Degrees to Seconds Converter
This converter turns an angle expressed in degrees into arcseconds and into seconds of time, the two units astronomers, surveyors and GPS users rely on for precise angular measurement. Choose your input format, decimal degrees or degrees, minutes and seconds (DMS), then enter your angle. Behind the scenes the tool applies the standard sexagesimal relationships: one degree equals 60 arcminutes and 3,600 arcseconds, and because Earth rotates 360 degrees in 24 hours, one degree also equals 240 seconds of time. Your results update instantly in four headline tiles: Decimal Degrees, Arcseconds, Arcminutes and Seconds of Time. Below that, a full breakdown shows your angle as decimal degrees, as a degrees minutes seconds value, as total arcminutes and total arcseconds, and its time equivalent in seconds, minutes, hours and an hours minutes seconds format. Use this when you need to convert a survey bearing or GPS coordinate into arcseconds for precision work, or when relating a celestial longitude in degrees to a time based coordinate such as right ascension. Arcseconds measure angle, while seconds of time measure duration, so keep the two separate even though both share the word seconds. Enter an angle beyond 360 degrees or below zero and the calculator still converts it correctly, but it does not normalise the value to a standard 0 to 360 degree range, so check your input if you need a normalised bearing.
1. Enter Your Angle
2. About This Conversion
Arcseconds measure angle: 1 degree = 60 arcminutes = 3,600 arcseconds. This is the unit used for star positions, survey bearings and coordinate precision.
Seconds of time relate angle to Earth's rotation: since Earth turns 360 degrees in 24 hours, 1 degree = 240 seconds of time. This is used for longitude and solar time calculations.
Full Breakdown
Time Equivalent
How to Convert Degrees to Seconds
An angle in degrees can be split into smaller sexagesimal units the same way an hour splits into minutes and seconds. One degree equals 60 arcminutes, and one arcminute equals 60 arcseconds, so one degree equals 3,600 arcseconds in total. To convert decimal degrees to arcseconds, multiply the decimal degree value by 3,600. For example, 10.5 degrees x 3,600 = 37,800 arcseconds.
Converting Degrees, Minutes, Seconds to Total Seconds
If your angle is already expressed in degrees, minutes and seconds (DMS), first convert it to decimal degrees using the formula: decimal degrees = degrees + (minutes / 60) + (seconds / 3600). Then multiply the result by 3,600 to get the total arcseconds. For example, 10 degrees 30 minutes 0 seconds converts to 10.5 decimal degrees, which equals 37,800 arcseconds.
Arcseconds vs Seconds of Time
It is easy to confuse two different meanings of "seconds" when dealing with degrees. Arcseconds are a unit of angle (3,600 per degree), used in astronomy, surveying and GPS coordinates to express angular precision. Seconds of time are a unit of duration related to Earth's rotation. Because Earth completes a full 360 degree rotation in 24 hours, each degree of rotation corresponds to 240 seconds of time (24 hours x 3,600 seconds per hour, divided by 360 degrees). Astronomers use seconds of time when converting between right ascension (measured in hours, minutes, seconds of time) and celestial longitude (measured in degrees).
| Unit | Conversion | Common Use |
|---|---|---|
| 1 degree | 60 arcminutes | Base angle unit |
| 1 degree | 3,600 arcseconds | Astronomy, surveying, GPS precision |
| 1 arcminute | 60 arcseconds | Navigation, map coordinates |
| 1 degree | 240 seconds of time | Longitude, right ascension conversion |
| 15 degrees | 1 hour of time | Time zones (360 deg / 24 hr) |
Why Arcseconds Matter for Precision
A single arcsecond is a very small angle: 1/3600th of a degree. At the distance of the Moon, one arcsecond corresponds to roughly 1.9 km. GPS coordinates are often expressed to a fraction of an arcsecond to pinpoint a location to within a few centimetres. Surveyors use arcseconds when recording bearings and boundary angles because degrees and even arcminutes are not precise enough for legal land descriptions. Astronomers use arcseconds to measure the apparent size and separation of objects in the sky, since most celestial objects appear only a few arcseconds to a few degrees across.
Worked Example
Take an angle of 10.5 decimal degrees. Multiplying by 3,600 gives 37,800 arcseconds. Expressed as degrees, minutes, seconds this is 10 degrees, 30 minutes, 0 seconds (since 0.5 degrees = 30 arcminutes exactly). Converting to seconds of time, 10.5 degrees x 240 = 2,520 seconds of time, which is 42 minutes 0 seconds, or 0 hours 42 minutes 0 seconds.
Related Angle Converters
- Angle Conversion Calculator: convert between degrees, radians, gradians and more.
- Degrees Minutes Seconds Calculator: work with DMS angle notation directly.
- Decimal Degrees to DMS Converter: the reverse conversion, decimal to DMS.
- DMS to Decimal Degrees Converter: convert DMS notation back to decimal degrees.
- Degrees to Radians Calculator: convert degrees to the radian angle unit used in calculus and physics.
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Sources: Standard sexagesimal angle unit definitions (1 degree = 60 arcminutes = 3,600 arcseconds), as used by the International Astronomical Union and national mapping agencies including Land Information New Zealand (linz.govt.nz) for survey coordinate precision.
This calculator performs a standard mathematical unit conversion and is accurate for any valid angle input. It does not account for angle normalisation (wrapping values above 360 degrees or below 0 degrees) unless you enter a pre-normalised value.