Angle Conversions

Geometry and Trigonometry

• Angle Conversions
  • Bearing to azimuth
  • Azimuth to bearing
  • Radians to degrees
  • Degrees to radians
  • Mils to degrees
  • Degrees to mils
  • Grads to degrees
  • Degrees to grads

Source: HP-45 Applications Book (HP 00045-90320 Rev. B Reorder 00045-66001, Dec 1974)

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Angle Conversions

Bearing to azimuth

Note: x = bearing

Example:
S 42.6°E = 137.40° = 137°24'

LINE	DATA	OPERATIONS	DISPLAY	REMARKS
1	x	MODE 1'DEG		If x is in decimal degrees,
				go to 3
2		HMS→	D
3				If Sx° E, go to 4,
				If Sx° W, go to 5,
				If Nx° W, go to 6,
				If Nx° E, go to 7.
4		1 8 0 x<>y -		Go to 7
5		1 8 0 +		Go to 7
6		+/- ENTER 3 6 0		Go to 7
		+
7				For degrees, minutes,
				seconds, go to 8.
				Otherwise, stop.
8		→HMS

Azimuth to bearing

Note: x = azimuth

Method:
If 0 < x < 90°, convert to ND°E
If 90 < x < 180°, convert to SD°E
If 180 < x < 270°, convert to SD°W
If 270 < x < 360°, convert to ND°W

Example:
226°23' = S46,38°W = S46°23'W

LINE	DATA	OPERATIONS	DISPLAY	REMARKS
1	x	MODE 1'DEC		If x is in decimal degrees,
				go to 3
2		HMS→	D
3				If 0 < x < 90, go to 7,
				If 90 < x < 180, go to 4,
				If 180 < x < 270, go to 5,
				If 270 < x < 360, go to 6.
4		1 8 0 x<>y -	D	Go to 7
5		1 8 0 -	D	Go to 7
6		3 6 0 + +/-	D	Go to 7
7				For degrees, minutes,
				seconds, go to 8.
				Otherwise, stop.
8		→HMS

Radians to degrees

Note: x = input data in radians

Example:

1. 1 radians = 57,30° (To see full display, press DISPLAY 4'ALL)
2. ³⁄₄ π radians = 135°

LINE	DATA	OPERATIONS	DISPLAY	REMARKS
1	x	→DEG

Degrees to radians

Note: x = input data in degrees

Example:

1. 1° = 0.02 radians (To see full display, press DISPLAY 4'ALL)
2. 266° = 4.64° radians

LINE	DATA	OPERATIONS	DISPLAY	REMARKS
1	x	→RAD

Mils to degrees

Example: 1571 mils = 90°

LINE	DATA	OPERATIONS	DISPLAY	REMARKS
1	x	→DEG
2		1 0 0 0 ÷

One circle has 6283 mils.
The US use 6400 divisions instead.
The Russians use 6000 mil divisions.
The French use 6280 mils, the Swedens use 6300 mils.

Degrees to mils

Note: x = input data in degrees

Example: 90° = 1571 mils

LINE	DATA	OPERATIONS	DISPLAY	REMARKS
1	x	→RAD
2		1 0 0 0 ×

Grad to degrees

Note: x = input data in grads

Example: 300 grads = 270°

LINE	DATA	OPERATIONS	DISPLAY	REMARKS
1	x	ENTER . 9 ×

Degrees to grad

Note: x = input data in degrees

Example: 360° = 400 grads

LINE	DATA	OPERATIONS	DISPLAY	REMARKS
1	x	ENTER . 9 ÷