12°30'15" is 12.50416667° (12° 30′ 15″), which is 0.21823888 rad, 13.89351852 grad or 0.0347338 of a turn.
Degrees + minutes/60 + seconds/3600.
12° 30′ 15″ (seconds rounded to at most 4 decimals).
Type an angle in any of seven units and it is converted to all the others. Degrees accept decimals or degrees, minutes and seconds: 1° = 60′ = 3,600″, so 12°30′15″ is 12 + 30/60 + 15/3600 = 12.5041667°. Radians use 180° = π rad, gradians 400 to a full turn and milliradians 1,000 to a radian. When the angle is a simple fraction of π, the π form is shown too, such as 5π/72 for 12.5°.
The default, 12°30′15″, is 0.2182389 rad or 45,015″. GPS coordinates and survey bearings are the usual case: a latitude written 33°51′35″ S becomes −33.8597222° for a spreadsheet or mapping tool, with south and west negative.
Only the last DMS part may carry decimals, and minutes and seconds must be below 60. Seconds are rounded to four decimal places, about 3 mm of latitude on the ground.
照合元：Python 3.8 fractions: 12 + 30/60 + 15/3600 = 3001/240; math.radians of that; ×10/9 for gradians
照合元：Python 3.8 math: degrees(1) = 57.29577951308232; 0.2957795…×60 = 17.7467707…′, 0.7467707…×60 = 44.80625″; 1/(2π)
照合元：π rad = 180° = 200 grad by definition
照合元：400 grad = 1 turn = 360° by definition
Add the minutes divided by 60 and the seconds divided by 3,600 to the whole degrees: 12°30′15″ = 12 + 0.5 + 0.0041667 = 12.5041667°. For a south latitude or a west longitude, make the result negative, so 33°51′35″ S is −33.8597222°. The sign applies to the whole angle, not only to the degrees.
Keep the whole number as degrees, multiply the fractional part by 60 for minutes, then multiply the new fractional part by 60 for seconds. For 57.2957795°: 0.2957795 × 60 = 17.7467707′, and 0.7467707 × 60 = 44.806″, giving 57°17′44.806″. That angle is one radian.
One radian is 180/π ≈ 57.2958°, or 57°17′44.8″. It is the angle at the centre of a circle cut off by an arc as long as the radius, so a full turn is 2π ≈ 6.2832 rad. The radian is the SI unit of plane angle; the degree, minute and second are accepted for use with the SI (BIPM SI Brochure, Table 8).
A gradian, or gon, is 1/400 of a full turn, so a right angle is exactly 100 grad and 1 grad = 0.9°. It is used mainly in surveying in parts of continental Europe, where splitting the right angle into 100 parts suits decimal arithmetic. 200 grad equals 180°, or π rad.
A milliradian (mrad) is one thousandth of a radian, about 0.0573° or 3.44 arcminutes. At a distance of 1,000 m it spans about 1 m, which is why rifle scopes use it for holdover and range estimates. The NATO mil used for artillery is a rounded version: 6,400 to a circle, against 6,283.2 true milliradians.
精度は入力値と計算方法の前提に依存します。十進演算には有効数字50桁を使いますが、推定、数値計算手法、元データの精度はそれより低い場合があります。表示の丸め処理でこれらの制約がなくなるわけではありません。 独立した出典の解答と照合した計算例：8。 例えば、「12°30'15" (DMS)」はPython 3.8 fractions: 12 + 30/60 + 15/3600 = 3001/240; math.radians of that; ×10/9 for gradiansと照合しています。
BIPM, The International System of Units (SI brochure, 9th ed.), Table 8 — degree, minute and second of arc; NIST SP 811 (2008), Appendix B.9 — factors for plane angle.
この計算機には、独立した出典の解答を使った計算例が 8 件あります。テストに組み込まれており、ここでも実行できます。