Angle Converter
Convert degrees, radians, gradians, arcminutes, arcseconds and full turns — the π-based formulas used in maths, CSS and code.
- InstantResults update as you type
- 27 categoriesFrom length to data storage
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How to use this tool
Steps for using the Unit Converter.
- Type a number into From — degrees are preselected. Commas and scientific notation such as 2.5e3 are accepted.
- Pick the units to convert between; the result in radians (or whichever unit you choose) updates as you type. Use the swap button to reverse the conversion.
- Set the decimal places, turn on Show formula to see the calculation, and copy or share the result.
- Below the converter, the table lists every angle unit with its exact definition, and the links open dedicated pages for the most common pairs.
Example
180 degrees to radians
180 °3.141593 rad
Formula: rad = ° ÷ 57.29577951Common use cases
- Feeding angles to trigonometric functions in code.
- CSS transforms and design tools.
- Surveying, navigation and astronomy.
Angle unit table
| Unit | Symbol | System | Definition | In degrees |
|---|---|---|---|---|
| Degree | ° | Other | 1/360 of a full turn | 1 |
| Radian | rad | SI | 180/π degrees ≈ 57.2958° | 57.2957795131 |
| Gradian | gon | Other | 1/400 of a full turn = 0.9° | 0.9 |
| Arcminute | ′ | Other | 1/60 degree | 0.0166666667 |
| Arcsecond | ″ | Other | 1/3600 degree | 0.0002777778 |
| Turn | tr | Other | One full rotation = 360° | 360 |
Other unit converters
- Length convertermm · cm · m · km · in · ft · yd · mi · nmi
- Weight convertermg · g · kg · t · oz · lb · st
- Speed converterm/s · km/h · mph · ft/s · kn
- Volume convertermL · L · cm³ · m³ · gal (US) · qt (US) · cup (US) · fl oz (US) · gal (UK) · fl oz (UK)
- Temperature converter°C · °F · K
- Area convertermm² · cm² · m² · km² · in² · ft² · yd² · ac · ha
- Time converterms · s · min · h · d · wk
- Pressure converterPa · kPa · MPa · bar · mbar · psi · atm · Torr · mmHg
About angle units
A full turn is 360 degrees, 2π radians or 400 gradians. The radian is the SI unit used in maths and programming: it's the angle at which the arc length equals the radius, so degrees = radians × 180/π.
Arcminutes (1/60°) and arcseconds (1/3,600°) are used in astronomy, navigation and optics. Most programming languages' trigonometric functions (Math.sin, numpy.sin) expect radians, while CSS accepts deg, rad, grad and turn.
Limitations
- Results are rounded for display only; the calculation keeps full precision (15 significant digits).
Frequently asked questions
How do I convert degrees to radians?
Multiply by π/180: 90° = π/2 ≈ 1.5708 rad.
What is a gradian?
1/400 of a full turn (0.9°), so a right angle is exactly 100 gradians. It's used in some surveying equipment.
How many arcseconds are in a degree?
3,600 (60 arcminutes × 60 arcseconds).
Are these angle conversions exact?
Each unit is defined from its official definition (for example 1 inch = 2.54 cm exactly). Results are calculated in double precision and only rounded to the decimal places you choose when shown.