Angle Converter
Convert degrees, radians, turns, and gradians.
This angle converter switches between degrees, radians, turns, and gradians - the main angle measurement systems used across geometry, trigonometry, engineering, and navigation.
Enter an angle in any supported unit, and the calculator returns the equivalent in your chosen target unit.
Worked Calculation Examples
| Scenario | Result | Calculation Step |
|---|---|---|
| 90 degrees to radians | π/2 ≈ 1.5708 radians | 90 × (π/180) = π/2 ≈ 1.5708 radians. |
| 2 radians to degrees | ≈114.59° | 2 × (180/π) ≈ 114.59°. |
Key Angle Conversion Factors
Radians = degrees x (pi/180). A full circle equals 360 degrees, 2*pi radians (about 6.2832), 1 turn, or 400 gradians. Radians are the standard unit in calculus and higher mathematics because they relate directly to arc length and radius (arc length = radius x angle in radians).
Why Radians Are Preferred in Advanced Math
Many calculus formulas involving trigonometric functions (like derivatives of sine and cosine) only take their simplest, cleanest form when angles are measured in radians rather than degrees - this mathematical convenience is why radians become the default unit once trigonometry moves into calculus-based applications.
How to Use the Angle Converter
- Open the Angle Converter and enter the values requested in the input fields.
- Check the units, percentages, dates, or time periods before reading the answer.
- Review the instant result and adjust any value to compare another scenario.
- Use the formula, example, and FAQs below to understand how the angle converter works.
Frequently Asked Questions
How do you convert degrees to radians?
Multiply the degree value by pi/180 (approximately 0.017453) to convert to radians.
How many radians are in a full circle?
A full circle equals 2*pi radians, approximately 6.2832 radians, equivalent to 360 degrees.
Why do some fields use gradians instead of degrees?
Gradians (400 per full circle) were designed to simplify certain calculations in surveying and some European engineering traditions, since a right angle equals exactly 100 gradians, a round number in that decimal-based system.
How do I use this angle converter?
Enter the known values, review the units or settings, and the calculator updates the result instantly. The formula and example on this page show how the answer is produced.
What does the Angle Converter calculate?
Convert degrees, radians, turns, and gradians. It is designed for fast browser-based calculations without sign-up, downloads, or manual spreadsheet setup.
What formula does this angle use?
The formula is: radians = degrees * pi / 180. Dividing a circle into 360 degrees traces back to ancient Babylonian astronomers roughly 4,000 years ago, likely connected to their base-60 number system and to 360 being a close approximation of the days in a year - radians, a more mathematically natural unit tied directly to a circle's radius, weren't formalized until the 19th century, when mathematician James Thomson (brother of Lord Kelvin) coined the term in 1873.
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Last updated: September 27, 2026.