# 각도 변환기: 도, 라디안, DMS와 그레이드

> 십진 도, 도-분-초(DMS), 라디안, 그레이드, 회전수, 각분, 각초, 밀리라디안 사이에서 각도를 변환하세요.

직접 계산할 수 있는 페이지: https://www.calcopenly.com/ko/geometry/angle-dms-converter
분야: 기하 계산기

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.

## 입력

- **각도**: 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** (선택 항목: Degrees (decimal or DMS), 라디안, Gradians (gon), Turns, Arcminutes, Arcseconds, Milliradians)

## 결과

- 도 (°) — 주요 결과
- Degrees, minutes, seconds
- 라디안 (rad)
- Radians as a multiple of π
- 그라디안 (grad)
- Turns
- Arcminutes (′)
- Arcseconds (″)
- Milliradians (mrad)
- Same direction within 0°–360° (°)

## 공식

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

## 계산 예제

### 12°30'15" (DMS)

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

### 1 radian

- 각도: 1
- Unit of the angle: 라디안
- **도: 57.2957795131 °**
- **Degrees, minutes, seconds: 57° 17′ 44.8062″**
- **Turns: 0.1591549431**
- 검증 출처: 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

- 각도: pi
- Unit of the angle: 라디안
- **도: 180 °**
- **Radians as a multiple of π: π**
- **그라디안: 200 grad**
- 검증 출처: π rad = 180° = 200 grad by definition

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

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

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

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

### Latitude 33°51'35" S

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

## 자주 묻는 질문

### 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.

### 1라디안은 몇 도인가요?

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).

### 그라디안이란 무엇인가요?

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.

### “각도 변환기: 도, 라디안, DMS와 그레이드”의 정확도는 어느 정도인가요?

정확도는 입력값과 계산 방법의 가정에 따라 달라집니다. 십진 연산은 유효숫자 50자리를 사용하지만, 추정값·수치해석 방법·원본 데이터의 정밀도는 더 낮을 수 있습니다. 표시값을 반올림해도 이러한 한계는 사라지지 않습니다. 독립적인 출처의 풀이와 대조한 계산 예시: 8. 예를 들어 “12°30'15" (DMS)”은 Python 3.8 fractions: 12 + 30/60 + 15/3600 = 3001/240; math.radians of that; ×10/9 for gradians와 대조해 확인합니다.

### 이 계산 방법의 출처는 무엇인가요?

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.

## 출처

- [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)