Angle Converter
Enter the angle value to convert. Negative values and values over 360 are supported.
Popular Conversions
Enter an Angle to Convert
Select your input unit and target unit, then type an angle value or use a preset button. The converted result and all equivalent units will appear here instantly.
How to Use the Angle Converter
Choose Your Input Mode
Select Decimal mode to enter a single number (e.g., 45.5 degrees), or switch to DMS mode to enter an angle as Degrees, Minutes, and Seconds (e.g., 45° 30' 0"). DMS mode always converts from degrees to your chosen target unit.
Set From and To Units
Use the From Unit and To Unit dropdowns to select your source and target angle units. Available units include degrees, radians, gradians, arcminutes, arcseconds, revolutions, quadrants, sextants, signs, octants, NATO mils, and milliradians. Use the swap arrow button to instantly reverse the direction.
Enter a Value or Use a Preset
Type your angle value in the input field, or click one of the Common Angle Presets (0°, 30°, 45°, 60°, 90°, 120°, 180°, 270°, 360°) for frequently used angles. The conversion updates automatically as you type — no need to press Convert.
Read Results and Export
The main result shows your converted value with the formula used. Below that, a visual diagram shows the angle on a circle, and the All Unit Equivalents table lists the angle in every supported unit. Use the copy icon on any row to copy that value, or click Export CSV to download all results as a spreadsheet.
Frequently Asked Questions
How do I convert degrees to radians?
To convert degrees to radians, multiply the degree value by π/180 (approximately 0.017453). For example, 90° × π/180 = π/2 ≈ 1.5708 radians. Conversely, to convert radians to degrees, multiply by 180/π (approximately 57.2958). So 1 radian ≈ 57.2958°. These relationships arise because a full circle equals 360° and also 2π radians — dividing both by 360 gives 1° = π/180 radians. Our converter applies this formula automatically, showing the exact multiplication factor used so you can verify the calculation yourself.
What is a gradian (gon), and when is it used?
A gradian (also called a gon or grad) divides a full circle into 400 equal parts, so a right angle equals exactly 100 gradians. This unit was introduced during the French Revolution as part of an effort to decimalize measurement systems. Gradians are still widely used in land surveying and civil engineering, particularly in continental Europe. Because 400 is a round number that aligns with percentage-based slope calculations, surveyors find the gradian system convenient for computing horizontal and vertical offsets. The conversion is straightforward: 1 gradian = 0.9 degrees, and 1 degree = 10/9 gradians ≈ 1.1111 gradians.
What is the difference between arcminutes and arcseconds?
Arcminutes and arcseconds are subdivisions of degrees used for precise angular measurements. One arcminute (') equals 1/60 of a degree, and one arcsecond (") equals 1/3600 of a degree (or 1/60 of an arcminute). These units are used in astronomy to describe the apparent size of celestial objects (the full Moon is about 30 arcminutes wide), in navigation for GPS coordinates (1 arcminute of latitude ≈ 1 nautical mile), and in optics for describing angular resolution. The DMS (Degrees, Minutes, Seconds) format, like 40° 26' 47", is the standard way to express latitude and longitude on maps and GPS devices.
What is a NATO mil and how does it differ from a milliradian?
The NATO mil divides a full circle into exactly 6,400 parts, so 1 NATO mil = 360/6400 = 0.05625 degrees. The milliradian (mrad) is 1/1000 of a radian, which equals approximately 0.05730 degrees — slightly larger than a NATO mil. The mil system was designed so that at a range of 1,000 meters, 1 mil corresponds to approximately 1 meter of lateral movement, making range and windage calculations easier for artillery and rifle scopes. Note that the Soviet mil uses 6,000 divisions per circle and the Swedish streck uses 6,300 — all three give slightly different values for 'one mil.' This converter uses the NATO standard of 6,400 mils per circle.
What does the DMS input mode do?
DMS stands for Degrees, Minutes, Seconds — a compound angle format used in navigation, cartography, astronomy, and surveying. Instead of writing 40.4464°, you can express the same angle as 40° 26' 47.04". In DMS mode, our converter accepts three separate fields for degrees, minutes, and seconds, then combines them into a decimal degree value using the formula: decimal degrees = D + M/60 + S/3600. The result is then converted to your chosen target unit. DMS mode always treats the input as degrees before converting, so the From Unit selector is disabled in that mode.
Why does the visual diagram only show 0–360°?
The circular angle diagram normalizes any input angle to the 0–360 degree range for display purposes, because a circle can only show one full revolution visually. If you enter 450 degrees, the diagram shows the equivalent position at 90 degrees (450 mod 360 = 90). Similarly, negative angles are mapped to their positive circular equivalent (for example, −90° maps to 270°). This normalization only affects the visual; the actual converted result shown in the main output and the all-units table uses the full, unnormalized value. For angles greater than 360 degrees, the result accurately reflects the multiple-revolution value (for example, 720 degrees = 4π radians, not 2π).