Angle
Angle converter online free. Convert degrees, radians, gradians, turns. Visual arc preview—trigonometry angle calculator.
Common Angles
Visual Representation
90°
Normalized Angle
📐
Angle Units
Degrees °
90Full circle = 360°
Radians rad
1.5708Full circle = 2π ≈ 6.283
Gradians grad
100Full circle = 400 grad
Turns turn
0.25Full circle = 1 turn
Common Angles
| Degrees | Radians | Gradians | Turns |
|---|---|---|---|
| 30° | 0.5236 | 33.3333 | 0.0833 |
| 45° | 0.7854 | 50 | 0.125 |
| 60° | 1.0472 | 66.6667 | 0.1667 |
| 90° | 1.5708 | 100 | 0.25 |
| 180° | 3.1416 | 200 | 0.5 |
| 270° | 4.7124 | 300 | 0.75 |
| 360° | 6.2832 | 400 | 1 |
Quick Reference
π rad = 180°
2π rad = 360°
90° = π/2 rad
100 grad = 90°
1 turn = 360°
1° ≈ 0.0175 rad
Features
- Convert degrees, radians, gradians, turns
- Visual arc preview for angle
- Trigonometric values (sin, cos, tan)
- Common angle quick reference
- Full circle and half circle calculations
- Angle normalization to 0-360°
Common Use Cases
- Convert CSS transform angles (deg to turn)
- Calculate trigonometric functions for canvas
- Convert between JavaScript Math (radians) and CSS (degrees)
- Understand rotation values in animations
- Calculate compass bearings
Angle Measurement Systems
Angles are measured in four main units: degrees (most common), radians (mathematics/programming), gradians (rare, engineering), and turns (CSS, intuitive).
Angle Units:
- Degree (°): 1/360 of a full circle, most intuitive (90° = right angle)
- Radian (rad): Arc length equal to radius, used in trigonometry (π radians = 180°)
- Gradian (grad): 1/400 of a full circle, rarely used (100 grad = 90°)
- Turn: Full rotations, used in CSS (0.25 turn = 90°, 1 turn = 360°)
Common Angles:
- Full circle: 360° = 2π rad = 400 grad = 1 turn
- Half circle: 180° = π rad = 200 grad = 0.5 turn
- Right angle: 90° = π/2 rad = 100 grad = 0.25 turn
- 45° angle: π/4 rad = 50 grad = 0.125 turn
Programming Context:
- JavaScript Math: Uses radians (Math.sin(Math.PI / 2) = 1)
- CSS: Accepts deg, rad, grad, turn (transform: rotate(90deg))
- Canvas: arc() uses radians, often needs conversion from degrees
- Conversion: radians = degrees × π/180, degrees = radians × 180/π
Why radians? In calculus and physics, radians make formulas simpler (arc length = radius × angle in radians). That's why programming languages use radians by default.
Examples
Valid - Right Angle
90° = 1.5708 rad = 0.25 turn Valid - Half Circle
180° = π rad = 0.5 turn Valid - CSS Rotation
transform: rotate(0.5turn) = 180°Frequently Asked Questions
Why does JavaScript use radians instead of degrees?
Radians are the mathematical standard because they simplify calculus and physics formulas. To convert: radians = degrees × Math.PI / 180. For 90°: 90 × π / 180 = π/2 ≈ 1.5708 radians.
What are turns in CSS and when should I use them?
Turns are full rotations: 1 turn = 360°, 0.5 turn = 180°. Use turns for animations that need multiple rotations (5 turns) or when fractions make sense (0.25 turn instead of 90deg). More intuitive than degrees for full rotations.
How do I convert degrees to radians?
Multiply by π/180: radians = degrees × (Math.PI / 180). Example: 45° × π/180 = 0.7854 rad. Or divide by 180 and multiply by π: 45/180 × π = π/4.
What are gradians and why don't we use them?
Gradians (1/400 of a circle) were designed so a right angle = 100 grad (easier decimal math). They're used in some surveying and engineering, but degrees and radians dominate because of historical adoption and mathematical convenience.
How do I normalize an angle to 0-360°?
Use modulo: normalized = angle % 360. For negative angles: normalized = (angle % 360 + 360) % 360. Example: 450° % 360 = 90°, -45° normalized = 315°. This ensures angles are in the standard 0-360° range.
💡 Tips
- For CSS animations with multiple rotations, use turns: @keyframes { from { rotate: 0turn } to { rotate: 5turn } }
- JavaScript Math.sin/cos/tan expect radians—convert first: Math.sin(90 * Math.PI / 180) = 1
- Radians cheatsheet: π/6 = 30°, π/4 = 45°, π/3 = 60°, π/2 = 90°, π = 180°, 2π = 360°
- For compass bearings: 0° = North, 90° = East, 180° = South, 270° = West