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Angle Unit Conversion

Enter a value in any unit input field, and the system will automatically convert and display corresponding values for all other units. Click the advanced module switches to expand more unit options.

Enter Angle

Enter a value in any unit input field, and other units will automatically sync and update. Negative values are allowed for angles.

Select the mil standard: Chinese mil (6000 per circle), NATO mil (6400 per circle, international standard), or Swedish mil (6300 per circle).

°
′
″
rad
grad
r
RA
Military Units
Navigation Units
Astronomy Units

Results are for reference only. By using this tool, you agree to the Disclaimer

Usage Instructions

About Angle Unit Converter

Angle Unit Converter is a fast and precise tool for converting between various angle units. It supports common units used in mathematics, physics, and engineering, as well as specialized units for military applications (mil), navigation (point), and astronomy (milliarcsecond).

Key Features

  • Common Units: Degree (°), arcminute (′), arcsecond (″), radian (rad), grad (grad), revolution (r), right angle (RA)
  • Military Units: Chinese mil (6000 per circle), NATO mil (6400 per circle), Swedish mil (6300 per circle)
  • Navigation Units: Point (32 per circle)
  • Astronomy Units: Milliarcsecond (mas)
  • Real-time Conversion: Instant conversion as you type
  • High Precision: Accurate conversion factors based on π with appropriate decimal precision
  • Mil Standard Selection: Switch between Chinese, NATO, and Swedish mil standards
  • Privacy Protection: All conversions performed locally in your browser

Conversion Standards

Base Unit

All conversions use radians (rad) as the base unit. Radians are the SI derived unit for angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. Every unit has a precise conversion factor to/from radians, ensuring accuracy and consistency.

Precision Rules

  • Common Units: Display up to 4 decimal places, automatically removing trailing zeros
  • Advanced Units: Display up to 6 decimal places for high precision
  • Very Large/Small Values: Use scientific notation for values ≥ 1e12 or ≤ 1e-6, or < 1e-30
  • Automatic Formatting: Values automatically switch to scientific notation when appropriate

Unit Categories

Common Units

  • Degree (°): 1° = π/180 rad ≈ 0.0174533 rad. The most commonly used angle unit, 1 circle = 360°.
  • Arcminute (′): 1′ = π/(180×60) rad ≈ 0.0002909 rad. 1° = 60′, commonly used in astronomy.
  • Arcsecond (″): 1″ = π/(180×3600) rad ≈ 4.8481×10⁻⁶ rad. 1′ = 60″, used in astronomical observations.
  • Radian (rad): SI derived unit, 1 rad = 1 rad (base unit). 1 circle = 2π rad ≈ 6.2832 rad.
  • Grad (grad): 1 grad = π/200 rad ≈ 0.015708 rad. European unit, 1 circle = 400 grad, 1 right angle = 100 grad.
  • Revolution (r): 1 r = 2π rad ≈ 6.2832 rad. Mechanical rotation unit, 1 r = 360°.
  • Right Angle (RA): 1 RA = π/2 rad ≈ 1.5708 rad. Geometric unit, 90° angle.

Military Units

Used for weapon aiming and ballistic calculations:

  • Chinese Mil (mil_cn): 1 circle = 6000 mil, 1 mil = 0.06°. Chinese/Soviet mil standard.
  • NATO Mil (mil_nato): 1 circle = 6400 mil, 1 mil = 0.05625°. US/NATO mil standard, international mainstream.
  • Swedish Mil (mil_se): 1 circle = 6300 mil, 1 mil ≈ 0.05714°. Swedish mil standard.

Note: Select the appropriate mil standard before using mil units. The default is NATO mil (6400 per circle).

Navigation Units

Used for ship heading and navigation positioning:

  • Point (pt): 1 circle = 32 points, 1 point = 11.25°. Traditional navigation unit.

Astronomy Units

High-precision units used in astronomical observations:

  • Milliarcsecond (mas): 1 mas = 10⁻³ arcseconds = 4.8481×10⁻⁹ radians. Used for measuring stellar parallax.

Use Cases

  • Mathematics & Physics: Convert between degrees and radians for trigonometric calculations
  • Engineering: Use grad units for European engineering calculations
  • Military Applications: Convert between mil standards for weapon aiming and ballistic calculations
  • Navigation: Use point units for ship heading and navigation positioning
  • Astronomy: Use milliarcseconds for high-precision stellar parallax measurements
  • Mechanical Engineering: Use revolution units for rotational calculations

Technical Notes

Mil Standard Selection

The tool provides a "Mil Standard" selector to choose between:

  • Chinese Mil: 6000 mil per circle (1 mil = 0.06°)
  • NATO Mil: 6400 mil per circle (1 mil = 0.05625°, default, international standard)
  • Swedish Mil: 6300 mil per circle (1 mil ≈ 0.05714°)

When switching mil standards, if you are currently using a mil unit, it will automatically switch to the selected standard.

Accuracy and Precision

  • All conversions use radians as the intermediate base unit to avoid precision loss
  • Conversion factors are based on π for maximum precision
  • Very small units (like milliarcsecond) use high-precision floating-point arithmetic
  • Scientific notation is automatically used for extremely large or small values

Negative Values

Unlike time units, angle units allow negative values. Negative angles are used to represent reverse angles, which is useful in many mathematical and engineering applications.

Privacy and Data

This tool is a pure frontend application. All conversions are performed locally in your browser. No data is sent to any server, and no account registration is required. Your input data is automatically saved to browser local storage and can be cleared at any time using the "Reset" button.

FAQ

Q: How do I reset all inputs?

A: Click the "Reset" button (rotating arrow icon) in the top-right corner of the input area to clear all input data and restore to the initial state.

Q: Which units are supported?

A: Supports common units (degree, arcminute, arcsecond, radian, grad, revolution, right angle), military units (Chinese mil, NATO mil, Swedish mil), navigation units (point), and astronomy units (milliarcsecond).

Q: What is the conversion precision?

A: All conversions use radians as the base unit with precise conversion factors. Common units retain up to 4 decimal places, advanced units retain up to 6 decimal places, and very large or very small values use scientific notation.

Q: Is data automatically saved? Will it be lost when refreshing the page?

A: Yes, input data is automatically saved to browser local storage. Refreshing the page won't cause data loss, and you can continue editing previously entered content. Data is automatically saved about 400ms after you stop typing.

Q: Can angle values be negative?

A: Yes, angle values allow negative input (unlike time units). Negative angles are used to represent reverse angles.

Q: What is the difference between different mil standards?

A: Chinese mil uses 6000 mil per circle (1 mil = 0.06°), NATO mil uses 6400 mil per circle (1 mil = 0.05625°, international standard), and Swedish mil uses 6300 mil per circle (1 mil ≈ 0.05714°). Select the appropriate standard based on your application.