How do I convert degrees to arcminutes and arcseconds?

Multiply degrees by 60 for arcminutes and by 3600 for arcseconds: 1° = 60′ = 3600″.

Angle Converter — Free Online Angle Converter

How do I convert angles between degrees, radians, gradians, arcminutes and turns?

Type a value into AnyTool Angle Converter and pick the units. It instantly converts both ways between degrees, radians, gradians (gon), arcminutes, arcseconds, milliradians, turns, quadrants, sextants and compass points, and shows the value in every unit at once in a copyable table. The radian uses the exact π factor (1 rad = 180/π°), and everything is calculated in your browser, so nothing is uploaded.

Live two-way conversion — type in either field and the other updates
Degrees, radians, gradians, arcminutes, arcseconds, mrad, turns and more
See the value in every unit at once, each row copyable
Radian and milliradian use the exact π factor (1 rad = 180/π°)
100% in your browser — no upload, no signup, works offline

What is

Angle Conversion

Angle conversion changes a plane angle from one unit to another — for example degrees to radians. A full turn can be expressed as 360 degrees, 2π radians, 400 gradians or one revolution, and every angle unit is a fixed fraction of a turn, so conversion is a single multiply and divide through a degree base. One radian is 180/π ≈ 57.295779513 degrees, because a full turn is 2π radians; one gradian is exactly 0.9 degrees; an arcminute is 1/60 of a degree and an arcsecond 1/3600.

Converters

Related terms

DegreeRadianGradianArcminuteTurn

Frequently Asked Questions

A radian relates to a degree by the factor 180/π, because a full turn is 2π radians and also 360 degrees, so 360 ÷ 2π = 180/π. That makes one radian about 57.295779513 degrees, and one degree about 0.0174533 radians. AnyTool applies the exact π factor with Math.PI, so degrees, radians and milliradians convert without rounding the constant by hand.

One radian is 180/π ≈ 57.295779513 degrees, and one degree is π/180 ≈ 0.0174533 radians.

The gradian, also called the gon, divides a full turn into 400 equal parts, so one gradian is 360 ÷ 400 = 0.9 degrees exactly, and a right angle is 100 gradians. To go the other way, multiply degrees by 10/9. AnyTool lists gradians alongside degrees, radians and turns so surveying and engineering values convert directly.

A gradian (gon) is exactly 0.9 degrees, because 400 gradians make a full turn and 100 make a right angle.

A degree is split into 60 arcminutes, and each arcminute into 60 arcseconds, so one degree is 60 arcminutes and 3600 arcseconds. These sexagesimal subdivisions are used in astronomy, navigation and geographic coordinates. AnyTool converts between degrees, arcminutes and arcseconds instantly and shows every angle unit at once, with automatic scientific notation for very small arcsecond values.

AnyTool Angle Converter computes every result locally in JavaScript using exact conversion factors through a degree base, with the radian derived from π. No value is uploaded, there is no tracking, and the page keeps working offline after the first load.

No. Every calculation runs in your browser, so nothing is sent to a server and it works offline.

Detailed Explanation

Methodology

How the Angle Converter Works

AnyTool Angle Converter performs every calculation in the browser. Each unit declares a single linear factor relative to a shared degree base — the exact number of degrees in one of that unit — so any unit converts to any other through degrees without an N-by-N table. The factors are the standard definitions: a radian is 180/π ≈ 57.295779513°, a milliradian 1/1000 of that, a gradian exactly 0.9°, an arcminute 1/60°, an arcsecond 1/3600°, a turn 360°, a quadrant 90°, a sextant 60°, and a compass point 11.25° (1/32 turn). A value is multiplied to degrees and then divided into the target unit, with the radian and milliradian computed from Math.PI for full precision.

Ten units spanning degrees, radians, gradians and traditional divisions
The degree is the shared base; each unit is one exact factor
Radian and milliradian use π, so they are exact rather than rounded
Conversion is value to base to value, so any unit maps to any other
All arithmetic is client-side JavaScript — no server round-trip

How It Works

Degrees, Radians and the Fractions of a Turn

Every plane-angle unit is a fixed fraction of one full turn. A turn is 360 degrees, 2π radians, 400 gradians, four quadrants, six sextants or 32 compass points at the same time. The only irrational factor is the radian: one radian is 180/π ≈ 57.295780° because a turn is 2π radians, and a milliradian is one thousandth of that, widely used in optics and ballistics. The sexagesimal subdivisions used in astronomy and navigation are exact — a degree is 60 arcminutes and 3600 arcseconds. A single input is shown in every unit at once in a copyable table, with adjustable precision and automatic scientific notation for very small magnitudes such as arcseconds or very large turn counts.

1 turn = 360° = 2π rad = 400 gon = 32 compass points
Radian = 180/π ≈ 57.295780° because one turn is 2π radians
1° = 60 arcminutes = 3600 arcseconds (exact)
Gradian = 0.9° exactly; 100 gon make a right angle
Convert-to-all table with adjustable precision and scientific notation

Privacy & Security

Privacy and Offline Use

Because all conversion runs in the browser, no value is sent to a server, there is no account or tracking, and the page works offline after first load. The converter is built on a shared, unit-tested conversion engine that other AnyTool unit converters reuse, so behaviour is consistent across the site.

Angle conversion: in-browser (AnyTool) vs typical online converters
Capability	AnyTool	Typical online converters
Processing	Runs in your browser	Often server-side
Units	10: degree, radian, gradian, arcminute, arcsecond, mrad, turn, quadrant, sextant, point	Often a handful (degree, radian, gradian)
Radian precision	Exact 180/π factor from Math.PI	Sometimes a rounded constant
Two-way input	Edit either field, both update	Usually one-direction with a button
All units at once	Yes, copyable table	Often one target at a time
Precision control	Adjustable decimals	Frequently fixed
Works offline	Yes (PWA)	No
Cost / signup	Free, no signup	Often ad-heavy or gated

AnyTool converts every unit locally through a degree base and uploads nothing.