Authoritative definitions of the International System of Units and SI prefixes.
Unit converters
Angle
Enter your values below for a clear, instant result.
AngleInstant result
Decimals
Formula result = input × 1 ÷ 0.017453292519943295. 1 rad = 57.2958 °
Common examples
One value, several units
Degrees57.2958 °
Gradians63.662 gon
Turns0.1592 turn
Arcminutes3,437.7468 ′
Arcseconds206,264.8062 ″
Conversion table
| rad | ° |
|---|---|
| 1 rad | 57.2958 ° |
| 2 rad | 114.5916 ° |
| 5 rad | 286.4789 ° |
| 10 rad | 572.9578 ° |
| 25 rad | 1,432.3945 ° |
| 50 rad | 2,864.789 ° |
| 100 rad | 5,729.578 ° |
Conversion chart
1 rad57.2958 °
5 rad286.4789 °
10 rad572.9578 °
25 rad1,432.3945 °
50 rad2,864.789 °
Worked example
A full turn is 360 degrees or 2π radians.
Unit definition
Radians (rad) One radians equals 1 radian.
Unit history
Radians is represented here using its modern SI definition or an internationally accepted relationship to an SI base unit.
Step by step
1. Parse the value, including fractions.
2. Convert rad to radian.
3. Convert the base value to ° and apply your display precision.
Understand the result before using it
Angle expresses the same plane angle in degrees, radians, gradians, turns, arcminutes, or arcseconds. The numerical value changes because the size and definition of the selected unit changes; the underlying quantity does not.
Calculated result
The conversion follows the displayed unit relationship. Display rounding can hide additional digits, and measured inputs cannot become more accurate merely by changing units.
Formula, assumptions, and example
Formula
result = input × 1 ÷ 0.017453292519943295
Assumptions
- The source and target selections represent the same physical quantity or supported notation.
- The entered value is valid for the selected relationship and uses the source unit shown.
- Published unit definitions and conventional conversion factors apply under their stated conditions.
Worked example
A full turn is 360 degrees or 2π radians.
When to use it
Good uses
- Translate a angle value found in a document, specification, recipe, or measurement.
- Compare values reported in different unit systems.
- Check a manual conversion and control the displayed precision.
Limitations
Common mistakes to avoid
- Unit conversion does not account for measurement uncertainty, instrument calibration, or context outside the unit definition.
- Do not add meaningful digits beyond the precision of the original measurement.
- Confirm regulated, safety-critical, laboratory, and contractual values against the controlling standard.
Sources and further reading
These references explain the underlying standards or provide authoritative context. Your own contract, institution, clinician, product documentation, local code, or governing standard may be the controlling source.
Guidance on unit names, symbols, conversions, and numerical presentation.
Questions about this calculation
What does the Angle converter do?
Angle expresses the same plane angle in degrees, radians, gradians, turns, arcminutes, or arcseconds. It does not change the physical quantity represented by the input.
What formula does the Angle converter use?
result = input × 1 ÷ 0.017453292519943295
Why can a Angle converter result be rounded?
UnitMora calculates with JavaScript double-precision numbers, then formats the result using your selected decimal or significant-figure setting. The unrounded value may contain more digits than are displayed.
What is the most common angle conversion mistake?
The most common mistake is selecting a similarly named but different unit or treating a rounded measurement as exact.
Clear answers, without the guesswork
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