📐 Angle
Convert angles free between degrees, radians and gradians. Essential for maths, engineering and programming. Instant.
📐 Angle
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About the Angle Tool
Degrees are what everyone learns first, but radians are what mathematics and most programming languages actually use. JavaScript’s Math.sin expects radians, not degrees — a mismatch that produces silently wrong results rather than an error, which makes it a persistent source of bugs.
A radian is the angle subtending an arc equal to the radius, which makes a full circle 2π radians rather than 360 degrees. Gradians divide the circle into 400, occasionally used in surveying. This converter handles all three in your browser.
How to Use Angle
- Enter the angle value.
- Select the source unit.
- Select the target unit.
- Read the converted result.
When to Use This Tool
- Converting degrees to radians for trigonometric functions in code
- Working with CAD or engineering drawings across conventions
- Converting survey bearings expressed in gradians
- Solving mathematics problems requiring radian measure
- Setting rotation values in graphics and animation code
Things Worth Knowing
- A full circle is 360 degrees, 2π radians, or 400 gradians.
- To convert degrees to radians, multiply by π/180.
- Most programming language trigonometric functions expect radians.
Quick Facts
| Tool name | Angle |
| Category | Unit Converters |
| Price | Free — no account, no trial, no watermark |
| Where it runs | Entirely in your browser (client-side) |
| Files uploaded | None — your data never leaves your device |
| File size limit | None imposed; limited only by device memory |
| Works offline | Yes, once the page has loaded |
| Platforms | Windows, macOS, Linux, Android, iOS |
Frequently Asked Questions
Why does mathematics use radians instead of degrees?
Because they make calculus work cleanly. The derivative of sin(x) is cos(x) only when x is in radians — in degrees you pick up an awkward constant factor. Radians are the natural unit for the mathematics.
How do I convert degrees to radians?
Multiply by π/180, approximately 0.01745. So 90 degrees becomes π/2, about 1.5708 radians.
Why does my JavaScript trigonometry give wrong answers?
Almost certainly because you passed degrees where radians were expected. Math.sin(90) returns 0.894, not 1, because it interprets 90 as radians. Convert first with degrees × Math.PI / 180.
What are gradians for?
They divide a right angle into exactly 100 units, which suits decimal arithmetic. They persist in some surveying and civil engineering contexts, particularly in parts of Europe, but are rare elsewhere.