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Second

Second

A unit of angle measure equal to The fraction 1/60 of a minute. There are 60 seconds in one minute and 3600 seconds in one degree. Seconds are indicated using the " symbol, so 12°45'33" means 12 degrees, 45 minutes, and 33 seconds, or 12 + 45/60 + 33/3600 degrees.

Key Formula

1′′=160 minute=13600 degree1'' = \frac{1}{60}\text{ minute} = \frac{1}{3600}\text{ degree}
Where:
  • ′′'' = The double-prime symbol representing one arcsecond
  • ′' = The single-prime symbol representing one arcminute
  • °° = The degree symbol representing one degree of arc

Worked Example

Problem: Convert the angle 25°18′45″ to decimal degrees.
Step 1: Start with the degrees. The whole-degree part stays as it is.
25°25°
Step 2: Convert the minutes to degrees by dividing by 60.
1860=0.3°\frac{18}{60} = 0.3°
Step 3: Convert the seconds to degrees by dividing by 3600.
453600=0.0125°\frac{45}{3600} = 0.0125°
Step 4: Add all three parts together.
25+0.3+0.0125=25.3125°25 + 0.3 + 0.0125 = 25.3125°
Answer: 25°18′45″ = 25.3125°

Another Example

Problem: Convert 73.2975° to degrees, minutes, and seconds (DMS) notation.
Step 1: The whole-number part gives the degrees.
73°73°
Step 2: Take the decimal part and multiply by 60 to get minutes.
0.2975×60=17.85′0.2975 \times 60 = 17.85'
Step 3: Take the decimal part of the minutes and multiply by 60 to get seconds.
0.85×60=51′′0.85 \times 60 = 51''
Step 4: Combine the results.
73°17′51′′73°17'51''
Answer: 73.2975° = 73°17′51″

Frequently Asked Questions

How many arcseconds are in a full circle?
A full circle contains 360 degrees. Since each degree has 3600 arcseconds, a full circle has 360 × 3600 = 1,296,000 arcseconds.
What is the difference between an arcsecond and a time second?
An arcsecond is a unit of angle (1/3600 of a degree), while a time second is a unit of duration (1/60 of a minute of time). They share the same subdivision pattern—60 seconds in a minute, 60 minutes in a larger unit—but they measure completely different quantities. Context usually makes it clear which one is meant.

Arcsecond (second of arc) vs. Arcminute (minute of arc)

Why It Matters

Arcseconds are essential whenever angles need to be measured with extreme precision. Astronomers use arcseconds to describe the apparent size of stars and planets, and to measure tiny shifts in star positions (parallax). Surveyors also rely on arcseconds to achieve the accuracy required for mapping land boundaries and aligning construction projects over long distances.

Common Mistakes

Mistake: Dividing seconds by 60 instead of 3600 when converting directly to degrees.
Correction: Remember that seconds are two levels below degrees. To go from seconds straight to degrees, divide by 3600 (which is 60 × 60). Dividing by 60 only converts seconds to minutes.
Mistake: Confusing the prime (′) and double-prime (″) symbols, writing minutes where seconds are intended or vice versa.
Correction: A single prime (′) always means minutes, and a double prime (″) always means seconds. A helpful mnemonic: the "bigger" symbol (two marks) represents the smaller unit.

Related Terms

  • Degree — The base unit: 1° = 3600 arcseconds
  • Minute — One step larger: 1′ = 60 arcseconds
  • Measure of an Angle — General concept of quantifying angles
  • Radian — Alternative angle unit based on arc length
  • Angle — The geometric figure being measured
  • Protractor — Tool for measuring angles in degrees