# محول الزوايا: الدرجات والراديان وDMS والغراد

> حوّل بين الدرجات العشرية والدرجات والدقائق والثواني (DMS)، والراديان والغراد والدورات والدقائق والثواني القوسية والميليراديان.

النسخة التفاعلية: https://www.calcopenly.com/ar/geometry/angle-dms-converter
الموضوع: حاسبات الهندسة

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.

## المدخلات

- **الزاوية**: Degrees accept DMS such as 12°30'15", 12 30 15 or 33°51'35" S; radians accept expressions such as pi/4
- **Unit of the angle** (الخيارات: Degrees (decimal or DMS), راديان, Gradians (gon), Turns, Arcminutes, Arcseconds, Milliradians)

## النتائج

- درجات (°) — النتيجة الرئيسية
- Degrees, minutes, seconds
- راديان (rad)
- Radians as a multiple of π
- غراديان (grad)
- Turns
- Arcminutes (′)
- Arcseconds (″)
- Milliradians (mrad)
- Same direction within 0°–360° (°)

## الصيغة

$$
1^\circ = 60' = 3600'' = \frac{\pi}{180}\,\text{rad} = \frac{10}{9}\,\text{grad} = \frac{1}{360}\,\text{turn}
$$

## أمثلة محلولة

### 12°30'15" (DMS)

- الزاوية: 12°30'15"
- Unit of the angle: Degrees (decimal or DMS)
- **درجات: 12.5041666667 °**
- **راديان: 0.2182388786 rad**
- **غراديان: 13.8935185185 grad**
- **Degrees, minutes, seconds: 12° 30′ 15″**
- **Arcseconds: 45,015 ″**
- مصدر التحقق: ⁨Python 3.8 fractions: 12 + 30/60 + 15/3600 = 3001/240; math.radians of that; ×10/9 for gradians⁩

### 1 radian

- الزاوية: 1
- Unit of the angle: راديان
- **درجات: 57.2957795131 °**
- **Degrees, minutes, seconds: 57° 17′ 44.8062″**
- **Turns: 0.1591549431**
- مصدر التحقق: ⁨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

- الزاوية: pi
- Unit of the angle: راديان
- **درجات: 180 °**
- **Radians as a multiple of π: π**
- **غراديان: 200 grad**
- مصدر التحقق: ⁨π rad = 180° = 200 grad by definition⁩

### 400 gradians (full turn, edge case)

- الزاوية: 400
- Unit of the angle: Gradians (gon)
- **درجات: 360 °**
- **Turns: 1**
- **Same direction within 0°–360°: 0 °**
- **Degrees, minutes, seconds: 360° 0′ 0″**
- مصدر التحقق: ⁨400 grad = 1 turn = 360° by definition⁩

### Minus half a degree written as −0°30' (sign edge case)

- الزاوية: -0°30'
- Unit of the angle: Degrees (decimal or DMS)
- **درجات: -0.5 °**
- **Degrees, minutes, seconds: −0° 30′ 0″**
- **Arcminutes: -30 ′**
- **Same direction within 0°–360°: 359.5 °**
- مصدر التحقق: ⁨The sign applies to the whole angle: −(0 + 30/60)⁩

### Latitude 33°51'35" S

- الزاوية: 33°51'35" S
- Unit of the angle: Degrees (decimal or DMS)
- **درجات: -33.8597222222 °**
- مصدر التحقق: ⁨Python 3.8 fractions: −(33 + 51/60 + 35/3600); south latitudes are negative⁩

## الأسئلة

### 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.

### كم درجة في الراديان الواحد؟

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).

### ما هو الغراد؟

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.

### ما مدى دقة «⁨محول الزوايا: الدرجات والراديان وDMS والغراد⁩»؟

تعتمد الدقة على مدخلاتك وافتراضات الطريقة. يستخدم الحساب العشري 50 رقمًا معنويًا، لكن التقديرات والأساليب العددية وبيانات المصدر قد تكون أقل دقة؛ تقريب القيم المعروضة لا يزيل هذه الحدود. أمثلة محلولة جرى التحقق منها بمصادر مستقلة: 8. مثلًا، يجري التحقق من «⁨12°30'15" (DMS)⁩» بالرجوع إلى ⁨Python 3.8 fractions: 12 + 30/60 + 15/3600 = 3001/240; math.radians of that; ×10/9 for gradians⁩.

### ما مصدر هذه الطريقة؟

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.

## المصادر

- [BIPM, The International System of Units (SI brochure, 9th ed.), Table 8 — degree, minute and second of arc](https://www.bipm.org/en/publications/si-brochure)
- [NIST SP 811 (2008), Appendix B.9 — factors for plane angle](https://www.nist.gov/pml/special-publication-811)