Radian-Degree Calculator
Hermetic Systems home page

radian definition The size of an angle is expressed in units of degrees and radians. There are 360 degrees in a circle (each degree is divided into 60 minutes, and each minute is divided into 60 seconds). A radian is the size of the angle formed at the center of a circle by an arc whose length is equal to the radius of the circle. 1 radian = 57.295779513 degrees (to 9 decimal places). 1 radian is also equal to 180/π degrees. Radians are not divided into smaller sub-units.

This program allows you to:

As the simplest example of use, to convert 1.5 radians to degrees enter "1.5" in the 'Radians' textbox and click on the 'Radians to degrees' button:

The number of decimal places in the results can be increased or decreased by setting the value for 'Significant figures' (from 6 through 9). Input values may be in the range -360° 0' 0" through 360° 0' 0" for degrees and the equivalent for radians (thus -2π through 2π). To perform an addition, e.g., 3.5 radians plus 2.5 radians, enter the 1st and 2nd values into the left and right 'radian' textboxes and click on '+'. (The result appears in the left 'radians' textbox.) The addition (and subtraction) of angles is performed modulo 2π, as shown in the example below, where adding 4.5 to 3.5 produces 1.716815 (which is 8 - 2π). Subtraction is performed similarly, e.g., 1.716815 - 4.5 gives 3.5.

screenshot of Radian-Degree Calculator

When the 'Round to minutes' checkbox is checked, the result in degrees is rounded to the nearest minute. When the 'Output in decimal' checkbox is checked, the result is given either in (a) decimal degrees or (b) degrees and decimal minutes. An input radian value may be negative. To input a negative degrees value, enter the value and click on the 'Change sign' button. All this is illustrated in the results shown below:

To convert decimal degrees (plus optionally decimal minutes and decimal seconds) into degrees, minutes and seconds, enter the degrees value and click on the 'Degrees to radians' button, then click on the 'Radians to degrees' button, as illustrated in the results shown below:

To convert decimal degrees into degrees plus decimal minutes, or vice-versa, enter the degrees value and click on the 'Degrees to radians' button, then click on the 'Radians to degrees' button, as illustrated in the results shown below. Make sure that the 'Output in decimal' checkbox is checked, and the decimal degrees/minutes selection is appropriate.

The 'arrow' button may used to transfer the value in the left textbox to the rightbox, if needed.

Addition and subtraction of angle values may be performed as follows:

These four operations are illustrated by the results shown below:

screenshot

As noted above, addition and subtraction of angles is performed modulo 2π.


How to obtain the software: A fully-functional version of the Radian-Degree Calculator software is available for free download from this website. Click on the following link to go to a web page with further information:

Download Radian-Degree Calculator ...