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Konverter sudut: derajat, radian, DMS dan gradian

Konversikan derajat desimal, derajat-menit-detik (DMS), radian, gradian, putaran, menit busur, detik busur dan miliradian.

Diperbarui Contoh terverifikasi: 8

Degrees accept DMS such as 12°30'15", 12 30 15 or 33°51'35" S; radians accept expressions such as pi/4
Coba
Derajat
°
Derajat: 12.5041666667 °
Tempat desimal maksimum: 10; Terdekat, jika berjarak sama menjauhi nol
Degrees, minutes, seconds
12° 30′ 15″
Radian
0.2182388786rad
Gradian
13.8935185185grad
Turns
0.0347337963
Arcminutes
750.25′
Arcseconds
45,015″
Milliradians
218.23887855mrad
Same direction within 0°–360°
12.5041666667°

12°30'15" is 12.50416667° (12° 30′ 15″), which is 0.21823888 rad, 13.89351852 grad or 0.0347338 of a turn.

The angle measured from the positive x-axis

12.5°
Cara menghitung S

  1. To degrees

    (12+3060+153600)=12.5041666667∘\left(12 + \frac{30}{60} + \frac{15}{3600}\right) = 12.5041666667^\circ

    Degrees + minutes/60 + seconds/3600.

  2. To radians

    12.5041666667∘×π180=0.2182388786 rad12.5041666667^\circ \times \frac{\pi}{180} = 0.2182388786\ \text{rad}

  3. To gradians and turns

    12.5041666667∘×109=13.8935185185 grad12.5041666667∘360∘=0.0347337963 turn\begin{gathered} 12.5041666667^\circ \times \frac{10}{9} = 13.8935185185\ \text{grad} \\[6pt] \frac{12.5041666667^\circ}{360^\circ} = 0.0347337963\ \text{turn} \end{gathered}

  4. To degrees, minutes, seconds

    12° 30′ 15″ (seconds rounded to at most 4 decimals).

Tentang Konverter sudut: derajat, radian, DMS dan gradian

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.

Contoh penyelesaian

12°30'15" (DMS)

Sudut
12°30'15"
Unit of the angle
Degrees (decimal or DMS)
Derajat
12.5041666667 °
Radian
0.2182388786 rad
Gradian
13.8935185185 grad
Degrees, minutes, seconds
12° 30′ 15″
Arcseconds
45,015 ″

Sumber pemeriksaan: Python 3.8 fractions: 12 + 30/60 + 15/3600 = 3001/240; math.radians of that; ×10/9 for gradians

1 radian

Sudut
1
Unit of the angle
Radian
Derajat
57.2957795131 °
Degrees, minutes, seconds
57° 17′ 44.8062″
Turns
0.1591549431

Sumber pemeriksaan: Python 3.8 math: degrees(1) = 57.29577951308232; 0.2957795…×60 = 17.7467707…′, 0.7467707…×60 = 44.80625″; 1/(2π)

π radians typed as an expression

Sudut
pi
Unit of the angle
Radian
Derajat
180 °
Radians as a multiple of π
π
Gradian
200 grad

Sumber pemeriksaan: π rad = 180° = 200 grad by definition

400 gradians (full turn, edge case)

Sudut
400
Unit of the angle
Gradians (gon)
Derajat
360 °
Turns
1
Same direction within 0°–360°
0 °
Degrees, minutes, seconds
360° 0′ 0″

Sumber pemeriksaan: 400 grad = 1 turn = 360° by definition

Pertanyaan

How do you convert degrees, minutes and seconds to decimal degrees?

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.

How do you convert decimal degrees to degrees, minutes and seconds?

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.

Berapa derajat dalam satu 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).

Apa itu gradian?

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.

What is a milliradian?

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.

Seberapa akurat “Konverter sudut: derajat, radian, DMS dan gradian”?

Akurasi bergantung pada masukan dan asumsi metode. Aritmetika desimal memakai 50 digit signifikan, tetapi perkiraan, metode numerik dan data sumber bisa kurang presisi; pembulatan yang ditampilkan tidak menghilangkan batasan itu. Contoh penyelesaian yang diperiksa dengan sumber independen: 8. Misalnya, “12°30'15" (DMS)” diperiksa dengan Python 3.8 fractions: 12 + 30/60 + 15/3600 = 3001/240; math.radians of that; ×10/9 for gradians.

Dari mana metode ini berasal?

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.

Tentang kalkulator ini

1∘=60′=3600′′=π180 rad=109 grad=1360 turn1^\circ = 60' = 3600'' = \frac{\pi}{180}\,\text{rad} = \frac{10}{9}\,\text{grad} = \frac{1}{360}\,\text{turn}

Sumber

  1. BIPM, The International System of Units (SI brochure, 9th ed.), Table 8 — degree, minute and second of arc
  2. NIST SP 811 (2008), Appendix B.9 — factors for plane angle

Diperiksa dengan referensi

Kalkulator ini mencakup 8 contoh perhitungan dengan jawaban dari sumber independen. Contoh tersebut dijalankan dalam rangkaian pengujian dan dapat Anda jalankan di sini juga.

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