Convert Angles to Various Formats

Convert Angles to Various Formats

This application converts angles you specify (in any format) to any or all of the formats you specify by the check boxes in the adjacent column.

Display Format:
123°34'56" 8h 14m 20s 2.15962R 34.3284% 123.58222
Angle Format Explanation and Definitions
Five Angle Formats

The Frosty Drew astronomy tools provide you the ability to specify angles in one of five basic formats with a lot of variations being acceptable as well. You may specify any of the five formats to be used in the output. The decimal format (the last format) ) is shown if all the check box are empty. Following customary practice, elevations displayed in hour angle format will appear as sexagesimal values. The ° symbol used in the sexagesimal format cannot be easily entered on the keyboard. As a substitute ^ may be used. If you wish to input sexagesimal numbers with a ° symbol, you can edit the existing default number, leaving the ° intact. The displayed results will always appear using the ° symbol. The first non-numerical character in the input following the first numerical character determines the format of the angle. Numerical characters include not only the digits but the space and the + and - signs. Other formatting characters including blanks may be used or omitted at will. The five formats are:

Angle Format Type letter Examples
Sexagesimal ° ^ 123°34'56" or 123^ 34 56
Hour : H h 8:14:20 or 8h 14m 20s or even 8:14.33333
Radian R r 2.15692R
Percent % 34.32840%
Decimal (blank) 123.58222

Each of these formats specifies the same angle. Each has its own purpose and is sometimes used in astronomical calculations.

  1. Sexagesimal is perhaps the most familiar - degrees, minutes and seconds. (See Sexagesimal below).
  2. Measuring angles in hours arose because astronomers wished to know when and where a star would be at a specific time. The radian angular measure seems odd to most people when they first encounter it. An oddity of this system is that hour angle only apply to circumferences. Elevations are always measured in sexagesimal. This is because the declination (elevation) angle doesn't change over time, only the equatorial (circumference) right ascension. Converting to and from hour angles simply requires multiplying or dividing the sexagesimal angle by 15. [15=360°/24 hours].
  3. Radians are the natural angle measurement of mathematics. It is based on the fact that a circle is always 2πR where R is its radius. One radian is 180°/π.
  4. Percentage of a complete revolution is frequently used in binary star calculations. One percentage point is 3.6°s.
  5. The decimal format is simply the sexagesimal format changed to a single decimal number. It is always displayed by default.
  6. A final format, arcseconds, is generated internally for very narrow angles such as planetary angular diameters and angular star separations. When angles exceed 600 arcseconds, this format reverts to sexagesimal format. There is no way provided to input angles in arcsecond format other than sexigesimal numbers with the degrees and minutes set to zero or small decimal fractions.

The word sexagesimal appears throughout this page and in the FDO Astronomical Utility Tools page. Sexagesimal refers to the modern version of the old Phoenician base sixty system. We use this for hours, minutes and seconds and also for angles. Astronomers use both hour angles (where a complete revolution occurs in 24 hours) and degrees (where a complete revolution is 360°).

Rules for specifying angles
  1. Measurements around the circumference are specified in [multiples of] the range 0° to 360° (see note). If your source uses the negative angles the program adjusts by adding multiples of 360°. For example -85° becomes (360+-85)° or 275°. Longitudes(λ), azimuths(A), and Right Ascensions(α) are all circumference angles. Circumference angle boxes appear first whenever the Tools provide boxes for angles.
  2. Measurements up or down along the elevation range from -90° to 90°. Values outside this range are logically adjusted to fall within this range. While we could have chosen any other range that spans 180°s, tradition favors -90° to 90°. Latitudes(β), altitudes(a) and declinations(δ) are all elevation angles. Elevation angle boxes are always the second of the pair of boxes.
User Location

Longitudes and latitudes on the surface of the Earth are traditionally measured East/West and North/South respectively. You may append one of these four words (or E, W, N, S) separated from the angle by a required space. The correct translations to 360° system and a -90° to 90° system will be made. For those who insist on using signs, southern and western hemisphere locations are negative.
