Degrees to Seconds Converter

How to use the degrees to arcseconds calculator

What this calculator does

This calculator converts an angle expressed in decimal degrees into seconds of arc, commonly called arcseconds. An arcsecond is an angular unit, not a unit of time: one degree is divided into 60 arcminutes, and each arcminute is divided into 60 arcseconds. The calculator therefore applies the exact identity 1 degree = 3,600 arcseconds. It also shows the same angle in arcminutes, radians, turns, and milliarcseconds so you can compare common angular notations. It does not determine a physical distance, apparent object size, telescope resolution, map scale, or positional uncertainty unless those quantities are supplied in a separate domain-specific calculation.

When to use it

Use this converter when reading astronomical coordinates or instrument specifications, checking angular resolution in optics, translating a surveying or navigation angle into a finer unit, or verifying a hand calculation in geometry. The unit is especially useful for very small angular separations. The NIST explanation of angle and SI usage provides context for radians, degrees, and accepted non-SI angle units.

How to calculate

1. The page opens with a complete demonstration value of 30 degrees. Its result and a validated example Excel workbook are available immediately.
2. Replace the value in Angle in degrees with any finite decimal. Use a period for decimals, such as 0.25, 12.5, or -3. Negative values are accepted because signed angles are meaningful in coordinate systems.
3. Read Angle in seconds of arc as the primary answer. Review Arcminutes, Radians, Turns, and Milliarcseconds when another notation is more convenient.
4. Use the Equivalent angle units table to compare the same angle across units. Select Download Excel to save the current input, outputs, formulas, and notes as a real XLSX workbook.
5. Select Reset to clear the demonstration and all calculated data. Download Excel is then disabled until a complete valid degree value is entered again.

Input guide

Angle in degrees is the only required input. Enter a plain decimal number in degrees, without the degree symbol or thousands separators. The accepted format uses a period as the decimal separator; scientific notation and decimal commas are intentionally rejected to avoid ambiguous interpretation. Examples include 30, 0.5, -12.75, and 360. A larger positive input produces proportionally larger positive outputs, while a negative input produces negative equivalents. Zero is valid and represents no angular displacement. A common mistake is entering degrees-minutes-seconds notation such as 12° 30′ 00″ into this decimal-only field; convert that notation to decimal degrees first.

Output guide

Angle in seconds of arc is the exact degree input multiplied by 3,600 and is displayed with the double-prime symbol ″. Arcminutes is the input multiplied by 60 and uses the prime symbol ′. Radians is the degree value multiplied by π/180, the standard relation used in mathematics and physics. Turns divides the degree value by 360, so one full revolution equals one turn. Milliarcseconds multiplies arcseconds by 1,000 and is useful for extremely small angular measurements. All outputs are exact unit conversions at the model level; displayed decimals are rounded only for readability. Zero outputs mean the entered angle is zero, and negative outputs preserve the direction implied by the signed input.

Worked example

The startup example uses 30 degrees. Multiplying by 3,600 gives 30 × 3,600 = 108,000 arcseconds. The same angle is 1,800 arcminutes because 30 × 60 = 1,800; approximately 0.523599 radians because 30 × π/180 = π/6; 0.083333 turn because 30/360 = 1/12; and 108,000,000 milliarcseconds. These values match the first-open cards, table, live summary, and workbook checkpoints.

Learn more

For the mathematical relationship between degrees and radians, see the Wolfram MathWorld overview of radians. For astronomical angle terminology and small-angle measurement, the NASA universe overview provides broader observational context.