Angle Converter

The division of a circle into 360 degrees originates from ancient Babylonians, who used a sexagesimal (base-60) system. The number 360 is highly divisible (by 2, 3, 4, 5, 6, 8, 9, 10, 12, etc.), making many fractional calculations easier. It's also close to the number of days in a year.

The sum of the interior angles in any Euclidean triangle is always 180 degrees (or π radians, or 200 gradians).

Using radians simplifies many calculus formulas involving trigonometric functions, such as the derivative of sin(x) being cos(x) only when x is in radians.

The Earth's axis is tilted at an angle of approximately 23.5 degrees relative to its orbital plane. This tilt is the primary cause of the seasons.

While degrees and radians measure two-dimensional (plane) angles, three-dimensional angles are measured in solid angles, with the SI unit being the steradian. A full sphere subtends a solid angle of 4π steradians.

In navigation, a 'bearing' or 'azimuth' is the horizontal angle between a reference direction (usually North) and the direction to an object. These are typically measured in degrees.

The Golden Angle, approximately 137.5 degrees, is related to the golden ratio. It appears frequently in nature, such as in the arrangement of florets in a sunflower head (phyllotaxis), as it provides optimal packing.

A sextant is an astronomical instrument used to measure the angle between any two visible objects. Its primary use is to determine the angle between a celestial object and the horizon, which is essential for celestial navigation.

When light passes from one medium to another, it bends or refracts. The relationship between the angles of incidence and refraction is described by Snell's Law, which is fundamental to the design of lenses and prisms.

In astronomy, the hour angle is a coordinate used in the equatorial coordinate system. It expresses the time since a celestial object last crossed the local celestial meridian, given as an angle.

The gradian (or gon) was invented as part of the metric system's effort to decimalize everything. Having a right angle as 100 gradians simplifies some surveying calculations, though it never achieved widespread use outside of specific fields.

Milliradians (mrads or 'mils') are used in long-range shooting to make corrections for bullet drop and wind. At 1000 meters, one mrad subtends exactly one meter, making it easy to calculate adjustments.

Parallax is the apparent shift in an object's position when viewed from two different lines of sight. By measuring this tiny angle (the parallax angle), astronomers can calculate the distance to nearby stars.

Just as a circle has 360 degrees, a full sphere has approximately 41,253 square degrees of solid angle. One steradian is about 3,283 square degrees.

In astrology and historical astronomy, the ecliptic (the Sun's apparent path) is divided into 12 'signs,' each occupying a 30-degree arc of the celestial sphere.

In physics, the angle of repose is the steepest angle of descent or dip relative to the horizontal plane to which a material can be piled without slumping. It's a key property for handling granular materials like sand or grain.

Brewster's angle is a specific angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. It's the principle behind polarizing filters on cameras and sunglasses.

Architects use angles for everything from ensuring walls are perpendicular (90 degrees) to creating aesthetically pleasing roof pitches and designing complex geometric structures like geodesic domes.