Angle Converter
Convert angles between degrees, radians, gradians, and turns. Includes a unit circle reference and common angle values.
Convert Angle
Common Angles
| Angle | Degrees | Radians | Gradians | Turns |
|---|---|---|---|---|
| 0° — Zero | 0 | 0 | 0 | 0 |
| 30° — π/6 | 30 | 1π/6 ≈ 0.523599 | 33.333333 | 0.083333 |
| 45° — π/4 | 45 | 1π/4 ≈ 0.785398 | 50 | 0.125 |
| 60° — π/3 | 60 | 1π/3 ≈ 1.047198 | 66.666667 | 0.166667 |
| 90° — Right angle | 90 | 1π/2 ≈ 1.570796 | 100 | 0.25 |
| 120° — 2π/3 | 120 | 2π/3 ≈ 2.094395 | 133.33333 | 0.333333 |
| 135° — 3π/4 | 135 | 3π/4 ≈ 2.356194 | 150 | 0.375 |
| 150° — 5π/6 | 150 | 5π/6 ≈ 2.617994 | 166.66667 | 0.416667 |
| 180° — π (straight) | 180 | π ≈ 3.141593 | 200 | 0.5 |
| 270° — 3π/2 | 270 | 3π/2 ≈ 4.712389 | 300 | 0.75 |
| 360° — 2π (full circle) | 360 | 2π ≈ 6.283185 | 400 | 1 |
How to Use Angle Converter
- 1Enter an angle in any unit.
- 2See all four units updated instantly.
- 3Browse the reference chart for common angles.
- 4Copy any converted value.
Zenovay
Privacy-first analytics for your website
Understand your visitors without invasive tracking. GDPR compliant, lightweight, and powerful.
Related Tools
Color ConverterConvert colors between HEX, RGB, HSL, and CMYK formats. Live preview with color picker.
Unit ConverterConvert between units of length, weight, temperature, area, volume, speed, and more.
Number Base ConverterConvert numbers between binary, octal, decimal, and hexadecimal bases.
Unix Timestamp ConverterConvert between Unix timestamps and human-readable dates. Show ISO 8601, UTC, local time, and relative time.
Frequently Asked Questions
What is a radian?▾
A radian is the SI unit of angle. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. A full circle = 2π radians = 360°. Since π ≈ 3.14159, 1 radian ≈ 57.296°. Radians are used in mathematics, physics, and programming — trigonometric functions (Math.sin, Math.cos) in most programming languages expect radians, not degrees.
What are gradians?▾
A gradian (grad, gon, or grade) divides a right angle into 100 parts, so a full circle = 400 gradians. 1 gradian = 0.9° = π/200 radians. Gradians were proposed during the French Revolutionary metric system as a decimal alternative to degrees. They are used in surveying and some European countries. A right angle is exactly 100 gradians, making right-angle arithmetic simpler.
How do I convert degrees to radians in code?▾
radians = degrees × π / 180. In JavaScript: const rad = degrees * Math.PI / 180. In Python: import math; rad = math.radians(degrees). To convert back: degrees = radians × 180 / π. In JavaScript: const deg = radians * 180 / Math.PI. Always convert before passing to trigonometric functions — most APIs accept radians.
What is a "turn" as an angle unit?▾
A turn (revolution, full rotation) is 360°, 2π radians, or 400 gradians. CSS uses turns for animation: transform: rotate(0.5turn) = rotate(180deg). The unit makes fraction-based angles intuitive: 1/4 turn = 90°, 1/3 turn ≈ 120°, 1/6 turn = 60°. JavaScript Math functions do not natively support turns — convert to radians first.
What are the common angles in trigonometry?▾
0° (0 rad): sin=0, cos=1. 30° (π/6 rad): sin=0.5, cos=√3/2. 45° (π/4 rad): sin=cos=√2/2. 60° (π/3 rad): sin=√3/2, cos=0.5. 90° (π/2 rad): sin=1, cos=0. 120° (2π/3 rad): sin=√3/2, cos=−0.5. 180° (π rad): sin=0, cos=−1. 270° (3π/2 rad): sin=−1, cos=0. 360° (2π rad): sin=0, cos=1.