# 角度换算器：度、弧度、度分秒与百分度

> 在十进制度、度分秒（DMS）、弧度、百分度、整周、角分、角秒和毫弧度之间换算。

交互版本：https://www.calcopenly.com/zh/geometry/angle-dms-converter
主题：几何计算器

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.

## 输入

- **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** (选项：Degrees (decimal or DMS), 弧度, Gradians (gon), Turns, Arcminutes, Arcseconds, Milliradians)

## 结果

- 度 (°) — 主要结果
- Degrees, minutes, seconds
- 弧度 (rad)
- Radians as a multiple of π
- 百分度 (grad)
- Turns
- Arcminutes (′)
- Arcseconds (″)
- Milliradians (mrad)
- Same direction within 0°–360° (°)

## 公式

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

## 计算示例

### 12°30'15" (DMS)

- 角度: 12°30'15"
- Unit of the angle: Degrees (decimal or DMS)
- **度: 12.5041666667 °**
- **弧度: 0.2182388786 rad**
- **百分度: 13.8935185185 grad**
- **Degrees, minutes, seconds: 12° 30′ 15″**
- **Arcseconds: 45,015 ″**
- 核验来源：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: 弧度
- **度: 57.2957795131 °**
- **Degrees, minutes, seconds: 57° 17′ 44.8062″**
- **Turns: 0.1591549431**
- 核验来源：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: 弧度
- **度: 180 °**
- **Radians as a multiple of π: π**
- **百分度: 200 grad**
- 核验来源：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″**
- 核验来源：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 °**
- 核验来源：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 °**
- 核验来源：Python 3.8 fractions: −(33 + 51/60 + 35/3600); south latitudes are negative

## 常见问题

### 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.

### 一弧度等于多少度？

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).

### 什么是百分度？

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.

### “角度换算器：度、弧度、度分秒与百分度”有多准确？

准确性取决于输入值和方法的假设。十进制运算使用50位有效数字，但估算、数值方法和源数据的精度可能较低；显示时的舍入并不能消除这些限制。 已按独立来源核验的计算示例：8。 例如，“12°30'15" (DMS)”根据Python 3.8 fractions: 12 + 30/60 + 15/3600 = 3001/240; math.radians of that; ×10/9 for gradians进行核验。

### 这种方法出自哪里？

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.

## 来源

- [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)