How many arcseconds are in 1 radian?

1 radian equals 206,264.8062 arcseconds, using the exact defined conversion factor rather than an estimate.

How do I convert radian to arcsecond?

Multiply the radian value by 206264.8062. The converter above does this instantly to whatever precision you set.

How do I convert arcsecond back to radian?

Use the reverse factor: 1 arcsecond equals 0.0000048481 radians. You can also use the swap control in the converter above to flip the direction instantly.

Arcsecond (arcsec) is a unit of angle.

Is the radian to arcsecond conversion exact?

Yes. Both radian and arcsecond are defined by fixed standards rather than physical artifacts, so the factor of 206264.8062 used above is exact to as many digits as you choose to display.

Radians to Arcseconds Converter

Q: What is a radian?

Radian (rad) measures angle. A radian is the angle subtended when the arc length equals the radius; a full circle is 2π radians. It is classified as a SI derived unit.

About Converting Radians to Arcseconds

Radian and Arcsecond are the two standard ways to measure angles — degrees for everyday and navigational use, radians for calculus and physics — so converting between them comes up constantly in math, engineering, and programming. Radian is most often used for calculus and trigonometry (derivatives of trig functions are simplest in radians).

Formula

arcseconds = radians × 206264.806247

This factor comes from each unit's defined relationship to the category's base unit: 1 radian equals 1 base unit, and 1 arcsecond equals 0.0000048481368111 base units, so dividing one by the other gives the direct radian-to-arcsecond factor of 206264.806247.

Simple example

1 rad × 206264.8062 = 206,264.8062 arcsec

1 radian = 206,264.8062 arcseconds.

Real-world example

90 rad × 206264.8062 = 18,563,832.56 arcsec

90 radians = 18,563,832.56 arcseconds.

Conversion table

Radian (rad)	Arcsecond (arcsec)
0 rad	0 arcsec
30 rad	6,187,944.187 arcsec
45 rad	9,281,916.281 arcsec
90 rad	18,563,832.56 arcsec
180 rad	37,127,665.12 arcsec
360 rad	74,255,330.25 arcsec

Reverse conversion: Arcsecond to Radian

1 arcsec × 0.000004848136811 = 0.0000048481 rad

1 arcsecond = 0.0000048481 radians.

radians = arcseconds × 0.0000048481368111

For a page dedicated to this direction, see Arcsecond to Radian.

Understanding the Radian

Radian (rad) measures angle. A radian is the angle subtended when the arc length equals the radius; a full circle is 2π radians. It is classified as a SI derived unit.

Where it's used: Standard angle unit in mathematics, physics, and engineering worldwide.

Uses of the Radian today

Calculus and trigonometry (derivatives of trig functions are simplest in radians)
Physics and engineering (angular velocity, rotational mechanics)
Computer graphics and robotics

History of the Radian

The radian was developed in the 1870s, with the term itself coined by James Thomson (brother of Lord Kelvin) around 1873, formalizing a ratio-based angle measure that mathematicians had used implicitly for calculus since Newton and Leibniz.

It was adopted as the SI derived unit of angle because it makes many physics and calculus formulas simpler than using degrees.

Historical origin. Radian was not the invention of a single named person; it developed through the process described above.

Understanding the Arcsecond (arcsec)

One arcsecond is 1/3600 degree.

Radian — sources

BIPM SI Brochure — Coherent derived units — Defines the radian as the SI unit of plane angle.

Radians to Arcseconds Converter — rad to arcsec

Angle Converter