📌 Overview

Convert angle units including degrees, radians, gradians, turns, arcminutes, arcseconds and milliradians.

📐 Angle Converter

Convert angle units including degrees, radians, gradians, turns, arcminutes, arcseconds and milliradians.

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📖 Deep Dive: Angle Converter

Ways to express angles

  • Degree (deg): a circle split into 360 parts, from ancient Babylonian base-60, the most common in daily life.
  • Radian (rad): the central angle whose arc equals the radius; a full circle is 2pi, the standard unit in math and programming.
  • Gradian (gon/grad): a circle split into 400 parts, with a right angle exactly 100, used in surveying.
  • Turn: a full circle equals 1, intuitive for animation and rotation parameters.

    • Key conversions

  • 1 turn = 360 deg = 2pi rad is about 6.28319 rad = 400 gon.
  • 1 deg = 60 arcminutes = 3600 arcseconds.
  • 1 rad is about 57.2958 deg.

    • A common programming pitfall

    JavaScript's Math.sin(90) does not return 1 because it treats 90 as radians. The correct form is Math.sin(90 * Math.PI / 180). This mistake is especially common in Canvas drawing and 3D rotation.

    Uses of arcminutes and arcseconds

    Latitude and longitude coordinates are often written in degrees-minutes-seconds like 39 deg 54' 27" N, and astronomical observation and GPS positioning rely heavily on arcseconds as a precision unit.