Angle Converter
Convert between degrees, radians, gradians, arc minutes, arc seconds, and more. Free, fast, and accurate angle conversions for math, engineering, and navigation.
Enter an angle to see conversions
Reference Table
| ° | rad | grad | turn |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 30 | 0.523598776 | 33.333333 | 0.083333333 |
| 45 | 0.785398163 | 50 | 0.125 |
| 60 | 1.047198 | 66.666667 | 0.166666667 |
| 90 | 1.570796 | 100 | 0.25 |
| 180 | 3.141593 | 200 | 0.5 |
| 270 | 4.712389 | 300 | 0.75 |
| 360 | 6.283185 | 400 | 1 |
All conversions happen in your browser. No data is sent to any server.
Embed This Tool
Add this tool to your website with customizable styling
How to Use
- 1 Enter your angle value in the input field. You can enter any number, including negative values and decimals (e.g., 90, 3.14159, -45).
- 2 Select your source unit from the "From" dropdown. Choose from 8 angle units including degrees, radians, gradians, arc minutes, arc seconds, turns, quadrants, and sextants.
- 3 Select your target unit from the "To" dropdown. Use the swap button to quickly reverse the conversion direction.
- 4 View your results instantly with pi notation for radians (e.g., π/2), angle type classification (acute, right, obtuse), and common equivalents.
Pro Tip: When converting to radians, common angles like 30°, 45°, 60°, 90° will show their pi notation (π/6, π/4, π/3, π/2) for easy reference in mathematical formulas.
Frequently Asked Questions
How do I convert degrees to radians?
To convert degrees to radians, multiply by π/180. For example, 90° = 90 × (π/180) = π/2 radians ≈ 1.5708. Our converter handles this automatically - just enter the degrees and select radians as the target unit. The formula is: radians = degrees × (π/180).
How do I convert radians to degrees?
To convert radians to degrees, multiply by 180/π. For example, π radians = π × (180/π) = 180°. Our converter shows the result instantly when you enter radians and select degrees. The formula is: degrees = radians × (180/π).
What is a gradian (gon)?
A gradian (also called gon or grade) is an angular unit where a right angle equals 100 gradians, making a full circle 400 gradians. This system is used in surveying because it makes calculations easier - 1 gradian = 0.9 degrees. The relationship is: 90° = 100 grad = π/2 rad.
What are arc minutes and arc seconds?
Arc minutes (′) and arc seconds (″) are subdivisions of degrees used for precise angular measurements, especially in astronomy and navigation. 1 degree = 60 arc minutes = 3,600 arc seconds. For example, the apparent diameter of the Moon is about 31 arc minutes.
What are the different angle types?
Angles are classified by their measure: Acute (0° to 90°), Right (exactly 90°), Obtuse (90° to 180°), Straight (exactly 180°), and Reflex (180° to 360°). Our converter automatically identifies the angle type based on your input.