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Açı dönüştürücü: derece, radyan, DMS ve grad

Ondalık derece, derece-dakika-saniye (DMS), radyan, grad, tur, yay dakikası, yay saniyesi ve miliradyan arasında dönüşüm yapın.

Güncellendi Doğrulanan örnekler: 8

Degrees accept DMS such as 12°30'15", 12 30 15 or 33°51'35" S; radians accept expressions such as pi/4
Dene
Derece
°
Derece: 12.5041666667 °
En fazla ondalık basamak: 10; En yakına; eşit uzaklıkta sıfırdan uzağa
Degrees, minutes, seconds
12° 30′ 15″
Radyan
0.2182388786rad
Gradyan
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°
Nasıl hesaplanır 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).

Açı dönüştürücü: derece, radyan, DMS ve grad hakkında

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.

Çözümlü örnekler

12°30'15" (DMS)

Açı
12°30'15"
Unit of the angle
Degrees (decimal or DMS)
Derece
12.5041666667 °
Radyan
0.2182388786 rad
Gradyan
13.8935185185 grad
Degrees, minutes, seconds
12° 30′ 15″
Arcseconds
45,015 ″

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

1 radian

Açı
1
Unit of the angle
Radyan
Derece
57.2957795131 °
Degrees, minutes, seconds
57° 17′ 44.8062″
Turns
0.1591549431

Doğrulama kaynağı: 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

Açı
pi
Unit of the angle
Radyan
Derece
180 °
Radians as a multiple of π
π
Gradyan
200 grad

Doğrulama kaynağı: π rad = 180° = 200 grad by definition

400 gradians (full turn, edge case)

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

Doğrulama kaynağı: 400 grad = 1 turn = 360° by definition

Sorular

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.

Bir radyan kaç derecedir?

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).

Grad nedir?

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.

“Açı dönüştürücü: derece, radyan, DMS ve grad” ne kadar doğru sonuç verir?

Doğruluk, girdilerinize ve yöntemin varsayımlarına bağlıdır. Ondalık aritmetik 50 anlamlı basamak kullanır; ancak tahminler, sayısal yöntemler ve kaynak veriler daha az hassas olabilir. Gösterilen değerin yuvarlanması bu sınırları ortadan kaldırmaz. Bağımsız kaynaklarla doğrulanan çözümlü örnek sayısı: 8. Örneğin “12°30'15" (DMS)”, Python 3.8 fractions: 12 + 30/60 + 15/3600 = 3001/240; math.radians of that; ×10/9 for gradians ile karşılaştırılarak doğrulanır.

Yöntemin kaynağı nedir?

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.

Bu hesaplayıcı hakkında

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}

Kaynaklar

  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

Kaynaklarla doğrulandı

Bu hesaplayıcı, yanıtları bağımsız kaynaklardan alınan 8 çözümlü örnek içerir. Bunlar test paketinde çalıştırılır; burada da çalıştırabilirsiniz.

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