Angle Converter: Degrees, Radians, Gradians, Mils

Real-world use cases

• Finish trigonometry homework without unit slips

  Your textbook gives an angle in degrees but the calculator wants radians, and a single mode mismatch turns a clean answer into nonsense. Type the degree value, read the radian equivalent next to it, and confirm whether 90 degrees should be entered as 1.5708 or as pi over 2. The reference row pins down right, straight and full angles so you can sanity check the whole worksheet at a glance.

• Read European survey plans in gradians

  A site plan drawn on the continent lists bearings in gon, but your field gear and crew think in degrees. Drop each gon value in and the tool returns degrees, so 100 gon becomes a familiar 90 degree right angle and 50 gon becomes 45 degrees. No mental factor of 0.9 to fumble while standing over a total station in the rain.

• Build artillery or long range shooting corrections

  Fire control tables and mil dot scopes work in mils, and you need the degree or radian equivalent to cross check a ballistic calculator. Convert 1600 mils to 90 degrees, or a small 5 mil hold to its tiny degree value, and verify your dope before the shot rather than after a miss downrange.

• Convert telescope pointing offsets to arcseconds

  Astronomy software reports a pointing error in degrees but the eyepiece field and guiding limits are quoted in arcseconds. Feed the degree offset in and read it as arcminutes and arcseconds, so a 0.01 degree drift shows up as 36 arcseconds, which tells you immediately whether your mount tracking is good enough for the exposure.

Common pitfalls

• Leaving the calculator in degree mode while feeding it radians (or the reverse). A sine of 1 means sin of 1 radian, not 1 degree, and the two answers differ wildly. Convert the angle first, then match the calculator mode to the unit you actually typed.

• Confusing a NATO mil with a true milliradian. The NATO system has 6400 mils per turn while a milliradian gives about 6283 per turn, a gap of roughly 2 percent. At long range that small difference becomes meters of miss, so always confirm which mil your scope or table uses.

• Mixing up gon with the calculator grad key, or reading 100 gon as 100 degrees. A right angle is 100 gon but 90 degrees, so a value that looks small in gon can be large in degrees. Pick the input unit before you read the number, not after.

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