Degrees Minutes Seconds to Decimal Degrees Converter

The rule

decimal = degrees + minutes/60 + seconds/3600

A base-60 system inside a decimal one

Degrees split into 60 minutes and each minute into 60 seconds — the same sexagesimal scheme as clock time, inherited from Babylonian astronomy. So the arithmetic is not decimal: 42° 30′ is 42.5°, not 42.30°.

Only the degrees carry the sign. Minutes and seconds are always positive magnitudes, which is why −33° 52′ 05″ is −33.8681°, not −33 + 52/60.

Degrees and radians

A full turn is 360° or 2π radians, so:

radians = degrees × π/180 and degrees = radians × 180/π

Degrees are convenient because 360 divides so many ways. Radians are the natural choice in mathematics because arc length becomes simply rθ and the calculus of sine and cosine comes out clean — derivatives pick up stray factors of π/180 in degrees.

Names worth knowing

• Acute — under 90°. Right — exactly 90°. Obtuse — between 90° and 180°.
• Straight — 180°. Reflex — over 180°.
• Complementary pairs add to 90°; supplementary pairs add to 180°.