# زاویہ تبدیل کریں: ڈگری، ریڈیئن، DMS اور گریڈیئن

> اعشاری ڈگری، ڈگری-منٹ-سیکنڈ (DMS)، ریڈیئن، گریڈیئن، مکمل چکر، قوسی منٹ، قوسی سیکنڈ اور ملی ریڈیئن کے درمیان زاویہ بدلیں۔

انٹرایکٹو صورت: https://www.calcopenly.com/ur/geometry/angle-dms-converter
موضوع: ہندسی کیلکولیٹر

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.

## اندراجات

- **زاویہ**: 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** (اختیارات: Degrees (decimal or DMS), ریڈیئن, Gradians (gon), Turns, Arcminutes, Arcseconds, Milliradians)

## نتائج

- درجے (°) — بنیادی نتیجہ
- Degrees, minutes, seconds
- ریڈیئن (rad)
- Radians as a multiple of π
- گریڈیئن (grad)
- Turns
- Arcminutes (′)
- Arcseconds (″)
- Milliradians (mrad)
- Same direction within 0°–360° (°)

## فارمولا

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

## حل شدہ مثالیں

### 12°30'15" (DMS)

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

### 1 radian

- زاویہ: 1
- Unit of the angle: ریڈیئن
- **درجے: 57.2957795131 °**
- **Degrees, minutes, seconds: 57° 17′ 44.8062″**
- **Turns: 0.1591549431**
- جانچ کا ماخذ: ⁨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

- زاویہ: pi
- Unit of the angle: ریڈیئن
- **درجے: 180 °**
- **Radians as a multiple of π: π**
- **گریڈیئن: 200 grad**
- جانچ کا ماخذ: ⁨π rad = 180° = 200 grad by definition⁩

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

- زاویہ: 400
- Unit of the angle: Gradians (gon)
- **درجے: 360 °**
- **Turns: 1**
- **Same direction within 0°–360°: 0 °**
- **Degrees, minutes, seconds: 360° 0′ 0″**
- جانچ کا ماخذ: ⁨400 grad = 1 turn = 360° by definition⁩

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

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

### Latitude 33°51'35" S

- زاویہ: 33°51'35" S
- Unit of the angle: Degrees (decimal or DMS)
- **درجے: -33.8597222222 °**
- جانچ کا ماخذ: ⁨Python 3.8 fractions: −(33 + 51/60 + 35/3600); south latitudes are negative⁩

## سوالات

### 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.

### ایک ریڈیئن میں کتنے درجے ہوتے ہیں؟

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).

### گریڈیئن کیا ہے؟

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.

### “⁨زاویہ تبدیل کریں: ڈگری، ریڈیئن، DMS اور گریڈیئن⁩” کتنا درست ہے؟

درستی آپ کی درج کردہ قدروں اور طریقے کے مفروضوں پر منحصر ہے۔ اعشاری حساب 50 بامعنی ہندسے استعمال کرتا ہے، مگر تخمینے، عددی طریقے اور ماخذ کا ڈیٹا کم درست ہو سکتے ہیں؛ دکھائی گئی قدروں کو راؤنڈ کرنے سے یہ حدود ختم نہیں ہوتیں۔ آزاد ذرائع کی حل شدہ مثالوں سے جانچ: 8۔ مثلاً، “⁨12°30'15" (DMS)⁩” کو ⁨Python 3.8 fractions: 12 + 30/60 + 15/3600 = 3001/240; math.radians of that; ×10/9 for gradians⁩ سے جانچا جاتا ہے۔

### اس طریقے کا ماخذ کیا ہے؟

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.

## ماخذ

- [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)