Angle Converter
Convert radians, milliradians, degrees, minutes of arc, seconds of arc, gradians, revolutions, circles, and angular mils. Change either value or unit to see your result instantly.
Convert Angles Instantly
Edit either number, change the units or choose a popular conversion.
180° equals approximately 3.14159265359 rad
Popular angle conversions
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How to Use the Angle Converter
Choose a source unit and a destination unit, then enter an angle. The tool converts the same angle between different units. You can enter a value in either field and use Swap to reverse the conversion.
Enter your angle
Type a positive or negative number into either measurement field.
Choose the units
Select any of the nine angle units, or tap a popular shortcut.
Use the result
Check the answer, conversion factor and table, then copy the value.
Angle Conversion Formula
Angles can be expressed using radians, degrees, arcminutes, revolutions or other units. This calculator first converts the entered angle to radians, then divides by the destination unit’s size in radians.
General formula
Converted angle = Input × (radians per source unit ÷ radians per destination unit)
Example: 180 degrees to radians
180 × π/180 = π radians, approximately 3.14159265359 rad.
Example: 45 degrees to gradians
45 × (400/360) = 50 gradians.
Example for your selected units: 5 ° × 0.0174532925199 ≈ 0.0872664625997 rad.
Important: The angular mil option uses 6,400 mils per circle. It is not the same as a milliradian (1/1,000 rad). Revolutions and circles are equivalent full-turn units.
Angle Conversion Table
The table below updates when you change the From or To unit. Calculations use π and exact unit relationships; displayed values are rounded for readability.
| Degrees (°) | Radians (rad) |
|---|---|
| 1 | 0.0174532925199 |
| 2 | 0.0349065850399 |
| 5 | 0.0872664625997 |
| 10 | 0.174532925199 |
| 25 | 0.436332312999 |
| 50 | 0.872664625997 |
| 100 | 1.74532925199 |
| 1,000 | 17.4532925199 |
Common source values: 1, 2, 5, 10, 25, 50, 100 and 1,000. Small results may use scientific notation.
Angle Units Explained
All nine choices refer to plane angles. Degrees split a full turn into 360 parts, gradians split it into 400 parts, and radians describe the ratio of arc length to radius. Minutes and seconds of arc are much smaller subdivisions of a degree.
Common angle reference points
A quarter turn equals 90° = π/2 rad = 100 gon = 0.25 revolutions = 1,600 angular mils. A half turn equals 180° = π rad = 200 gon. A complete circle equals 360° = 2π rad = 400 gon.
Why are circles and revolutions both included?
They are two names for the same full-turn angle. Both appear in reference materials, so we let users choose either. Converting one circle to revolutions returns one revolution.
Frequently Asked Questions
How many radians are in 180 degrees?
180 degrees equals π radians, approximately 3.14159265359 rad. A full 360-degree turn equals 2π radians.
How do I convert degrees to radians?
Multiply the value in degrees by π/180. For example, 90° × π/180 = π/2 rad, approximately 1.57079632679 rad.
How do I convert radians to degrees?
Multiply the value in radians by 180/π. For example, π radians equals 180°.
How many arcminutes and arcseconds are in a degree?
One degree is 60 arcminutes or 3,600 arcseconds. One arcminute is 60 arcseconds.
Are a circle and a revolution the same angle?
Yes. Both describe one complete turn: 360°, 2π radians, or 400 gradians.
What is the difference between milliradians and mils?
One milliradian is 0.001 rad. In this tool, one angular mil is 1/6400 of a circle. They are close in size but not equal.
How many mils are in a complete circle?
This calculator uses the 6,400-mils-per-circle convention. Other definitions exist, so check the convention in your source measurement.
How many gradians are in a right angle?
A right angle is 90 degrees, 100 gradians, or π/2 radians.
Can I enter negative angles?
Yes. Negative values are accepted for signed angles; the unit conversion preserves the sign.
Does this convert degrees, minutes and seconds together?
This converter accepts one numeric unit at a time. For a combined angle such as 12° 30′ 15″, use the dedicated DMS converter.
Can I convert slope percentages here?
No. Slope percent depends on a tangent relationship rather than a simple unit factor. Use a separate slope calculator.
Why does the calculator show scientific notation?
Very small or large results may be displayed in scientific notation so that meaningful nonzero values are not rounded to zero.
Related Angle Calculators
Combined degree-minute-second formats and slope percentages use a different input or formula, so they are kept separate from this general Angle Converter.
Conversion References
Angle unit relationships follow the NIST Guide to the SI, Appendix B.9 and the NIST SI reference on plane angles. Calculations use π directly rather than a shortened decimal for intermediate steps.
Measurement note: Angular mil conventions can differ. This tool uses 6,400 angular mils per full circle; if your source uses another convention, verify it before converting.