Degree to Grad (Gon)
°
grad
Conversion History
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|---|---|---|
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Quick Reference Table (Degree to Grad (Gon))
| Degree (°) | Grad (Gon) (grad) |
|---|---|
| 30 | 33.33333333333333333333 |
| 45 | 50 |
| 60 | 66.66666666666666666667 |
| 90 | 100 |
| 120 | 133.33333333333333333333 |
| 180 | 200 |
| 270 | 300 |
| 360 | 400 |
About Degree (°)
The degree (°) is the most widely used unit of angular measure, dividing a full rotation into 360 equal parts. This base of 360 originates in ancient Babylonian astronomy, which used a sexagesimal (base-60) number system and approximated the solar year at 360 days. One degree is subdivided into 60 arcminutes, each subdivided into 60 arcseconds. Degrees are the standard unit in navigation, aviation, geography, engineering drawing, and everyday geometry. The full circle being 360° means that right angles are conveniently 90° and straight angles 180°, making mental arithmetic with common fractions straightforward.
A right angle in a door frame or building corner is exactly 90°. A compass bearing of due north is 0°, east is 90°, south 180°, and west 270°.
Etymology: From the Latin word "gradus" (step or grade), via Old French "degré". The 360-division traces to Babylonian astronomers around 1000 BCE who used base-60 arithmetic and observed approximately 360 days in a year.
About Grad (Gon) (grad)
The grad (also called gon or grade, symbol: grad or g) divides a full circle into 400 equal parts, so a right angle is exactly 100 grad. It was introduced during the French metric reform of the late 18th century to create a decimal-friendly angular system compatible with metric measurements. The grad persists in civil engineering, land surveying, and mining in continental Europe, particularly in France, Germany, and Scandinavia. Most scientific calculators include a GRAD mode alongside DEG and RAD.
A slope of 1 grad in road engineering is a 1 gon incline from horizontal — used in surveying instruments and tachymeters across Europe.
Etymology: From the French "grade", introduced around 1793 as part of the revolutionary metric system. The 400-division was chosen so that a right angle equals exactly 100 grad, aligning with decimal arithmetic.
Degree – Frequently Asked Questions
Why did the Babylonians choose 360 degrees for a circle instead of a rounder number like 100?
The Babylonians used base-60 arithmetic and noticed the year was close to 360 days — convenient because 360 divides evenly by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, and more. That ridiculous number of factors makes slicing a circle into halves, thirds, quarters, fifths, sixths, and eighths all come out to whole numbers. A base-100 system would only divide cleanly by 2, 4, 5, 10, 20, 25, and 50 — far less flexible for geometry and land surveying.
Why do pilots and sailors still use degrees instead of radians?
Navigation requires quick mental arithmetic with headings, bearings, and wind corrections. "Turn right to heading 270" is instantly understood in a cockpit; "turn right to 4.712 radians" would get someone killed. Compass roses, runway numbers (which are headings divided by 10), and nautical charts all assume a 360° circle. The entire global aviation and maritime infrastructure — from VOR stations to AIS transponders — is calibrated in degrees.
What is the degree symbol (°) and how do you type it?
The degree symbol is a small raised circle placed immediately after the number with no space (45°, not 45 °). On Windows, hold Alt and type 0176 on the numpad. On Mac, press Option+Shift+8. On phones, long-press the zero key. In HTML, use ° or °. A common mistake is using a superscript letter "o" or the ring-above diacritic — these look similar but are different Unicode characters and can break search or data parsing.
How do degrees, minutes, and seconds (DMS) relate to decimal degrees in GPS?
One degree equals 60 arcminutes, and one arcminute equals 60 arcseconds — so 1° = 3,600″. To convert DMS to decimal, divide minutes by 60 and seconds by 3,600, then add them to the degree value. For example, 40°26′46″N becomes 40 + 26/60 + 46/3600 = 40.4461°. Google Maps uses decimal degrees internally but lets you enter either format. At the equator, one degree of longitude spans about 111 km.
Are there any alternatives to 360 degrees that countries have actually tried to adopt?
Yes — the French Revolutionary government introduced the gradian (grad), dividing a circle into 400 parts to match the metric system. A right angle became exactly 100 grad. They also tried decimal time (10-hour days) and a decimal calendar. The time and calendar experiments died within a few years, but gradians survived and are still used in French and German surveying. Every scientific calculator has a GRAD mode because of this 230-year-old French experiment.
Grad (Gon) – Frequently Asked Questions
Why did the French Revolution create the gradian when degrees already worked fine?
The revolutionaries wanted to decimalize everything — length (meter), mass (kilogram), time (decimal hours), and angle. The gradian divided a right angle into exactly 100 parts, making it compatible with the new metric system and decimal arithmetic. A slope of 1% grade corresponds neatly to gradian-based calculations. Decimal time flopped within a year, the Republican Calendar lasted 12 years, but the gradian quietly survived in surveying because it genuinely simplifies land measurement calculations.
What is the difference between a gradian, a gon, and a grade?
They're all the same unit — 1/400 of a circle. "Gradian" is the international English term, "gon" is preferred in German-speaking countries and ISO standards, and "grade" is the original French name. The symbol varies too: grad, gon, or superscript g. This naming mess is partly why the unit never gained traction outside continental Europe — nobody could agree on what to call it.
Where are gradians still actually used today?
Primarily in civil engineering and land surveying in France, Germany, Switzerland, and Scandinavia. Total stations (electronic surveying instruments) from Leica and other European manufacturers default to gon. Mining engineers in Germany use gon for underground surveys. French national mapping uses grades for geodetic calculations. If you buy a Leica total station in Europe, you may need to switch it from gon to degrees before using it elsewhere.
Why does every scientific calculator have a GRAD mode that almost nobody uses?
Calculator manufacturers include DEG, RAD, and GRAD modes because international standards (particularly IEC 60747) require it, and European civil engineering exams expect students to work in gradians. The mode exists for a real user base — it's just a user base concentrated in specific countries and professions. The most common calculator accident in the world is probably getting wrong trig answers because the calculator was accidentally left in GRAD mode after someone else used it.
How do you convert between gradians and degrees?
Multiply gradians by 0.9 to get degrees, or multiply degrees by 10/9 to get gradians. A right angle is 100 grad = 90°. The conversion factor is 9/10 because 400/360 = 10/9. This means 50 grad = 45°, 200 grad = 180°, and 300 grad = 270°. The relationship is simple enough to do in your head, which is one of the few nice things about having two competing angular systems.