Angle Converter

Converter

Angle Input

Input Unit

Standard degree notation (0–360°)

Angle Valuee.g. 45 or -30.5

Output Precision

Decimal places in results

Quick Reference Angles:

What Is the Angle Converter?

The Angle Converter is a free, browser-based tool that instantly translates any angle value between twelve units: Decimal Degrees, Degrees-Minutes-Seconds (DMS), Radians, Radians in π form, Gradians (gon), Turns (rev), Arcminutes, Arcseconds, Milliradians (mrad), NATO Mils (6400), Artillery Mils (6000), and Compass Bearings. Every conversion is shown in a single table alongside a live compass rose and trigonometric function values — no page reload needed.

Angle Units at a Glance

Unit	Symbol	Full circle	Common use
Decimal Degrees	`°`	360°	Navigation, GIS, everyday geometry
Degrees-Minutes-Seconds	`° ′ ″`	360°	Astronomy, surveying, GPS
Radians	`rad`	2π ≈ 6.2832 rad	Mathematics, physics, programming
Radians (π form)	`×π`	2π	Exact expression in symbolic math
Gradians / Gon	`gon`	400 gon	Surveying (metric countries)
Turns / Revolutions	`rev`	1 rev	Rotational mechanics, motors
Arcminutes	`′`	21,600 ′	Astronomy, angular resolution
Arcseconds	`″`	1,296,000 ″	Telescopes, stellar parallax
Milliradians	`mrad`	≈ 6,283 mrad	Optics, ballistics, sniper scopes
NATO Mils	`mil₆₄₀₀`	6,400 mil	NATO military artillery
Artillery Mils	`mil₆₀₀₀`	6,000 mil	Soviet/Russian artillery
Compass Bearing	`N/S…E/W`	—	Marine & air navigation

How to Use the Angle Converter

Follow these steps for an instant multi-unit conversion:

Select the input unit from the dropdown (e.g. "Decimal Degrees" or "Radians (π form)").
Type the value — a plain number, a DMS string such as 12°34′56″, a π expression like 3π/4, or a bearing like N45°E.
Choose a normalization mode if you want the angle wrapped into a specific range (e.g. [0°, 360°) or (−π, π]).
Select output precision (0 – 10 decimal places).
The full conversion table, compass rose, DMS breakdown, and trigonometric values appear automatically with Auto-convert enabled (or press Enter / the Convert button).

Entering DMS Angles

Degrees-Minutes-Seconds is the sexagesimal system where one degree is divided into 60 minutes and each minute into 60 seconds. Conversion to decimal degrees uses:

decimal° = D + M/60 + S/3600

The tool accepts all of these DMS formats:

12°34′56″ (Unicode prime/double-prime) 12°34'56" (ASCII apostrophe/quote) 12d 34m 56s (letter suffixes) 12 34 56 (space-separated) -45°30′00″ (negative angle)

Using π (Pi) Expressions

When working with exact fractions of π, select Radians (π form) as the input unit. Accepted patterns:

π (= 1 × π ≈ 3.14159) π/4 (= 45°) 3π/2 (= 270°) -5π/6 (negative) 1.5π (decimal coefficient) pi/3 (type "pi" instead of "π")

The converter identifies the nearest reduced fraction (up to denominator 100) and shows it alongside the decimal. For example, 45° yields π/4, and 120° yields 2π/3.

Compass Bearings and Azimuth

A quadrantal bearing specifies an angle from North or South toward East or West. The tool parses bearings and maps them to a clockwiseazimuth (0° = North):

Bearing	Azimuth (°)
N45°E	45°
S30°E	150°
S60°W	240°
N10°W	350°
N (due North)	0°
S (due South)	180°

The interactive compass rose updates in real-time to visualize where the angle points, with the needle measuring clockwise from North.

Angle Normalization (Wrapping)

Large or negative angles (e.g. 450° or −90°) can be wrapped into a standard range using modular arithmetic:

[0°, 360°) deg = (deg % 360 + 360) % 360 (−180°, 180°] wrap to [0,360) then if > 180°: subtract 360° [0, 2π) rad = (rad % 2π + 2π) % 2π (−π, π] wrap to [0,2π) then if > π: subtract 2π

Select None to keep the original, possibly large value. When normalization is applied, a badge indicates which range was used.

Military Mils: NATO vs. Artillery

Mils are angular units used in military targeting where even small angular errors translate to large positional errors at long distances. Two incompatible conventions exist:

NATO (STANAG) mils: 6,400 mils per full circle → 1 mil ≈ 0.05625°

Soviet/Artillery mils: 6,000 mils per full circle → 1 mil = 0.06°

The converter outputs both simultaneously so you can verify values across different field manuals or targeting systems.

Conversion Formulas (Radians as Base)

Internally the tool converts every input to radians first, then derives all other units:

To radians…	Formula
Degrees	rad = deg × π / 180
Gradians	rad = gon × π / 200
Turns	rad = rev × 2π
Arcminutes	rad = ′ / 60 × π / 180
Arcseconds	rad = ″ / 3600 × π / 180
Milliradians	rad = mrad / 1000
NATO Mils	rad = mil × 2π / 6400
Artillery Mils	rad = mil × 2π / 6000

Practical Conversion Examples

45° in all units

Decimal Degrees 45° DMS 45° 00′ 00.00″ Radians 0.785398 rad Radians (π) π/4 Gradians 50 gon Turns 0.125 rev Arcminutes 2,700′ Arcseconds 162,000″ Milliradians 785.398 mrad NATO Mils 800 mil₆₄₀₀ Artillery Mils 750 mil₆₀₀₀ Bearing N45°E

1 Radian in degrees

1 rad = 57.295779° = 57° 17′ 44.81″ = 63.661977 gon = 0.159155 rev

Tips & Keyboard Shortcuts

Press Enter in the value field to trigger conversion without clicking the button.
Use the Quick Reference Angles buttons (30°, 45°, 90°…) to prefill common values instantly.
Click the copy icon on any table row to copy just that unit's value, or use Copy CSV to grab all values for spreadsheet use.
Switch Auto: On to see results update as you type (300 ms debounce), or turn it off and press Convert for batch work.
For angles beyond ±360° (e.g. winding rotations), use Normalization: None to preserve the original value.

Is the Angle Converter free?

Yes, Angle Converter is totally free :)

Can I use the Angle Converter offline?

Yes, you can install the webapp as PWA.

Is it safe to use Angle Converter?

Yes, any data related to Angle Converter only stored in your browser (if storage required). You can simply clear browser cache to clear all the stored data. We do not store any data on server.

What units does the Angle Converter support?

The Angle Converter supports Decimal Degrees (°), Degrees-Minutes-Seconds (DMS), Radians (rad), Radians in π form (e.g. π/4), Gradians (gon), Turns/Revolutions (rev), Arcminutes (′), Arcseconds (″), Milliradians (mrad), NATO Mils (6400 per circle), Artillery Mils (6000 per circle), and Compass Bearings (e.g. N45°E).

What is the difference between radians and degrees?

Degrees divide a full circle into 360 equal parts, while radians relate the arc length to the circle's radius. A full circle is 2π radians ≈ 6.2832 rad. Radians are the SI standard in mathematics and physics because they simplify trigonometric formulas.

How do I enter DMS (Degrees Minutes Seconds) input?

You can enter DMS in several formats: '12°34′56″', '12d 34m 56s', '12 34 56' (space-separated), or '12°34\'56"'. Negative angles use a minus sign before the degrees (e.g. -45°30′00″). Minutes must be 0–59 and seconds must be 0–59.999.

How do I enter an angle as a π expression?

Type expressions like 'π/4', '3π/2', '2π', '-5π/6', or '1.5π'. The converter parses these exactly and shows both the π form and the decimal value. You can also type 'pi' instead of 'π'.

What are NATO mils and Artillery mils?

Both mil systems divide a full circle into a rounded number of units for military use. NATO (STANAG) uses 6400 mils per circle, while the older Soviet-derived artillery convention uses 6000 mils per circle. The Angle Converter lets you choose the base when converting.

How does the normalization / wrapping feature work?

Normalization wraps any angle into a chosen range: [0°, 360°) keeps all values non-negative, (−180°, 180°] centres around zero, [0, 2π) and (−π, π] do the same in radians. Select 'None' to keep the original (possibly large or negative) value.