Degree to Radian

The 360-degree circle originated with the ancient Babylonians around 1500 BC. They used a base-60 (sexagesimal) number system and observed that the sun advances roughly one degree per day through the sky. 360 is highly divisible (by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180), making it practical for calculations.

A radian is the angle subtended when the arc length equals the radius (about 57.3°). Radians are preferred in calculus and physics because they simplify formulas—for example, the derivative of sin(x) is cos(x) only when x is in radians.

To convert degrees to radians, multiply by π/180. For example, 90° = 90 × (π/180) = π/2 radians ≈ 1.571 radians. Common conversions: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 360° = 2π.

A gradian (also called gon or grade) divides a right angle into 100 parts, so a full circle is 400 gradians. Invented during the French Revolution as part of metric standardization, gradians are mainly used in surveying and some European countries. One gradian equals 0.9 degrees.