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Angle Converter
Convert between degrees, radians, gradians, arcminutes, and arcseconds with formula display.
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What is Angle Converter?
Angle is a measure of rotation between two lines or rays. Different fields use different units to measure angles. Degrees are common in everyday use, radians are standard in mathematics and physics, gradians are used in surveying and engineering, while arcminutes and arcseconds are used in astronomy and navigation.
This converter supports conversion between all five common angle units with formula display. The conversion uses exact mathematical relationships: π radians = 180°, 90° = 100 gradians, 1° = 60 arcminutes = 3600 arcseconds.
Common Angle Conversions
These exact relationships are used by the converter and are handy to memorize for quick mental math:
| Degrees | Radians | Gradians | Arcminutes |
|---|---|---|---|
| 0° | 0 rad | 0 grad | 0′ |
| 30° | π/6 rad | 33.33 grad | 1,800′ |
| 45° | π/4 rad | 50 grad | 2,700′ |
| 90° | π/2 rad | 100 grad | 5,400′ |
| 180° | π rad | 200 grad | 10,800′ |
| 360° | 2π rad | 400 grad | 21,600′ |
How to Use
- Enter Value — Type the numeric angle value you want to convert.
- Select Units — Choose the source unit (From) and target unit (To) from the dropdowns.
- View Result — The converted value appears instantly along with the conversion formula.
- Swap Units — Click the Swap button to reverse the conversion direction.
- Use Examples — Click "90°" to see a right angle conversion, or "π rad" for pi radians.
Frequently Asked Questions
What is the difference between degrees and radians?
A degree (1/360 of a full circle) is the most common unit for measuring angles. A radian is the angle where the arc length equals the radius. There are π radians in 180° (about 3.14159 rad = 180°). Radians are preferred in calculus and physics because they simplify formulas involving trigonometric functions.
What are gradians used for?
Gradians (or gons) divide a right angle into 100 units, making a full circle 400 gradians. They are primarily used in surveying, civil engineering, and some European countries for land measurement. The advantage is that a quarter circle is exactly 100 gradians, making decimal calculations simpler.
When should I use arcminutes and arcseconds?
Arcminutes (′) and arcseconds (″) are subdivisions of degrees used when precision matters. 1° = 60′ (arcminutes), 1′ = 60″ (arcseconds). They are commonly used in astronomy (measuring star positions), navigation (GPS coordinates), optics (lens specifications), and surveying (property boundaries).
Is my data stored anywhere?
No. All conversions happen instantly in your browser. Your input never leaves your device.
Last updated: 6 Aug 2026
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