Angle Converter

How to Convert Units of Angles?

To convert units of angles, you will need to use a conversion factor. A conversion factor is a ratio of two equivalent units. For example, there are 360 degrees in a circle. This means that 1 degree is equivalent to 360/1, or 360 degrees. Thus, the conversion factor for converting degrees to radians is 360/1, or 360 degrees. To convert from degrees to radians, you would multiply the number of degrees by this conversion factor. For example, if you wanted to convert 45 degrees to radians, you would multiply 45 by 360/1, or 45 * 360/1 = 16,200/1 = 16.2 radians.

There are no units or symbols specifically for angular conversion to radians. However, the mathematical process of converting angles from one unit to another is the same regardless of the units used. The most common units for angles are degrees, radians, and gradians. There are 360 degrees in a circle, 2π radians in a circle, and 400 gradians in a circle. To convert from one unit to another, you simply need to know the conversion factor. For example, to convert from degrees to radians, you would use the following conversion factor: 1 degree = (π/180) radians. To convert from radians to degrees, you would use the following conversion factor: 1 radian = (180/π) degrees.

What is Angular Mils?

An angular measurement equal to 1/6400 of a complete circle. At 1000 metres, one mil subtends about one metre (~0,98 m). 1/6000 and 1/6300 are used in other countries

What is Arcminutes?

An arcminute is an angular measurement that is equal to 1/60th of a degree, or 60 arcseconds.

What is Arcseconds?

An arcsecond is an angular measurement equal to 1/3600 of a degree or 1/60 of an arcminute. There are also 206,264.5" in a radian, so that 1" = 4.848 ×10-6 radians.

What is Binary Degrees?

The unit of angular measure used in those methods is called binary radian (brad) or binary degree. These representations of angles are often used in numerical control and digital signal processing applications, such as robotics, navigation, computer games, and digital sensors.

What is Centesimal System of Angle Measurement?

The original plan for the metric system was to replace existing time and angle units. However, the French revolutionaries introduced a decimal division of the day and angles.

The Centesimal system of angle measurement is based on 100 equally divided parts, called Grades. Each Grade is then divided into 100 minutes, and each minute is divided into 100 seconds. This system is used to measure very small angles.

1 right angle = 100g (100 grades)

1 grade = 100” (100 minutes)

1 minute = 100’ (100 seconds)

This system is more convenient than sexagesimal.

In the Sexagesimal centesimal system of angle measurement, minutes and seconds are different.

A right angle equals ninety degrees, sixty minutes, or five thousand four hundred sexagesimal minutes.

A right angle is equal to 100 times 100, or 10,000 centesimal minutes.

What is Turn (angle)?

A turn is a unit of plane angle measurement. It is equal to 2π radians, 360 degrees, or 400 gradians. A turn can also be referred to as a cycle (abbreviated cyc. or cyl.), revolution (abbreviated rev.), complete rotation (abbreviated rot.), or full circle. Subdivisions of a turn include half-turns, quarter-turns, centiturns, milliturns, points, etc.

A turn can be divided into 100 centiturns or 1000 milliturns. Each milliturn corresponds to an angle of 0.36°, which can also be written as 21′ 36″. A protractor divided into centiturns is normally called a percentage protractor.

Binary fractions of turns are also used by sailors to measure compass points. The binary degree, or brad, is 1/256th of a turn. This system is used in computing so that angles can be represented with the maximum possible precision in a single byte. There are also other measures of angle used in computing that are based on dividing one whole turn into 2n equal parts.

What is Degree (angle)?

The reason for choosing 360 degrees in a circle is unclear. One suggestion is that it has to do with the fact that there are about 360 days in a year. Ancient astronomers noticed that the sun seemed to move about one degree each day as it followed the ecliptic path over the course of the year. Some ancient calendars, such as the Persian and Babylonian calendars, used 360 days for a year. Therefore, the use of 360 degrees in a circle may be related to the use of sexagesimal numbers in ancient calendars.

The Babylonians and Greeks used a method of trigonometry that was based on the chords of a circle. The length of the chord was equal to the radius, and they divided it into 60 parts. One sixtieth of this was a degree.

Aristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to adapt and use Babylonian astronomical knowledge and techniques. Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide a circle into 360 degrees, each made up of 60 arc minutes. Eratosthenes used a simpler sexagesimal system, dividing a circle into 60 parts.

The number 360 may have been chosen because it is easily divisible. It has 24 divisors, which makes it one of only 7 numbers that can't be divided by any number less than twice its size. 360 is also divisible by every number from 1 to 10, except 7. This property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention.

According to the theory, the number of days in a year is approximately 365 because of the apparent movement of the sun against the celestial sphere. The number was rounded to 360 for some of the mathematical reasons cited above.

What is Diameter (of a circle)?

The diameter of a circle is the length of the line through the center and touching two points on its edge. As demonstrated in the figure above, the diameter never changes.

The diameter of a circle is the line that goes through the middle of the circle, dividing it into two equal halves. The diameter is also the length of the line.

A diameter is a chord that runs through the center point of the circle, making it the longest possible chord of any circle. Any other chord on the circle is simply a line joining two points on the circle.

The center of a circle is the midpoint of its diameter. This means that it is equally distant from the circle's edge at any point. The radius is half the diameter.

What is Gradians?

The gradian is a unit of measurement of an angle, defined as one hundredth of the right angle. In other words, there are 100 gradians in 90 degrees. It is equivalent to 1/400 of a turn, 9/10 of a degree, or π/200 of a radian. Measuring angles in gradians is said to employ the centesimal system of angular measurement.

In continental Europe, there were two different words for 100th of a degree - centigrade and centesimal minute of arc. To avoid confusion, the word Celsius was adopted as the name of the temperature scale.

Although the gradian is not an SI unit, it is legal to use it in the European Union and Switzerland for surveying, mining, and geology.

What is Hexacontades?

According to Eratosthenes, a hexacontade is a unit of measurement equal to 6°. This means that a full rotation is composed of 60 hexacontades.

What is Hour Angles?

The angle between the observer's meridian and the hour circle of a celestial object, measured westward from the meridian. Meridian of an observer and the hour circle of a celestial body, measured westward through 360°.

The hour angle is the angle between the meridian plane (containing Earth's axis and the zenith) and the hour circle (containing Earth's axis and a given point of interest).

The angle may be measured in degrees (positive westward from 0° to 360°) or in time (24h = 360° exactly), depending on the application. In celestial navigation, the angle is typically measured in degrees westward from the prime meridian (Greenwich hour angle, GHA), from the local meridian (local hour angle, LHA), or from the first point of Aries (sidereal hour angle, SHA).

The hour angle and declination can be used together to pinpoint a specific location on the celestial sphere using the equatorial coordinate system.

What is Minutes Of Time?

The minute is a unit of time usually equal to 1/60 of an hour, or 60 seconds.

A minute is equal to 1/60 of an hour, or 60 seconds. In the UTC time standard, a minute sometimes has 61 seconds because of leap seconds. Although it's not an SI unit, the minute is accepted for use with SI units. The symbol for minute or minutes is min. The prime symbol is also sometimes used informally to denote minutes of time.

The word minute comes from the Latin word for "small part." This small part was then divided into even smaller parts, with the second small part being called a "second." The term "third" (1⁄60 of a second) is still used in some languages, for example Polish (tercja) and Turkish (salise). However, most modern usage subdivides seconds by using decimals. The symbol notation of the prime for minutes and double prime for seconds can be seen as indicating the first and second cut of the hour (similar to how the foot is the first cut of the yard or perhaps chain, with inches as the second cut).

What is Seconds Of Time?

The second is the base unit of time in the International System of Units (SI), and is commonly understood and defined as 1/86400 of a day. This factor is derived from the division of the day into 24 hours, then 60 minutes, and finally 60 seconds. Analog clocks and watches often have sixty tick marks on their faces, representing seconds (and minutes), and a "second hand" to mark the passage of time in seconds. Digital clocks and watches often have a two-digit seconds counter. The second is also a part of several other units of measurement like meters per second for speed, meters per second per second for acceleration, and cycles per second for frequency.

Although the historical definition of the unit was based on the division of the Earth's rotation cycle, the formal definition in the International System of Units (SI) is a much steadier timekeeper:

The second is equal to the duration of 9192631770 periods of the radiation corresponding to the transition between the hyperfine levels of the unperturbed ground state of the 133Cs atom.

A leap second is added at irregular intervals to clock time to keep clocks in sync with Earth's rotation.

Multiples of seconds are most often counted in hours and minutes. Fractions of a second are usually expressed in tenths or hundredths. In scientific work, smaller fractions of a second are often counted in milliseconds (thousandths), microseconds (millionths), nanoseconds (billionths), or even smaller units of time. An everyday experience with tiny fractions of a second is a 1-gigahertz microprocessor, which has a cycle time of 1 nanosecond. Camera shutter speeds are frequently expressed in fractions of a second, such as 1⁄30 second or 1⁄1000 second.

Sexagesimal divisions of the day, or the use of base 60 to measure time, date back to the third millennium BC. However, these divisions were not based on seconds, as we understand them today. Smaller divisions of time could not be accurately measured back then, so they were derived mathematically. The first timekeepers that could accurately count seconds were pendulum clocks, invented in the 17th century. In the 1950s, atomic clocks became more accurate than even Earth's rotation, and they continue to set the standard today.

What is Octants?

An instrument for measuring the altitude of a celestial body from a moving ship or aircraft.

A space can be divided into eight parts by three coordinate planes.

An octant in solid geometry is one of eight sections of a three-dimensional Euclidean coordinate system that is determined by the signs of the coordinates. It is similar to a two-dimensional quadrant or a one-dimensional ray.

What is Pechus?

A Greek unit of length is part of the cubit family of units, which means it changes over time. It has also been written as pechys, pecheus, and pecheuse.

In Greece, the metric system was established in 1836 by royal decree. The Greeks gave the new metric units old names, distinguishing them from the old units by calling them “royal”. The meter was named the royal pechus. In 1920, Greece adopted the international system. In 1959, use of the meter was made compulsory by legislative decree, and subsequent legislation has followed the changes made by the CGPM. The meter is now called μετρητής or μέτρο.

What is Points of the Compass?

The points of the compass are a set of horizontal, radially arrayed compass directions used in navigation and cartography. A compass rose is primarily composed of four cardinal directions—north, east, south, and west—each separated by 90 degrees, and secondarily divided by four ordinal (intercardinal) directions—northeast, southeast, southwest, and northwest—each located halfway between two cardinal directions. Some disciplines such as meteorology and navigation further divide the compass with additional azimuths. Within European tradition, a fully defined compass has 32 'points' (and any finer subdivisions are described in fractions of points).

Compass points are useful because they help people orient themselves without having to calculate or remember degrees.

What is Quadrants?

In its simplest form, mathematics is the study of relationships. Everything in our universe can be quantified and analyzed using mathematics, from the movement of planets to the behavior of atoms. By understanding the language of mathematics, we can make predictions about how the universe works and uncover the hidden patterns that govern everything around us.

Coordinate geometry is the branch of mathematics that allows us to graph the past and present of a phenomenon into simple figures and draw insights to predict future outcomes. In this article, we will focus on the most essential elements of coordinate geometry, namely the Coordinate Plane and its Quadrants.

What is Radians?

The radian is the standard unit of angular measure used in many areas of mathematics, and is defined in the SI as being a dimensionless unit with 1 rad = 1. Its symbol is accordingly often omitted, especially in mathematical writing.

One radian is defined as the angle formed by two lines that intersect at the center of a circle, with one line being the radius of the circle and the other line being the arc length of the circle. In other words, the magnitude of a radian is equal to the ratio of the arc length to the radius of the circle. A right angle is exactly π/2 radians.

One radian is equal to 180/π degrees, which is approximately 57.295779513082320876 degrees. This means that 2π radians is equal to 360 degrees, or one complete revolution.

The radian is the SI unit for measuring angles, and is specified by the International Bureau of Weights and Measures and the International Organization for Standardization. The symbol most commonly used for the radian is rad; however, other symbols that were used 100 years ago include c (the superscript letter c, for "circular measure"), the letter r, or a superscript R. These variants are now infrequently used, as they may be mistaken for a degree symbol (°) or a radius (r). Therefore, a value of 1.2 radians would most commonly be written as 1.2 rad; other notations that can be used include 1.2 r, 1.2rad, 1.2c, or 1.2R.

One radian is the angle at the center of a circle that is subtended by an arc whose length is equal to the radius. Radians are equal to about 57.3 degrees.

What is Sextants?

A sextant is a navigation instrument that uses two mirrors to measure the angular distance between two visible objects. The primary use of a sextant is to measure the angle between an astronomical object and the horizon for the purposes of celestial navigation.

The estimation of the angle of altitude is known as sighting or shooting the object, or taking a sight. The angle, and the time when it was measured, can be used to calculate a position line on a nautical or aeronautical chart—for example, sighting the Sun at noon or Polaris at night (in the Northern Hemisphere) to estimate latitude (with sight reduction). Sighting the height of a landmark can give a measure of distance off and, held horizontally, a sextant can measure angles between objects for a position on a chart.[1] A sextant can also be used to measure the lunar distance between the moon and another celestial object (such as a star or planet) in order to determine Greenwich Mean Time and hence longitude. The principle of the instrument was first implemented around 1731 by John Hadley (1682–1744) and Thomas Godfrey (1704–1749), but it was also found later in the unpublished writings of Isaac Newton (1643–1727).

In 1922, Gago Coutinho modified it for aeronautical navigation.

What is Signs?

A sign is an indicator of the presence or occurrence of something else. A natural sign has a causal relation to its object, such as thunder being a sign of a storm. A conventional sign is agreed upon by a group to signify something, such as a full stop at the end of a sentence. Words and expressions in a language, as well as bodily gestures, can also be signs with specific meanings. The most common physical objects referred to as signs are notices and road signs, which usually provide information or instructions using text, symbols, or pictures.

The nature of signs and symbols and their signification is a topic of interest for semiotics, epistemology, logic, and the philosophy of language. These fields of study are concerned with exploring the nature of signs and how they signify. According to classic sources on the topic, such as Aristotle, Augustine, and Aquinas, significance is a relationship between two sorts of things: signs and the kinds of things they signify (intend, express or mean), where one term necessarily causes something else to come to the mind. The traditional theory of signs (Augustine) sets the following threefold partition of things: all sorts of indications, evidences, symptoms, and physical signals, there are signs which are always signs (the entities of the mind as ideas and images, thoughts and feelings, constructs and intentions); and there are signs that have to get their signification (as linguistic entities and cultural symbols). So, while natural signs serve as the source of signification, the human mind is the agency through which signs signify naturally occurring things, such as objects, states, qualities, quantities, events, processes, or relationships.