Grad (Gon) to Turn
grad
turn
Conversion History
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|---|---|---|
| No conversion history to show. | ||
Quick Reference Table (Grad (Gon) to Turn)
| Grad (Gon) (grad) | Turn (turn) |
|---|---|
| 25 | 0.0625 |
| 50 | 0.125 |
| 100 | 0.25 |
| 200 | 0.5 |
| 300 | 0.75 |
| 400 | 1 |
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.
About Turn (turn)
A turn is a unit of angle equal to one full rotation — 360° or 2π radians. It is preferred in modern mathematics and computer graphics as an intuitive, human-readable unit that avoids the factor of 2π that appears throughout formulas when using radians. Some programming libraries and notations (notably "tau" advocates) argue that expressing angles in turns simplifies many relationships: a quarter-circle is 0.25 turns rather than π/2 radians. The turn is identical in size to the revolution and the circle.
Turning a steering wheel halfway around is 0.5 turns (180°). A full barrel roll in aviation is 1 turn.
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.
Turn – Frequently Asked Questions
What is tau (τ) and why do some people want it to replace 2π?
Tau (τ = 2π ≈ 6.2832) represents one full turn. Its advocates argue that using τ instead of 2π makes formulas cleaner: a quarter-circle is τ/4 instead of π/2, circumference is τr instead of 2πr, and Euler's identity becomes e^(iτ) = 1 (arguably more elegant than e^(iπ) = −1). The Tau Manifesto, published in 2010 by Michael Hartl, sparked a genuine mathematical subculture. Tau Day is June 28 (6.28). The argument has merit but π is so deeply entrenched that adoption remains niche.
How are turns used in computer graphics and game engines?
Some game engines and shader languages let you specify rotations in turns (0 to 1) rather than degrees (0 to 360) or radians (0 to 2π). Turns map naturally to normalized values — a progress bar from 0.0 to 1.0 directly represents angle completion. The GLSL function fract() wraps any number to the 0–1 range, making turn-based angle arithmetic trivially simple for procedural animations, circular gradients, and clock-face layouts.
How does thread pitch work and why do plumbers count turns when tightening fittings?
Thread pitch is the axial distance a bolt or pipe fitting advances per complete turn. A standard ½-inch NPT pipe thread has 14 threads per inch, so one turn advances it about 1.8 mm into the fitting. Plumbers specify "finger tight plus 2–3 turns" because torque wrenches are impractical in cramped spaces. Spark plug manufacturers use the same approach — "hand tight plus X turns" achieves correct seating force without needing a torque wrench in the field.
How do speed-cubers define turns when counting the minimum moves to solve a Rubik's Cube?
Two metrics exist: HTM (half-turn metric) counts any face rotation — 90° or 180° — as one move, while QTM (quarter-turn metric) counts each 90° as one move and each 180° as two. "God's Number" — the maximum moves needed to solve any scramble — is 20 in HTM and 26 in QTM. Computer solvers like Kociemba's algorithm are tuned to HTM because it produces shorter sequences. Human world-record holders now solve random scrambles in under 4 seconds.
How many turns does a combination lock typically require?
Most padlock-style combination locks require you to turn the dial about 3.5 to 4.5 full turns during the opening sequence — multiple full clockwise turns to clear the mechanism, then reverse to the first number, forward to the second, and back to the third. This multi-turn protocol isn't about security (the number of combinations handles that); it's about mechanically engaging and disengaging the internal disc cams in the correct sequence.