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Angle Conversion
Tool Description
Angle Conversion is an online angle unit conversion tool that supports mutual conversion between degree (°), radian (rad), gradian (grad), arcminute (′), arcsecond (″), milliradian (mrad), microradian (μrad), and circle. Simply enter any value and unit to instantly view the corresponding results in all other units — ideal for mathematical calculations, engineering surveying, physics research, and more.
How to Use
- Enter a value: Enter the value to convert in the input box. Both integers and decimals are supported, e.g.
180,3.14159 - Select source unit: Choose the angle unit of the current value from the dropdown (degree/
radian/ gradian/ arcminute/ arcsecond/ milliradian/ microradian/ circle) - View results: Click the "Convert" button or press Enter — the results area below will display the corresponding values in all units, with a copy button beside each result
Use Cases
- Math Learning: Quickly switch between degrees and radians in trigonometric calculations, e.g. converting 30° to π/6 rad; unifying angle units when solving geometry problems
- Engineering Surveying: DMS (degrees-minutes-seconds) conversion in surveying, e.g. converting latitude/longitude from DMS to decimal degrees; converting between mils (milliradians) and degrees in military targeting
- Physics Research: Angular velocity unit conversion in circular motion; comparing extremely small angles (microradian level) with other units in optics
Core Advantages
- Free to Use
Completely free. Simply open the page to use it — no software installation, no registration or login required.
- Private & Secure
All conversions run entirely in your browser. Your input data is never uploaded to any server, protecting your privacy.
- Comprehensive Units
Supports mutual conversion among degree, radian, gradian, arcminute, arcsecond, milliradian, microradian and circle, covering mainstream unit systems.
- Instant Conversion
Results are calculated in real time as you type, with high precision and support for both integers and decimals — no manual click needed to see all unit results.
- Simple & Easy
The interface is clean and intuitive, with no learning curve. Works smoothly on both desktop and mobile for unit conversion anytime, anywhere.
Angle Unit Conversion Relationships
The following shows the conversion relationships between angle units, with degree (°) as the base unit:
| Unit Name | Abbr | Conversion | Equivalent Degrees |
|---|---|---|---|
| Degree | ° | 1° = π/180 rad | 1 |
| Radian | rad | 1 rad = 180/π ° | ≈ 57.2958 |
| Gradian | grad | 1 grad = 0.9° | 0.9 |
| Arcminute | ′ | 1′ = 1/60° | 1/60 |
| Arcsecond | ″ | 1″ = 1/3600° | 1/3600 |
| Milliradian | mrad | 1 mrad = 10⁻³ rad | ≈ 0.0573 |
| Microradian | μrad | 1 μrad = 10⁻⁶ rad | ≈ 5.73×10⁻⁵ |
| Circle | circle | 1 circle = 360° | 360 |
About Radians and Degrees
Radian (rad) is the SI unit for angle, defined as the central angle subtended by an arc length equal to the radius. One full circle equals 2π radians, i.e. 360°.
Gradian (grad), also known as "gon", is used in some European countries and surveying. It divides a right angle into 100 parts, so one full circle = 400 grad, meaning 1 grad = 0.9°.
Milliradian (mrad) is widely used in military and optical applications. The NATO standard divides a circle into 6400 mils (approximately 6283 mrad). 1 mrad ≈ 0.0573°, which at a distance of 1 km corresponds to approximately 1 meter of arc length.
FAQ
1 radian (rad) = 180/π ≈ 57.29578°. This follows from the definition of a radian: when the arc length equals the radius, the corresponding central angle is 1 radian. Since the full circumference is 2πr, a full circle = 2π rad = 360°, so 1 rad = 360°/(2π) = 180°/π.
1° = 60′ (arcminutes), 1′ = 60″ (arcseconds), therefore 1° = 3600″. For example: 30°15′50″ = 30 + 15/60 + 50/3600 ≈ 30.2639°. The DMS (Degrees-Minutes-Seconds) format is very common in latitude/longitude notation.
A gradian (grad or gon) divides a right angle (90°) into 100 equal parts, so one full circle = 400 grad. Conversion: 1 grad = 0.9°, 1° = 10/9 ≈ 1.111 grad. Gradians are mainly used in European surveying and have the advantage of avoiding base-60 notation — everything is decimal.
Not exactly. 1 mrad ≈ 0.0573°. The "mil" differs across standards: NATO standard divides a circle into 6400 mils (1 mil ≈ 0.05625°), while the Warsaw Pact standard uses 6000 mils. This tool uses the mathematical milliradian (mrad), which is 1/1000 of a radian.
No. All conversion calculations run entirely in your browser using pure JavaScript math. Your input data never leaves your device.
This tool uses JavaScript double-precision floating-point numbers (64-bit IEEE 754) for calculations, which is sufficiently accurate for the vast majority of everyday scenarios. Radian-to-degree conversion uses the full double-precision value of π (approximately 3.141592653589793). Decimal portions are capped at 6 significant decimal places, and excessively long decimals are automatically truncated.
This tool supports 8 common angle units: degree (°), radian (rad), gradian (grad), arcminute (′), arcsecond (″), milliradian (mrad), microradian (μrad) and circle. Enter any value and unit to convert it into all the others at once.
There is no fixed upper limit on the value. It handles most everyday integers and decimals. Subject to the browser's double-precision limit, extremely large or small values may show tiny precision errors that have virtually no practical impact.
Instant. All calculations run locally in your browser in real time, displaying all results with almost zero delay and without waiting for network requests.
Completely free, no registration needed. You can use all features directly by opening the page — no fees, no login.
Yes. The page is responsive and works properly on phones, tablets and desktops, with smooth conversion in mobile browsers as well.
Local computation is safer and lighter. Compared with desktop software that requires file uploads, this tool needs no installation and is ready to use instantly; compared with some online tools, all calculations are done locally and data is never uploaded, balancing speed and privacy.
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