Angle Converter
Fast, accurate, and free online Angle Converter tool that runs directly in your browser.
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1Enter data
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2Click the button
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3Get the result
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Other tools you may find usefulAngular unit converter - degrees, radians, minutes, seconds, gon, mils and more in one place
Online angular unit converteris a practical tool that in a few moments converts an angle written in degrees, radians, minutes and angular seconds, signs, octants, sextants, quadrants, revolutions, gons and mils to all other units. You enter one value, select a unit, clickCalculate- and the tabular preview shows precise results, ready to be copied to a report, project or notes.
The tool is useful in mathematics, geometry, geodesy, navigation, military, astronomy, as well as in education and everyday work with trigonometry. You don't have to remember formulas likedegrees = radians × 180 / π- the converter will do everything for you.
What angle units does the tool support?
The angle converter has been designed to cover bothschool and academicunits, as well as those used in surveying, navigation and the military. You can convert one angle to:
| Unit | Description | Full rotation |
|---|---|---|
| Radian (rad) | A mathematical unit related to the length of an arc equal to the radius of a circle. | 2π rad |
| Degree (°) | The most commonly used unit of angle in geometry and everyday life. | 360° |
| Angular minute (') | 1/60of a degree, used in surveying and navigation. |
21,600' |
| Arc second (") | 1/60of a minute, or1/3,600of a degree, for very small angles. |
1,296,000" |
| Sign | Astrological unit, 1/12 of a complete circle. | 12 characters(30° each) |
| Octant | 1/8 of a full angle, used in navigation. | 8 octants(45° each) |
| Sextant | 1/6 of a complete circle, unit associated with a navigational instrument. | 6 sextants(60° each) |
| Quadrant | 1/4 full turn, classic 90°. | 4 quadrants |
| Rotation | Full rotation around a point, basic 360°. | 1 revolution |
| Gon (hail) | A unit used in surveying, a full circle is 400 gon. | 400 gon |
| Mil | Military unit, 1/6400 of a full circle (NATO version). | 6,400 miles |
Thanks to this, you can analyze one angle in several systems simultaneously - without manual formulas and intermediate conversions.
How does the angular unit converter work?
Step 1: Enter the value and source unit
Enter the angle value (e.g.45, 3.14159, 90) and select the unit:degrees, radians, gon, mil, rotationor another unit available on the list.
If you work with exact values, you can use more decimal places - the converter will maintain the accuracy of the calculations.
Step 2: Select the result range
You can choose from:
- single output- e.g. only "degrees → radians" or "radians → gon",
- full conversion table- one value converted to all supported units.
In table mode, you can immediately see how many degrees, radians, gons, revolutions your angle has.
Step 3: Set precision and format
For convenient work, you can adjust:
- number of decimal places - e.g. from 0 to 10-12 places,
- notation type -standard notationorscientific,
- grouping of numbers - e.g. spaces or no thousands separators.
This is especially useful when you paste the results into a report, technical documentation or script.
Step 4: Calculate and Copy Results
ClickCalculate, and the tool will show the result in selected units or the full table. Then:
- copy a single value,
- or use the"Copy Table"option to transfer the complete conversion to a spreadsheet.
If necessary, you can alsoreset the formor load sample test data.
Most important angle unit conversion formulas
The converter performs these operations automatically, but knowing the basic formulas makes it easier to understand the results.
- Radians to degrees
degrees = radians × (180 / π) - Degrees to radians
radians = degrees × (π / 180) - Degrees to minutes and arcseconds
minutes = degrees × 60seconds = minutes × 60 = degrees × 3600 - Degrees to gon
gon = degrees × (400 / 360) - Degrees to miles(6400 miles / 360° version)
miles = degrees × (6400 / 360) - Degrees per revolutions
revolutions = degrees / 360 - Degrees per signs, octants, sextants, quadrants
signs = degrees / 30octants = degrees / 45sextants = degrees / 60quadrants = degrees / 90
In practice, it is often easiest to reduce everything todegreesorradians, and then use the above relations - this is exactly how your converter works.
Example conversions of angular units
| Input value | Selected results | Application |
|---|---|---|
| π rad | 180° · 200 gon · 0.5 revolution | Trigonometry, signal analysis |
| 90° | π/2 rad · 1 quadrant · 100 gon · 1600 miles | Geometry, right angles in engineering drawings |
| 1° | 60' · 3600" · ~0.01745 rad | Geodesy, astronomy, optics |
| 30° | 1 sign · π/6 rad · 0.0833 rotation | Astrology, division of a circle into 12 parts |
| 400 gon | 360° · 2π rad · 1 rotation | Geodesy, coordinate systems |
| 6,400 miles | 360° · 400 gon · 1 revolution | Aiming and bearing in the military |
Where will you use the angular unit converter?
Navigation: shipping, aviation, land navigation
In navigation, angles appear in the form of courses, bearings, azimuths or deviations. The converter helps:
- convert degrees to mils (military angular units),
- convert degrees to gon in surveying solutions,
- facilitate the analysis of headings and heading errors in various recording systems.
Surveying and Engineering
Gons and arcseconds are often used in field surveys and engineering projects. Angular unit converter:
- converts instrument results into the desired format,
- allows you to coordinate data from different countries and systems,
- minimizes errors resulting from manual conversions and rounding.
Astronomy, Physics, Mathematics
Radians are a natural unit in trigonometry and the analysis of functions, while degrees, minutes, and arcseconds are usually used to describe the positions of objects in the sky. Converter:
- makes it easier to switch between degrees and radians in equations,
- allows you to save small angular differences in arc seconds,
- checks the consistency of measurement data from different sources.
Military and Aiming Systems
The mil (artillery mil) is a convenient unit for determining small directional deviations. Converter:
- converts mils to degrees, gon and radians,
- facilitates data integration with civil and military systems,
- speeds up the preparation of reports and training.
Typical problems with manual conversion of angles
Manual conversion of angular units can be time-consuming and error-prone, especially when:
- you are converting multi-degree values (degrees-minutes-seconds) to radians,
- you are working with very small angles (arc seconds, thousandths of a degree),
- you need to go through some intermediate units (e.g. degrees → radians → mils).
Additionally, there arerounding errors- different tools use different numbers of decimal places, which may lead to discrepancies in longer calculation chains. Angular unit converter:
- applies a consistent level of precision throughout the table,
- allows you to set the number of decimal places,
- eliminates errors resulting from typing values.
FAQ – frequently asked questions
What is the difference between a radian and a degree?
Radiandefines an angle based on the ratio of the length of the arc to the radius of the circle - a full circle is2π rad. A degreedivides a full revolution into 360 equal parts. Both units describe the same quantity (angle), but in different systems.
How to convert radians to degrees?
Use the formula:degrees = radians × (180 / π). For example:π rad = 180°, π/2 rad = 90°. In the converter, simply select "radian" as the source unit and "degree" as the target unit, or enable the full table.
How to convert degrees to minutes and arc seconds?
Angular minutes: minutes = degrees × 60
Arc seconds: seconds = degrees × 3600
The tool will calculate them automatically and provide them in the table, so you don't have to separate the integer and fractional parts manually.
Can I copy the entire conversion table at once?
Yes. Set the direction to "all" units, clickCopy Table, and then paste the data into a spreadsheet, document or instant messenger - with a consistent number format.
Can the tool be used without logging in?
Yes. The angular unit converter workswithout registering and logging in. You open the page, enter the value, select units - the result is immediately ready.
Summary - fast and precise online angle conversion
Theangle unit converter allows you to convert a value expressed in radians, degrees, minutes, arc seconds, signs, octants, sextants, quadrants, revolutions, gons and miles into any other unit in a few seconds - while maintaining high precision and a readable format.
- supports all popular angle units,
- allows you to adjust the precision and writing style,
- generates complete conversion tables ready for copying,
- eliminates manual conversion and rounding errors.
Regardless of whether you are calculating the angle in a trigonometry problem, analyzing azimuths, designing a structure, or working with geodetic data - theonline angular unit converterwill speed up your work and ensure the correctness of the results.