An angle converter helps you instantly convert angle measurements between degrees (°), radians (rad), and gradians (grad). This is essential for students studying trigonometry, engineers working with different measurement systems, surveyors, and anyone who needs to switch between angle units quickly without manual calculation.

Degrees (°) divide a full circle into 360 equal parts — the most common unit in everyday use and geometry. Radians (rad) are based on the radius of a circle; one full circle equals 2π (≈6.283) radians. Radians are the standard unit in higher mathematics, calculus, and physics because they simplify many formulas. Gradians (grad or gon) divide a full circle into 400 equal parts, making a right angle exactly 100 grad. Gradians are primarily used in some European countries for surveying and land measurement.

To convert degrees to radians, multiply the degree value by π/180 (approximately 0.0174533). For example, 90° × π/180 = π/2 ≈ 1.5708 radians. You can use our converter above for instant results — just enter your angle in degrees and the radian equivalent appears immediately.

Radians are considered the "natural" unit for angles because they emerge directly from the geometry of circles. When using radians, the derivative of sin(x) is simply cos(x), and the Taylor series expansions are cleaner — without extra conversion factors. In physics, angular velocity in radians per second directly relates to linear velocity (v = ωr). Using degrees would introduce awkward constants like π/180 into nearly every formula.

Gradians (also called gons or grads) divide a right angle into 100 units, making a full circle 400 grad. This decimal-based system was introduced during the French Revolution alongside the metric system. Today, gradians are still commonly used in surveying and civil engineering in parts of Europe, especially in France, Switzerland, and some Eastern European countries. Many scientific calculators include a GRAD mode alongside DEG and RAD.

Our converter uses JavaScript's 64-bit floating-point arithmetic (IEEE 754), providing up to 15-17 significant decimal digits of precision. Results are displayed to 6 decimal places for radians and 4 decimal places for degrees and gradians, which is more than sufficient for virtually all practical applications including engineering, academics, and scientific work.

Yes! The converter handles any real number input — negative angles, angles larger than 360° (or 2π radians, or 400 gradians), and decimal values. Negative angles simply represent clockwise rotation (when positive is counterclockwise). The visual indicator normalizes the angle to the 0–360° range for display purposes, but the numerical conversions preserve the exact input value.

Here are key angle equivalents: 30° = π/6 rad ≈ 0.5236 rad = 33.33 grad; 45° = π/4 rad ≈ 0.7854 rad = 50 grad; 60° = π/3 rad ≈ 1.0472 rad = 66.67 grad; 90° = π/2 rad ≈ 1.5708 rad = 100 grad; 180° = π rad ≈ 3.1416 rad = 200 grad; 360° = 2π rad ≈ 6.2832 rad = 400 grad. These are worth memorizing for quick mental conversions.