Convert Gradian (grad) to Degree (°) instantly. Enter any value and get the result immediately.
grad → ° Converter
| Gradian (grad) | Degree (°) |
|---|---|
| 0.1 grad | 0.09 ° |
| 0.5 grad | 0.45 ° |
| 1 grad | 0.9 ° |
| 2 grad | 1.8 ° |
| 5 grad | 4.5 ° |
| 10 grad | 9 ° |
| 20 grad | 18 ° |
| 50 grad | 45 ° |
| 100 grad | 90 ° |
| 200 grad | 180 ° |
| 500 grad | 450 ° |
| 1000 grad | 900 ° |
| 5000 grad | 4500 ° |
| 10000 grad | 9000 ° |
Converting gradians to degrees is the reverse of the degree-to-gradian conversion — moving from the decimal-friendly metric angular system back to the universally familiar 360-degree system. Gradians are the standard unit on professional surveying instruments across much of Europe, so surveyors, civil engineers, and GIS professionals regularly encounter gradian-based angle readings that must be expressed in degrees for use in general-purpose calculations, design drawings, and international documentation. To convert, multiply the gradian value by 0.9 (or equivalently, multiply by 9 and divide by 10). Use the converter above for instant results, or follow the formula and examples below.
Step-by-step example — Convert 100 grad to degrees:
Step-by-step example — Convert 200 grad to degrees:
Step-by-step example — Convert 50 grad to degrees:
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 equal parts. Introduced during the French Revolution as part of the broader effort to decimalize all units of measurement, the gradian was designed so that a right angle equals exactly 100 grad — a clean, base-10 value that simplifies calculations involving perpendicular lines and right-angle geometry. The gradian is the standard angular unit on theodolites, total stations, and digital levels used by professional surveyors in France, Germany, the Netherlands, Scandinavia, and many other European countries. On scientific calculators, the GRAD mode (sometimes labeled GON) corresponds to this system. One gradian equals 0.9 degrees or π/200 radians.
Degree (°) is the world's most widely used unit of angular measurement, dividing a full circle into 360 equal parts. This convention originates in ancient Babylonian astronomy, whose base-60 number system and 360-day calendar year made 360 a natural choice for circle division. Degrees are used globally in navigation (compass bearings, latitude and longitude), geometry, architecture, aviation, and everyday science. The key reference angles — 90° (right angle), 180° (straight angle), and 360° (full rotation) — are universally understood. Unlike gradians, degrees are subdivided sexagesimally into 60 arcminutes and 3,600 arc-seconds, giving the DMS (Degrees, Minutes, Seconds) system used in geographic coordinates and astronomical catalogs worldwide.
| Gradians (grad) | Degrees (°) | Common Reference |
|---|---|---|
| 0 grad | 0° | No rotation |
| 25 grad | 22.5° | One-sixteenth of a full circle |
| 50 grad | 45° | Half a right angle — diagonal direction |
| 100 grad | 90° | Right angle — quarter circle |
| 133.33 grad | 120° | Interior angle of equilateral triangle |
| 150 grad | 135° | Interior angle of regular octagon |
| 200 grad | 180° | Straight angle — half circle |
| 300 grad | 270° | Three-quarter rotation |
| 400 grad | 360° | Full circle — one complete rotation |
| 1 grad | 0.9° | Basic gradian increment |
One gradian equals exactly 0.9 degrees. This clean decimal relationship — 1 grad = 9/10° — is one of the most straightforward unit conversions in angular measurement, making mental arithmetic between the two systems relatively simple.
The formula is: ° = grad × 0.9. Multiply any gradian value by 0.9 (or by 9/10) to get the equivalent angle in degrees. For the reverse conversion, divide degrees by 0.9 (or multiply by 10/9) to get gradians.
100 grad = 90°. This is the single most important gradian-to-degree benchmark: 100 gradians is a right angle. It perfectly illustrates why surveyors value the gradian system — right angles produce clean, round numbers in gradians that are immediately recognizable in field work.
400 grad = 360°. A full circle contains exactly 400 gradians — the defining property of the gradian system. This means 400 grad = 360° = 2π radians = 1 full turn, all representing one complete rotation.
200 grad = 180°. A straight angle (half circle) is exactly 200 gradians — again a clean, round number that reflects the decimal convenience built into the gradian system.
No — these are completely different terms. A gradian (grad or gon) is a unit of angular measurement equal to 1/400th of a full circle. A gradient is a measure of slope or rate of change — in road design, a 5% gradient means a 5-meter rise over 100 meters of horizontal distance. Despite the similar spelling, the two have no mathematical relationship. Confusing the two is a common error, particularly in civil engineering contexts where both terms appear regularly.
Gradians (gons) are predominantly used in France, Germany, the Netherlands, Sweden, Switzerland, and other continental European countries for professional land surveying and civil engineering. Surveying instruments manufactured by European companies such as Leica Geosystems, Trimble (for European markets), and Sokkia routinely support gradian mode. In North America, the UK, and most of Asia and Africa, degrees are the standard angular unit in surveying and engineering, though gradian mode is available on all scientific calculators and professional instruments worldwide.
Use the simple ×0.9 rule: multiply the gradian value by 9, then divide by 10. For key benchmarks, memorize: 100 grad = 90°, 200 grad = 180°, 400 grad = 360°. For any other value, the mental arithmetic is straightforward — for example, 250 grad: 250 × 9 = 2,250 ÷ 10 = 225°.