How many radians is 1 arcminute?

1 arcminute equals π/10800 radians, which is approximately 0.000290888 radians. This follows from 1 arcminute being 1/60 of a degree, and 1 degree being π/180 radians.

What is the formula to convert arcminutes to radians?

Multiply the arcminute value by π/10800. For example, 60 arcminutes (= 1 degree) × (π/10800) = π/180 ≈ 0.017453 radians.

What is an arcminute?

An arcminute (symbol: ′) is a unit of angular measurement equal to 1/60 of a degree or 1/21600 of a full circle. It is widely used in astronomy (e.g., angular diameter of celestial objects), navigation, and optics.

How does an arcminute relate to an arcsecond?

1 arcminute equals 60 arcseconds. So 1 arcsecond = π/648000 radians ≈ 0.00000484814 radians.

Why are radians preferred over arcminutes 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 arcminute-based data.

Arcminutes to Radians Converter

Convert arcminutes to radians instantly using the exact formula: radians = arcminutes × π/10800.

Enter Angle in Arcminutes

Arcminutes (′)

Formula: radians = arcminutes × π / 10800

Common Arcminute Reference Table

Click any row to load that value into the converter.

Arcminutes (′)	Degrees	Radians (decimal)

Copied!

Summary

This tool converts angle measurements from arcminutes to radians using the formula: radians = arcminutes × (π / 10800). An arcminute (also written as 1′) is 1/60 of a degree, making it a fine-grained unit used in astronomy, navigation, and optics. Radians are the SI standard for angles in mathematics and physics. Enter any arcminute value to get the precise radian equivalent as both a decimal and a multiple of π.

How it works

Enter an angle in arcminutes in the input field.
The converter applies the formula: radians = arcminutes × (π / 10800).
The result is displayed as a decimal radian value and as a multiple of π.
Use the reference table to look up common arcminute values instantly.
Click any row in the reference table to load that value into the converter.

Use cases

Converting telescope pointing offsets from arcminutes to radians for astronomy software.
Calculating angular resolution in optics and camera systems.
Converting navigation bearing adjustments to radians for programming.
Studying the relationship between arcminutes, degrees, and radians in trigonometry.
Verifying hand-calculated radian values for fine angular measurements.
Preparing arcminute angles for use in WebGL, Canvas, or physics simulations.

Frequently Asked Questions

Last updated: 2026-06-19 · Reviewed by Nham Vu