Angle Unit Conversion Tool
In mathematics, physics, engineering drafting, astronomy, geodetic surveying, and even game development, angles are represented in a variety of units. Different fields favor different conventions:
- Radians (rad): The SI standard unit, used extensively in advanced mathematics and physics.
- Degrees (°): The most widely recognized unit, commonly used in everyday contexts and basic education.
- Gradians (grad): Also known as "gons" or "percentages of a right angle," frequently used in parts of Europe and civil engineering.
- Arcminutes (arcmin) and arcseconds (arcsec): Employed in astronomy, navigation, and optics to express very small angular measurements.
Manually converting between these units is not only tedious but also prone to errors—especially when dealing with π or base-60 systems. To address this, we present a professional Angle Unit Conversion Tool that supports seamless, high-precision conversion among the following five common angular units:
- Radians (rad)
- Degrees (deg)
- Gradians (grad)
- Arcminutes (arcmin)
- Arcseconds (arcsec)
Simply input a value, select the source and target units, and obtain an accurate result instantly!
🔁 Core Conversion Formulas
All conversions are based on the definition of a full circle = 360°.
| Unit | Equivalent in Degrees (°) |
|---|---|
| 1 rad | ≈ 57.295779513° |
| 1 grad | = 0.9° |
| 1 arcmin | = 1/60° ≈ 0.0166667° |
| 1 arcsec | = 1/3600° ≈ 0.000277778° |
💡 Key Constants:
- π radians = 180° → 1 rad = 180/π ≈ 57.2958°
- A full circle = 400 gradians (the gradian system defines a right angle as 100 grad)
Common Conversion Formulas
| Direction | Formula |
|---|---|
| deg → rad | rad = deg × π / 180 |
| rad → deg | deg = rad × 180 / π |
| deg → grad | grad = deg × 10/9 |
| grad → deg | deg = grad × 0.9 |
| deg → arcmin | arcmin = deg × 60 |
| arcmin → deg | deg = arcmin ÷ 60 |
| arcmin → arcsec | arcsec = arcmin × 60 |
| deg → arcsec | arcsec = deg × 3,600 |
| rad → arcsec | arcsec = rad × (180/π) × 3,600 ≈ rad × 206,264.8 |
📐 Reference Conversion Table
| deg (°) | rad | grad | arcmin (′) | arcsec (″) |
|---|---|---|---|---|
| 1 | 0.0174533 | 1.11111 | 60 | 3,600 |
| 10 | 0.174533 | 11.1111 | 600 | 36,000 |
| 45 | 0.785398 | 50 | 2,700 | 162,000 |
| 90 | 1.57080 | 100 | 5,400 | 324,000 |
| 180 | 3.14159 | 200 | 10,800 | 648,000 |
| 360 | 6.28319 | 400 | 21,600 | 1,296,000 |
| — | 1 | 57.2958 | 3,437.75 | 206,265 |
| — | — | 1 | 54 | 3,240 |
| — | — | — | 1 | 60 |
✅ Typical References:
- Right angle = 90° = π/2 rad = 100 grad
- Apparent diameter of the Moon ≈ 30 arcmin (i.e., 0.5°)
- GPS positioning accuracy can reach 1 arcsec (≈ 30 meters on Earth’s surface)
✨ Tool Highlights
- Comprehensive coverage: Supports all 5 major angular units for applications across mathematics, engineering, astronomy, and surveying.
- High precision: Uses π ≈ 3.141592653589793 for scientific-grade accuracy.
- Real-time conversion: Instant results upon input; supports decimals and negative angles.
- Free to use: No ads, no registration required.
- Responsive design: Works seamlessly on mobile, tablet, and desktop devices.
🌐 Try it now!
📐 Make angle conversion simple, professional, and error-free!
Whether you're solving trigonometric equations, calibrating instruments, observing celestial objects, or completing homework assignments, this tool is your ideal companion.
🌌 Give it a try—achieve precise control over every angle!