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Degrees to Seconds Converter

Convert degrees to arcseconds and arcseconds to degrees using 3600 arcseconds per degree, with formulas, exact examples, and DMS context.

Published

Arcseconds
Angle in arcseconds
5,400 arcseconds
Degrees entered
1.5 °
Equivalent arcminutes
90 arcminutes
Arcseconds per degree
3,600

1.5 ° equals 5,400 arcseconds.

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°

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Degrees to Seconds Converter

Arcseconds are the second-level subdivision of an angular degree. A degree contains 60 arcminutes, and each arcminute contains 60 arcseconds, so one degree contains 3600 arcseconds. This converter moves directly between degrees and arcseconds and also reports the intermediate arcminute value.

Use this page when a whole degree is far too coarse for the measurement you are handling. Astronomy, optics, geodesy, surveying, navigation, camera alignment, and high-precision map work often need angles expressed in seconds of arc. The calculator still performs a pure angle-unit conversion. It does not apply a map projection, choose a coordinate datum, or decide whether a value is north, south, east, or west. For broader angle units, use the angle converter. For degree-minute-second notation, use the degrees minutes seconds calculator. For latitude and longitude formatting, use the coordinates converter.

What the calculation does

The converter has two directions. In Degrees to arcseconds mode, the active input is the angle in degrees. The calculation checks that this degree value is finite. It then multiplies degrees by 3600 to get the primary arcsecond result. It also multiplies degrees by 60 to show equivalent arcminutes and includes a fixed reference item, 3600, for arcseconds per degree.

In Arcseconds to degrees mode, the active input is the angle in arcseconds. The calculation checks that this arcsecond value is finite. It divides by 3600 to get degrees and divides by 60 to get equivalent arcminutes. The primary result is the degree value. The item list includes the entered arcseconds and the calculated arcminutes.

The result uses unit words in the primary arcsecond output: arcseconds rather than the double-prime symbol. In degree output, it uses the degree symbol. Degree results in reverse mode display up to eight decimal places, while arcsecond values display up to four decimal places. There is no rule in the calculation that rejects negatives, values above a full circle, or fractional arcseconds.

Formula

Degrees to arcseconds:

arcseconds=degrees×3600\text{arcseconds} = \text{degrees} \times 3600

Arcseconds to degrees:

degrees=arcseconds3600\text{degrees} = \frac{\text{arcseconds}}{3600}

Arcminutes sit between the two:

arcminutes=degrees×60=arcseconds60\text{arcminutes} = \text{degrees} \times 60 = \frac{\text{arcseconds}}{60}

A worked conversion

The default forward input is 1.5°. The calculator multiplies 1.5 by 3600:

arcseconds=1.5×3600=5400\text{arcseconds} = 1.5 \times 3600 = 5400

It also multiplies the degree value by 60:

arcminutes=1.5×60=90\text{arcminutes} = 1.5 \times 60 = 90

The primary result is 5400 arcseconds. The item list shows 1.5°, 90 arcminutes, and 3600 as the number of arcseconds per degree. The note says that 1.5° equals 5400 arcseconds, which matches the values returned by the calculation.

For the reverse direction, the default value is 5400 arcseconds. The calculation divides by 3600, so the primary result is 1.5°. It divides 5400 by 60 for the supporting value, so equivalent arcminutes are again 90 arcminutes.

Reference table

DegreesArcminutesArcsecondsContext
0.000277778°0.0166667′1″One arcsecond
0.0166667°1′60″One arcminute
0.25°15′900″Quarter degree
1°60′3,600″One degree
1.5°90′5,400″Default example
30°1,800′108,000″Large reference angle

Domains and interpretation

Astronomy uses arcseconds because celestial separations can be tiny. A telescope resolution or star-position uncertainty may be far below one arcminute. Surveying and geodesy also need small angular units when describing bearings, coordinate precision, or deflection angles. Navigation and mapping use seconds in DMS coordinates, especially in printed references. Optics and mechanical alignment may use seconds of arc to describe very fine pointing error.

The same arithmetic can appear in math, CAD, and geographic contexts, but the meaning differs. In a geometry drawing, -30 arcseconds may simply be a small clockwise rotation or a signed tolerance. In longitude, a negative decimal degree value normally means west of Greenwich. In latitude, a negative value means south of the equator. This converter does not attach those meanings; it only changes units. If you are preparing a coordinate for software that expects decimal degrees, first make sure the hemisphere sign is correct and then use a coordinate-specific tool if necessary.

Common pitfalls

  • Confusing arcseconds with seconds of time, especially in astronomy where both time and angle are used.
  • Treating DMS seconds as decimal digits. A value of 10° 0′ 30″ is 10.008333°, not 10.0030°.
  • Rounding too early. Very small angles can lose all meaningful precision if converted and rounded before the final calculation.
  • Assuming the word second always means the same unit. Context and symbols matter.
  • Expecting a projection result. Arcseconds are angular units; UTM eastings and northings are meter coordinates from a projection.

Sources

Frequently asked questions

How many arcseconds are in one degree?
One degree contains exactly 3600 arcseconds. The reason is that one degree contains 60 arcminutes and each arcminute contains 60 arcseconds, so 60 multiplied by 60 gives 3600. The calculator uses that exact factor in both conversion directions for every finite input.
How do I convert degrees to arcseconds?
Multiply the degree value by 3600. The calculator also multiplies the same degree value by 60 to show equivalent arcminutes. For the default 1.5 degree example, the primary result is 5400 arcseconds and the supporting arcminute value is 90 arcminutes.
How do I convert arcseconds to degrees?
Divide the arcsecond value by 3600. The reverse mode also divides arcseconds by 60 to show equivalent arcminutes. For example, the default reverse input of 5400 arcseconds becomes 1.5 degrees and 90 arcminutes, using the same exact DMS subdivision.
Does the calculator allow negative arcseconds?
Yes. The calculator only checks that the active numeric input is finite. Negative degrees become negative arcseconds, and negative arcseconds become negative degrees. That behavior is helpful for signed angular offsets, but geographic coordinates still need hemisphere or sign conventions handled consistently.
Are arcseconds the same as seconds of time?
No. Arcseconds measure angle, while seconds of time measure duration. The shared word comes from the base-60 subdivision pattern. In astronomy the two can appear together, which makes labels important: an arcsecond uses angular symbols or angle context, not a clock unit.

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