ 9). Multiply any degree value by 10/9 (or 1.11111111) to get the equivalent angle in gradians.
90° = 100 grad. This is one of the most useful relationships between the two systems — a right angle is exactly 100 gradians, which is why gradians are preferred in surveying and civil engineering where right angles are central to calculations.
180° = 200 grad. A straight angle (half circle) equals 200 gradians.
360° = 400 grad. A full circle equals exactly 400 gradians — which is the defining characteristic of the gradian system and the source of its decimal convenience.
A gradian is also commonly called a gon or a grade. The symbol is grad or gon. The term "gon" is preferred in ISO standards and is widely used in European surveying and engineering. All three names — gradian, gon, and grade — refer to exactly the same unit: 1/400th of a full circle.
The gradian system is useful because it aligns angular measurement with the decimal (base-10) number system. Since a right angle equals exactly 100 grad and a full circle equals exactly 400 grad, calculations involving right angles, quarter circles, and slope percentages become simpler and less error-prone compared to the degree system. This makes gradians especially valuable in surveying, where 90° turns and slope calculations are routine, and where instrument readings must be computed quickly and accurately in the field.
Degrees are far more commonly used in everyday life, education, navigation, and general engineering worldwide. Gradians are a specialist unit primarily used in professional land surveying, European civil engineering, and some military applications. Most scientific calculators support both modes, and conversion between the two is straightforward using the 10/9 multiplier.