# 角度変換：度・ラジアン・度分秒・グラード

> 十進度、度分秒（DMS）、ラジアン、グラード、回転数、角分、角秒、ミリラジアンの間で角度を変換します。

操作できるページ：https://www.calcopenly.com/ja/geometry/angle-dms-converter
分野：幾何の計算機

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.

## 入力

- **角度**: 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** (選択肢：Degrees (decimal or DMS), ラジアン, Gradians (gon), Turns, Arcminutes, Arcseconds, Milliradians)

## 結果

- 度 (°) — 主な結果
- Degrees, minutes, seconds
- ラジアン (rad)
- Radians as a multiple of π
- グラジアン (grad)
- Turns
- Arcminutes (′)
- Arcseconds (″)
- Milliradians (mrad)
- Same direction within 0°–360° (°)

## 計算式

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

## 計算例

### 12°30'15" (DMS)

- 角度: 12°30'15"
- Unit of the angle: Degrees (decimal or DMS)
- **度: 12.5041666667 °**
- **ラジアン: 0.2182388786 rad**
- **グラジアン: 13.8935185185 grad**
- **Degrees, minutes, seconds: 12° 30′ 15″**
- **Arcseconds: 45,015 ″**
- 照合元：Python 3.8 fractions: 12 + 30/60 + 15/3600 = 3001/240; math.radians of that; ×10/9 for gradians

### 1 radian

- 角度: 1
- Unit of the angle: ラジアン
- **度: 57.2957795131 °**
- **Degrees, minutes, seconds: 57° 17′ 44.8062″**
- **Turns: 0.1591549431**
- 照合元：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

- 角度: pi
- Unit of the angle: ラジアン
- **度: 180 °**
- **Radians as a multiple of π: π**
- **グラジアン: 200 grad**
- 照合元：π rad = 180° = 200 grad by definition

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

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

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

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

### Latitude 33°51'35" S

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

## よくある質問

### 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.

### 1ラジアンは何度ですか？

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).

### グラードとは何ですか？

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.

### 「角度変換：度・ラジアン・度分秒・グラード」の精度はどのくらいですか？

精度は入力値と計算方法の前提に依存します。十進演算には有効数字50桁を使いますが、推定、数値計算手法、元データの精度はそれより低い場合があります。表示の丸め処理でこれらの制約がなくなるわけではありません。 独立した出典の解答と照合した計算例：8。 例えば、「12°30'15" (DMS)」はPython 3.8 fractions: 12 + 30/60 + 15/3600 = 3001/240; math.radians of that; ×10/9 for gradiansと照合しています。

### この計算方法の出典は何ですか？

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.

## 出典

- [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)