How many radians is 1 arcsecond?

1 arcsecond equals π/648000 radians, which is approximately 0.00000484814 radians (4.84814 microradians). This follows from 1 arcsecond being 1/3600 of a degree, and 1 degree being π/180 radians.

What is the formula to convert arcseconds to radians?

Multiply the arcsecond value by π/648000. For example, 3600 arcseconds (= 1 degree) × (π/648000) = π/180 ≈ 0.017453 radians.

What is an arcsecond?

An arcsecond (symbol: ″) is a unit of angular measurement equal to 1/3600 of a degree or 1/60 of an arcminute. It is widely used in astronomy (e.g., measuring stellar parallax and angular separation), geodesy, and high-precision optics.

How does an arcsecond relate to an arcminute?

1 arcminute equals 60 arcseconds. So 1 arcminute = π/10800 radians ≈ 0.000290888 radians, while 1 arcsecond = π/648000 radians ≈ 0.00000484814 radians.

Why are radians preferred over arcseconds in math?

Radians are dimensionless and directly relate arc length to radius (arc = r × θ). Most programming languages and mathematical functions (sin, cos, tan) expect angles in radians, making conversion necessary when working with arcsecond-based data from telescopes or GPS systems.

Arcseconds to Radians Converter

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

Convert arcseconds to radians instantly using the exact formula: radians = arcseconds × π/648000.

Enter Angle in Arcseconds

Arcseconds (″)

Formula: radians = arcseconds × π / 648000

Common Arcsecond Reference Table

Click any row to load that value into the converter.

Arcseconds (″)	Degrees	Radians (decimal)

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Summary

Convert arcseconds to radians instantly using the exact formula: radians = arcseconds × π/648000.

How it works

Enter an angle in arcseconds in the input field.
The converter applies the formula: radians = arcseconds × (π / 648000).
The result is displayed as a decimal radian value and as a multiple of π.
Use the reference table to look up common arcsecond values instantly.
Click any row in the reference table to load that value into the converter.

Use cases

Converting telescope pointing offsets from arcseconds to radians for astronomy software.
Calculating angular resolution of optical instruments and cameras.
Converting very fine navigation bearing adjustments to radians for programming.
Studying the relationship between arcseconds, arcminutes, degrees, and radians.
Verifying hand-calculated radian values for fine angular measurements in geodesy.
Preparing arcsecond angles for use in WebGL, Canvas, or physics simulations.

Frequently Asked Questions

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