About

Precision in angular measurement is non-negotiable for ballistics, surveying, and navigation. A slight deviation in artillery firing solutions or land plotting results in significant errors over distance. This tool standardizes conversion between common angular units used in mathematics and military applications. It handles the cyclical nature of geometry by normalizing inputs. The converter also bridges the gap between Decimal Degrees used in digital mapping and the Degrees Minutes Seconds format used in traditional cartography. Engineers use these translations to align CAD models with real-world geospatial data.

Formulas

Angular conversion relies on ratios relative to a full circle rotation. Different disciplines divide the circle into varying segments.

Degrees to Radians:

rad = deg × π180

Degrees to Mils (NATO):

mil = deg × 6400360 ≈ deg × 17.778

DMS to Decimal Degrees:

DD = D + M60 + S3600

Gradians divide a right angle into 100 units rather than 90. This system simplifies mental arithmetic in surveying but is less common in pure mathematics.

Reference Data

Degrees (°)	Radians (rad)	Gradians (grad)	Mils (NATO)	Sin(θ)	Cos(θ)
0°	0	0	0	0	1
30°	π6	33.33	533.33	0.5	√3/2
45°	π4	50	800	√2/2	√2/2
57.296°	1	63.66	1018.6	0.84	0.54
60°	π3	66.67	1066.7	√3/2	0.5
90°	π2	100	1600	1	0
180°	π	200	3200	0	−1
270°	3π2	300	4800	−1	0
360°	2π	400	6400	0	1

Frequently Asked Questions

A circle is divided into 6400 mils in NATO standards. This creates an easy approximation where 1 mil equals 1 meter at 1 kilometer distance. Soviet or Warsaw Pact standards divide the circle into 6000 mils. This tool uses the NATO standard of 6400.

Negative angles represent clockwise rotation in standard mathematical convention. An input of -90 degrees is geometrically identical to 270 degrees. This tool provides the normalized positive coterminal angle in the results for clarity.

DMS (Degrees-Minutes-Seconds) is the standard for legal land descriptions, maritime navigation, and astronomy. Decimal Degrees are required for digital applications like GIS software, GPS data entry, and code libraries.

Yes. The Gradian system was designed to decimalize the right angle. A full circle is 400 Gradians. This means 100 Gradians is a right angle, making it strictly perpendicular.