What is the formula to convert radians to arcseconds?

Multiply the radian value by 648000/π. Because one degree equals 3600 arcseconds and one radian equals 180/π degrees, one radian equals 180/π × 3600 = 648000/π arcseconds, which is approximately 206264.806″.

How many arcseconds are in 1 radian?

1 radian equals 648000/π arcseconds, approximately 206264.806″. This constant is widely used in astronomy and is sometimes written as 1 rad ≈ 206265″.

What is an arcsecond?

An arcsecond (symbol ″) is 1/3600 of a degree, or equivalently 1/1296000 of a full circle. It is the standard unit for expressing very small angles in astronomy, geodesy, and precision optics.

How many arcseconds are in a full circle?

A full 360° circle contains 1,296,000 arcseconds (360 × 60 × 60). In radians that is 2π, so the conversion constant is 1,296,000 / (2π) = 648000/π per radian.

Is the decimal result exact?

Because π is irrational, the result is always an approximation. This tool displays up to 6 significant decimal places, which is sufficient for virtually all practical applications.

Radians to Arcseconds Converter

Name: Radians to Arcseconds Converter
Availability: InStock
Author: Nham Vu

Convert any angle from radians to arcseconds (″) using the formula arcseconds = radians × 648000/π, with a step-by-step breakdown and reference table.

Enter Angle in Radians

Radians (rad)

Enter a decimal value. For π/2 enter 1.5707963…

Common Angle Reference Table

Click any row to load that radian value into the converter.

Angle	Radians	Arcseconds (″)

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Summary

Convert any angle from radians to arcseconds (″) using the formula arcseconds = radians × 648000/π, with a step-by-step breakdown and reference table.

How it works

Enter an angle in radians in the input field (for example, 0.000004848 for roughly 1 arcsecond).
The converter applies the formula: arcseconds = radians × (648000 / π).
The constant 648000/π is approximately 206264.806…, the number of arcseconds per radian.
The result is displayed rounded to six significant decimal places.
A step-by-step breakdown shows each multiplication stage so you can verify the math.
Click any row in the reference table to load a common angle into the converter.

Use cases

Converting angular measurements from astronomical catalogs given in radians to arcseconds.
Checking small-angle values in optics and telescope aperture calculations.
Verifying coordinate precision in geodesy and satellite positioning systems.
Converting radian outputs from trigonometry libraries into human-readable arcseconds.
Teaching the relationship between radians and the DMS (degrees-minutes-seconds) scale.
Cross-checking angular resolution specifications in photonics and interferometry.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu