Angle Converter

Because the radian is defined geometrically, not by convention. One radian is the angle subtended at the center of a circle by an arc whose length equals the radius. A full circle has an arc length of 2*pi*r, so it subtends 2*pi radians. Any calculus identity involving trig functions - the derivative of sin, the Taylor series of cos, Euler's formula - comes out clean only when angles are measured this way. It is inherently an irrational multiple of pi; there is no way to pick a different natural value.

A gradian - also called gon or grad - is one-hundredth of a right angle, or 1/400 of a full turn. France introduced it in 1793 as part of the broader metric reform. It survives in European civil engineering and surveying, particularly cadastral measurement, where having a right angle equal to exactly 100 units simplifies mental arithmetic. ISO 80000-3 lists the gradian but does not recommend it; degrees and radians dominate most modern work.

No. The conversion runs inside the Preact component in your browser - one multiply, one divide. There is no fetch or websocket for the number, so the tool works offline after the page loads. Google Analytics logs the pageview but does not record your input. Open DevTools, switch to the Network tab, and confirm no request fires when you type.

Because 90 degrees equals pi/2 radians exactly, and pi/2 is an irrational number. The IEEE 754 double-precision representation closest to pi/2 is 1.5707963267948966, and that is what shows up. For arithmetic, the tool uses that double throughout; for display it truncates to ten significant digits. Any engineering application that needs exact rational multiples of pi should be done symbolically (SymPy, Mathematica) rather than in floating point.

One arcsecond is 1/3600 of a degree, or about 4.85 microradians. It is the standard precision unit in astronomy and high-precision optics. Hubble Space Telescope's diffraction-limited resolution is about 0.05 arcseconds; a human eye resolves about 60 arcseconds at best. Parsec, the astronomical distance unit, is defined as the distance at which one astronomical unit subtends one arcsecond - about 3.26 light-years.

Divide arcminutes by 60 and arcseconds by 3600, then add. 40 degrees 15' 30" equals 40 + 15/60 + 30/3600 = 40.25833... degrees. The converter does not accept compound input directly; do the addition yourself and paste the decimal. Typical GIS and navigation software supports DMS input natively, and some phones have it under "Coordinates" display options.

Yes, and they propagate through every conversion linearly because angle conversion is pure scaling. A negative angle usually means a clockwise rotation (in the convention where counter-clockwise is positive). If you need to normalize to the [0, 360) degree range or [-pi, pi] radian range, apply modulo math after the conversion; the tool returns the exact multiple without wrapping.

A turn (also called a revolution or cycle) is one full 360-degree rotation, or 2*pi radians, or 400 gon. It is the most intuitive unit for angular velocity problems ("3600 rpm is 60 turns per second"), gearing, and some educational contexts where pi-based radians feel abstract. Mathematicians Michael Hartl and Bob Palais have argued for "tau" (2*pi) as a more natural constant than pi - the turn is closely related to that proposal.

1 radian = 180/pi degrees = 180/pi * 3600 arcseconds, which is approximately 206,264.806 arcseconds. Astronomers sometimes round this to 206,265 as a handy constant - the conversion factor between small-angle physics and observational data. It appears, for instance, in the parallax formula that defines the parsec.

Use radians everywhere in math libraries (<code>Math.sin</code>, <code>numpy.sin</code>, GLSL <code>sin</code>) because that is what those functions expect. Convert to degrees only at input/output boundaries for humans, and keep the internal representation radian throughout. Mixing the two inside a pipeline is a well-documented source of bugs - the 1999 Mars Climate Orbiter crash involved a unit mismatch of that flavor, though not specifically radian/degree. Document angle units in comments and type names when you can.