Degree to Second of Arc Converter (° to ″)

How to Convert Degrees to Seconds of Arc

Converting degrees to seconds of arc takes angular measurement to its finest practical subdivision in the classical sexagesimal system. While a degree is broad enough for compass bearings and geometry, and an arcminute is used for navigation and visual acuity, arc-seconds are the unit of choice whenever extreme angular precision is required — from tracking stars across the sky to pinpointing a GPS coordinate to within a few meters. One degree contains exactly 3,600 arc-seconds (60 arcminutes × 60 arc-seconds). To convert, multiply the degree value by 3,600. Use the converter above for instant results, or follow the formula and examples below.

Step-by-step example — Convert 2° to arc-seconds:

Step-by-step example — Convert 0.5° to arc-seconds:

Step-by-step example — Convert 0.25° to arc-seconds:

What is a Degree and a Second of Arc?

Degree (°) is the universally recognized unit of angular measurement, dividing a full circle into 360 equal parts. The 360-degree system originates in ancient Babylonian astronomy, which used a base-60 number system and observed a solar year of approximately 360 days. Degrees are used in navigation, geography, architecture, and general engineering for expressing directions, slopes, bearings, and geometric angles. A right angle equals 90°, a straight angle is 180°, and a complete rotation is 360°. Each degree is subdivided into 60 arcminutes (′), and each arcminute into 60 arc-seconds (″), creating the DMS — Degrees, Minutes, Seconds — coordinate system that has served navigators, surveyors, and astronomers for over two thousand years.

Second of Arc (″), also called an arc-second or arcsecond, is the smallest unit in the classical sexagesimal angle system, equal to 1/60th of an arcminute and 1/3,600th of one degree. The double-prime symbol (″) distinguishes it from the arc-minute (′). Despite being an extremely small angle, the arc-second carries enormous practical significance: on Earth's surface, 1 arc-second of latitude corresponds to approximately 30.9 meters — a distance relevant to precision GPS, land surveying, and cadastral mapping. In astronomy, stellar parallax — the apparent shift in a nearby star's position due to Earth's orbital motion — is measured in arc-seconds; a star at a distance of 1 parsec shows a parallax of exactly 1 arc-second (the word "parsec" derives from "parallax of one arc-second"). The Hubble Space Telescope achieves an angular resolution of about 0.05 arc-seconds, allowing it to resolve objects separated by less than 2.5 meters at a distance of 10 kilometers.

Degree to Second of Arc Quick Reference Chart

Degrees (°)	Arc-Seconds (″)	Common Reference
0.000278°	1″	≈ 30.9 m on Earth's surface (latitude)
0.00167°	6″	Typical consumer GPS accuracy limit
0.0167°	60″ (= 1′)	1 arcminute = 1 nautical mile of latitude
0.25°	900″	Quarter degree — fine angular step
0.5°	1,800″	Apparent radius of the full Moon
1°	3,600″	1 degree — full DMS subdivision
5°	18,000″	Angular width of outstretched hand at arm's length
45°	162,000″	Half a right angle — diagonal direction
90°	324,000″	Right angle — quarter circle
360°	1,296,000″	Full circle — one complete rotation

Real World Uses of Degree to Second of Arc Conversion

• Astronomy & Stellar Measurement: Arc-seconds are the fundamental unit for expressing angular separations, stellar diameters, and positional accuracy in astronomy. The apparent diameter of the Sun is about 1,920″, Jupiter's disk spans roughly 50″ at opposition, and Mars at its closest approach subtends about 25″. When astronomers receive star catalog data in decimal degrees and need to calculate angular separations for telescope pointing, double-star measurement, or astrometric plate solving, they convert to arc-seconds to work at the precision level their instruments — and the physics — demand. Modern astrometry missions like Gaia measure stellar positions to micro-arc-second accuracy, built on the arc-second as the foundational unit.
• Precision GPS & Geodetic Surveying: Geographic coordinates in WGS-84 (the system used by GPS) are expressed in decimal degrees, but positional accuracy and coordinate resolution are most meaningfully described in arc-seconds. One arc-second of latitude equals approximately 30.9 meters, one-tenth of an arc-second equals about 3 meters, and one-hundredth of an arc-second equals roughly 30 centimeters. Geodetic surveyors converting between decimal degree coordinates and DMS notation — required by many cadastral, legal boundary, and civil engineering systems — must apply the ° to ″ conversion precisely. High-accuracy GNSS receivers achieving centimeter-level positioning are resolving angles smaller than 0.001 arc-seconds.
• Telescope Design & Optical Resolution: The angular resolution of any optical instrument — telescope, camera, microscope, or satellite sensor — is specified in arc-seconds. The Rayleigh criterion and Dawes limit for resolving double stars are both expressed in arc-seconds as a function of aperture diameter. Optical engineers designing telescope mirrors, satellite imaging systems, and adaptive optics arrays convert degrees (used in wide-field system specifications) to arc-seconds when calculating resolving power, diffraction limits, detector pixel scale, and image sampling ratios. A typical amateur 8-inch telescope achieves about 0.6″ resolution — far finer than a single degree.
• Seismology & Earth Science: Earthquake epicenter locations are reported in decimal degrees of latitude and longitude, but the precision of those locations — and the uncertainty bounds around them — are described in arc-seconds or fractions thereof, since arc-seconds directly correspond to distances on Earth's surface. Seismologists converting epicenter coordinates from decimal degrees to DMS format for publication, for comparison with historical records stored in DMS notation, or for input into legacy GIS and seismic hazard mapping systems rely on the degree-to-arc-second conversion as a routine step in data processing pipelines. A location uncertainty of ±5″ corresponds to a spatial uncertainty of approximately ±155 meters — a critical distinction in urban seismic risk assessment.

Frequently Asked Questions

How many arc-seconds are in a degree?

There are exactly 3,600 arc-seconds in one degree. This comes from the sexagesimal subdivision: 1° = 60′ (arcminutes), and 1′ = 60″ (arc-seconds), so 1° = 60 × 60 = 3,600″.

What is the formula to convert degrees to arc-seconds?

The formula is: ″ = ° × 3,600. Multiply any degree value by 3,600 to get the equivalent angle in arc-seconds. For the reverse, divide arc-seconds by 3,600 to get degrees.

What is 1 degree in arc-seconds?

1° = 3,600″ (three thousand six hundred arc-seconds). A full circle therefore contains 360 × 3,600 = 1,296,000 arc-seconds — over one million arc-seconds in a single rotation, illustrating how fine this unit truly is.

What is 1 arc-second in degrees?

1″ = 0.000277778° (approximately 2.778 × 10⁻⁴ degrees). One arc-second is a vanishingly small fraction of a degree — yet it corresponds to a physically meaningful distance of about 30.9 meters on Earth's surface and a resolvable stellar separation for a large telescope.

What is an arc-second also called?

An arc-second is also called an arcsecond (one word) or a second of arc. It is symbolized by the double-prime mark (″). In astronomy it is sometimes informally abbreviated as as or written as arcsec. Fractions of arc-seconds are expressed as milli-arc-seconds (mas = 0.001″) and micro-arc-seconds (μas = 0.000001″) in high-precision astrometry.

What is the relationship between degrees, arcminutes, and arc-seconds?

The full DMS hierarchy is: 1° = 60′ = 3,600″. One degree contains 60 arcminutes; one arcminute contains 60 arc-seconds; therefore one degree contains 3,600 arc-seconds. This three-level system — inherited from Babylonian base-60 mathematics — is the foundation of DMS coordinate notation used in GPS, navigation charts, star catalogs, and surveying records worldwide.

How far is 1 arc-second on Earth's surface?

Along a meridian (north-south), 1 arc-second of latitude equals approximately 30.9 meters (about 101 feet). Along a parallel (east-west), the distance per arc-second of longitude varies with latitude — it equals about 30.9 meters at the equator but decreases to zero at the poles. This direct relationship between arc-seconds and ground distance makes arc-seconds the natural precision unit for high-accuracy GPS, cadastral surveying, and geodetic calculations.

Why are arc-seconds used in astronomy instead of degrees?

Most astronomical objects and angular separations of interest are far smaller than one degree — often smaller than one arcminute. Arc-seconds provide a conveniently scaled unit for describing the apparent sizes of planets, the separations of binary stars, parallax angles used to measure stellar distances, and the resolving power of telescopes. Using degrees for these measurements would produce unwieldy decimals with many leading zeros, while arc-seconds give clean, human-readable numbers that correspond directly to the practical precision of astronomical instruments.