Angle Conversion Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
To convert an angle, it's first brought back to degrees, then converted to the target unit. An angle of 90° equals π/2 radians (about 1.5708 rad) and 100 gradians.
Explanation
Three units are commonly used to measure an angle. The degree (°) divides a full circle into 360 equal parts; it's the most intuitive and widely used unit in everyday life. The radian (rad) is the SI unit, defined from the circle's radius (2π radians for a full turn); it's the unit expected by most trigonometric functions in programming and scientific computing. The gradian (or gon), rarer today, divides the circle into 400 equal parts and was long used in surveying and civil engineering, notably in France, to simplify certain calculations thanks to its decimal base. Conversion between these units is purely proportional: 360° = 2π rad = 400 gradians.
Example: converting 90° to radians
Inputs
Value: 90. Starting unit: degrees. Target unit: radians.
Calculation
90° equals 90 × (π ÷ 180) = 90 × 0.0174533 ≈ 1.570796 radians, exactly π ÷ 2.
Result
90° is about 1.5708 radians.
Frequently asked questions
Why are radians used in scientific computing?
The radian is the natural unit for trigonometric functions in mathematics: it simplifies many formulas (derivatives, series expansions) compared to degrees. That's why most programming languages and scientific calculators expect angles in radians for their sin, cos, and tan functions.
Is the gradian still used today?
Its use has declined a lot, but it remains present in some surveying and geodesy instruments and software, particularly in France and other European countries, where its decimal base (400 gradians per turn, 100 gradians per right angle) makes certain manual calculations easier.
How can I quickly convert an angle from degrees to radians in my head?
A useful reference value: 180° = π radians. For common angles, 90° = π/2 rad, 45° = π/4 rad, and 30° = π/6 rad. This calculator gives the exact decimal value for any angle.