Degrees to Arc Seconds Converter
Convert any angle expressed in degrees–minutes–seconds (DMS) notation into total arc seconds, decimal degrees and radians in one step.
°
′
″
The angle expressed entirely in arc seconds (1° = 3 600″)
- 1
Decimal degrees
45° + 30′ ÷ 60 + 0″ ÷ 3600 = 45.5Combine degrees, arc minutes and arc seconds into one decimal angle. - 2
Total arc seconds
45.5 × 3600 = 163,800
How does this calculator work?
An angle of D degrees, M arc minutes and S arc seconds equals D + M/60 + S/3600 decimal degrees. Multiply by 3 600 for total arc seconds, or by π/180 for radians. Example: 45°30′0″ = 45.5° = 163 800″ ≈ 0.794 rad.
Formula
How this is calculated
Angles are traditionally written in degrees–minutes–seconds (DMS) notation, adapted from the same sexagesimal (base-60) system used for time. One degree is divided into 60 arc minutes (′) and each arc minute into 60 arc seconds (″). The calculator converts DMS to decimal degrees by computing D + M/60 + S/3600, then multiplies by 3 600 to get total arc seconds or by 60 for arc minutes.
Arc seconds are the unit of choice for astronomy (star coordinates, parallax angles), geodesy (high-precision latitude/longitude), and navigation, where even one arc second represents about 31 metres on the ground at the equator. Decimal degrees are preferred by digital systems (GPS, GIS) because arithmetic on a single float is simpler than on sexagesimal strings.
Radians — the SI unit for angles — are required by most physics and engineering formulae. A full circle is 360° = 1 296 000″ = 2π rad. The conversion is exact; there is no rounding in the formula itself, only in how the result is displayed.
Frequently asked questions
Exactly 3 600 arc seconds per degree (60 arc minutes × 60 arc seconds per minute). A full circle contains 360 × 3 600 = 1 296 000 arc seconds.
Arc seconds (″) measure angle — 1/3 600 of a degree. Time seconds (s) measure duration. Astronomers use both: right ascension in hours:minutes:seconds of time, declination in degrees:arcmin:arcsec — entirely different quantities sharing the same word.
Digital systems store coordinates as floating-point numbers. A single float per axis is easier to handle than three integers with different scales. Arithmetic (averaging, interpolation, distance) is straightforward in decimal degrees and requires a conversion step from DMS.
Also known as
TG we-Calculate Editorial Team. (2026). Degrees to Arc Seconds Converter [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/degrees-to-seconds-calculator
TG we-Calculate Editorial Team. "Degrees to Arc Seconds Converter." TG we-Calculate. 2026. https://we-calculate.com/calculator/degrees-to-seconds-calculator.
TG we-Calculate Editorial Team, "Degrees to Arc Seconds Converter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/degrees-to-seconds-calculator
@misc{wecalculate_degrees_to_seconds_calculator, title = {Degrees to Arc Seconds Converter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/degrees-to-seconds-calculator}}, year = {2026}, note = {TG we-Calculate} }
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