Category:Angular Measure
This category contains results about Angular Measure.
Definitions specific to this category can be found in Definitions/Angular Measure.
The usual units of measurement for angle are as follows:
Degree
The degree (of angle) is a measurement of plane angles, symbolized by $\degrees$.
\(\ds \) | \(\) | \(\ds 1\) | degree | |||||||||||
\(\ds \) | \(=\) | \(\ds 60\) | minutes | |||||||||||
\(\ds \) | \(=\) | \(\ds 60 \times 60 = 3600\) | seconds | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac 1 {360}\) | full angle (by definition) |
Minute
The minute (of angle) is a measurement of plane angles, symbolized by $'$.
\(\ds \) | \(\) | \(\ds 1\) | minute | |||||||||||
\(\ds \) | \(=\) | \(\ds 60\) | seconds | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac 1 {60}\) | degree of angle (by definition) |
Second
The second (of angle) is a measurement of plane angles, symbolized by $''$.
\(\ds \) | \(\) | \(\ds 1\) | second | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac 1 {60}\) | minute of angle (by definition) | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac 1 {60 \times 60} = \dfrac 1 {3600}\) | degree of angle |
Radian
The radian is a measure of plane angles symbolized either by the word $\radians$ or without any unit.
Radians are pure numbers, as they are ratios of lengths. The addition of $\radians$ is merely for clarification.
$1 \radians$ is the angle subtended at the center of a circle by an arc whose length is equal to the radius: