Degree (angle)

Imagine you spin in a full circle.

A full turn is 360 degrees. This number is very helpful. It can be split into many parts. You can divide it by many numbers. One reason for this is the sun. The sun moves about one degree each day.

Some people use smaller parts too. They use minutes and seconds. These help us be very exact. This is useful for maps and stars.

Imagine you spin in a full circle. We measure that turn in degrees. A full turn is 360 degrees.

Why use the number 360? We do not know for sure. One idea links it to the sun. The sun seems to move one degree each day. Some old calendars used 360 days for a year. Another idea is that 360 is easy to divide. You can split 360 into many equal parts. It can be divided by almost every small number. This helps us split the world into 24 time zones. Each zone is 15 degrees wide.

Sometimes we need to be very exact. We can split one degree into smaller bits. One degree has 60 minutes. Each minute has 60 seconds.

Scientists also use a unit called a radian. A full turn is 2 radians.

In the past, some used a unit called the gon. A full circle in gon is 400. This was part of a plan to use a metric system. Most people still use degrees today.

Imagine you are spinning in a circle. We can measure how much you turn using a unit called a degree. A full, complete rotation is always assigned the value of 360 degrees.

You might see a small circle symbol, like this °, used to show degrees. While scientists often use a unit called a radian, degrees are still very common. In fact, the SI brochure says degrees are an accepted unit. One full turn of 360 degrees is equal to exactly 2 radians.

This helps us understand how different ways of measuring angles relate to each other.

Why did people choose the number 360? We do not know the exact reason. One theory is that it relates to the sun. Ancient astronomers saw the sun move about one degree each day along its path. Because of this, some old calendars used 360 days for a year. The Persian and Babylonian calendars are examples of this. Another idea is that 360 is very easy to divide into parts. It has 24 different divisors. It can be divided by every number from 1 to 10, except for the number 7. This makes it very useful for splitting things up.

History shows us that many smart people used these measurements. The Babylonians used a system based on the number 60. They might have used the angle of an equilateral triangle as a base.

They used chords of a circle to do early math. Greek scientists like Hipparchus and Aristarchus used Babylonian knowledge too. Other Greeks like Archimedes and Timocharis also worked with these divisions. They helped divide the circle into 360 degrees. Eratosthenes used a simpler system with 60 parts. These early thinkers helped build the math we use today.

Sometimes a single degree is not precise enough for a job. This happens in places like astronomy or when looking at maps. We can make a degree even smaller by splitting it up. One degree can be divided into 60 parts called minutes. Each minute can be divided into 60 parts called seconds. These are also known as arcminutes and arcseconds. You might see them written with tiny marks like ′ or ″. Sailors use these small measurements on maritime charts to stay on course. They use decimal minutes to help them find their way.

There have been other attempts to change how we measure turns. In France, people tried to use a system called the gon. In this system, a full circle is 400 gon instead of 360 degrees. This was part of a plan to use a metric system. This idea was eventually abandoned by Napoleon, but grades are still used in some tools. Some military tools use a different unit called a mil. In the Russian army, they used a system with 600 units. Even with these different ways, the degree remains a very important tool for our world.

A degree, or degree of arc, is a unit used to measure a plane angle. It measures how much something has rotated or turned. In this system, one full rotation is assigned a value of 360 degrees. You will often see it written with a small circle symbol: °. While it is not the official SI unit for angular measure, the SI brochure lists it as an accepted unit. The official SI unit is actually the radian. Because a full rotation equals 2 radians, one degree is equivalent to π/180 radians.

To understand how degrees work, we can look at how they are subdivided for precision. For many tasks, a whole degree is enough. However, astronomers and geographers need more detail. They use a system called DMS notation, which stands for degrees, minutes, and seconds. One degree is divided into 60 equal parts called minutes of arc. Each minute is then divided into 60 smaller parts called seconds of arc. These are also called arcminutes and arcseconds.

These subdivisions use specific symbols to save space. An arcminute is represented by a single prime mark (′). An arcsecond is represented by a double prime mark (″). For example, a measurement might look like 40° 11.25′. Maritime charts often use degrees and decimal minutes to help sailors. On these charts, one minute of latitude is equal to one nautical mile. Some people also use decimal degrees, which is a different way to write precise angles. An example of decimal degree notation is 40.1875°.

Historians do not know the exact reason why 360 was chosen for a full rotation. One theory suggests it relates to the movement of the sun. Ancient astronomers noticed the sun moves about one degree each day along the ecliptic path. Because of this, some ancient calendars used 360 days for a year. The Persian and Babylonian calendars are examples of this. Another theory is that the Babylonians used a sexagesimal system. This is a number system based on 60. They may have used the angle of an equilateral triangle as a basic unit.

In the earliest trigonometry, mathematicians used chords of a circle. A chord with a length equal to the circle's radius provided a natural base. The Babylonians used their sexagesimal system to divide this into 60 parts, creating a degree. Several Greek scientists used these Babylonian techniques. Aristarchus of Samos and Hipparchus were among the first to use them systematically. Other Greeks, including Timocharis, Aristillus, Archimedes, and Hipparchus, helped divide the circle into 360 degrees. Eratosthenes used a simpler system that divided the circle into only 60 parts.

The number 360 is very useful because it is highly divisible. It has 24 different divisors. These include 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360. In fact, 360 is one of only seven numbers where no number less than twice its size has more divisors. It is also divisible by every number from 1 to 10, except for 7. This makes it much easier to use than the number 2520. This mathematical property helps us divide the world into 24 time zones. Each time zone is nominally 15° of longitude. This aligns with our 24-hour day convention.

There have been other attempts to create different angular units. During the invention of the metric system, France tried to use decimal degrees. This unit is called the gon or gradian. In this system, a full circle is 400 gon. This means a right angle is 100 gon. Although Napoleon abandoned this idea, grades are still used in some scientific calculators. Some military applications use an angular mil. There are different versions of the mil, but it is close to a milliradian. In the imperial Russian army, they used a system of 600 units based on an equilateral chord. This shows how many different ways humans have tried to measure the turning of the world.