Angle converter
Convert degrees, radians, gradians and turns while retaining signed rotations.
Your inputs
Your results
Ready when you areYour results will appear here.
How it works
Convert signed plane angles between degrees, radians, gradians, turns and angular minutes or seconds. Negative angles and multiple revolutions are preserved rather than wrapped to a single turn.
A few things to know
Decimal angle input only; does not parse degrees-minutes-seconds notation or perform angle wrapping. Arcminutes and arcseconds are angular units, not elapsed time. Radian conversions involving pi are floating-point approximations. No bearing reference, rotation direction or coordinate system is inferred. Display uses up to 12 significant digits; this is not arbitrary-precision arithmetic or a measurement calibration. Numeric magnitude is bounded to 1e100, with nonzero inputs at least 1e-100.
When to use this tool
An angle may be recorded in degrees, radians, gradians or fractions of a turn. This converter expresses the same signed plane angle in each system, including angular minutes and seconds. It preserves negative values and multiple revolutions rather than wrapping everything into a single circle. That makes it useful when an accumulated rotation or direction of rotation matters. Input is a decimal angle; degrees-minutes-seconds strings, compass references and rotation conventions are not inferred from the number.
- Translate a degree value into radians for a separate mathematical calculation.
- Compare a gradian-based angle with a specification written in degrees.
- Express an accumulated or negative rotation in turns while retaining its sign and full magnitude.
How to use angle converter
Enter a decimal angle
Put the angle in Value. Negative numbers and values larger than one revolution are supported; compound degrees-minutes-seconds text is not parsed.
Choose the angular source unit
Set From unit. Arcminutes and arcseconds mean angular subdivisions, while gradians use 400 per full turn.
Read the converted angle
Choose To unit and calculate. Check Converted value or the full table, keeping the original sign and reference convention in your own records.
Half a turn expressed in radians
Inputs
Value 180; From unit Degrees (°); To unit Radians (rad).
Result
Converted value is 3.14159265359 radians. The table also gives 0.5 turns, 200 gradians and 10,800 arcminutes.
What it means
A full revolution is 2π radians, so half a revolution is π. The displayed radian value is a decimal approximation, whereas the symbolic relationship remains exactly π.
Common mistakes to avoid
Confusing angular minutes with time
An arcminute is one-sixtieth of a degree. It is not an elapsed minute and cannot be converted by a duration tool.
Expecting automatic angle wrapping
A 720-degree input remains two turns. It is not reduced to zero even though those angles can share a final orientation.
Losing the rotation reference
Units do not determine whether positive means clockwise, counterclockwise or a bearing from north. Preserve that context separately.
Frequently asked questions
Definitions, edge cases, and practical next steps for this tool. Search all tool FAQs ↗
How do degrees convert to radians?
Multiply degrees by π/180. The inverse multiplies radians by 180/π. The calculator uses a floating-point representation of π, so values such as π radians appear as a decimal approximation rather than an exact symbolic expression.
How many gradians are in a turn?
A full turn contains 400 gradians, compared with 360 degrees. One gradian therefore equals 0.9 degree. This is the gon-based option in the unit list, which should not be confused with a radian or an angular minute.
What are arcminutes and arcseconds?
One degree contains 60 arcminutes and 3,600 arcseconds. An arcsecond is one-sixtieth of an arcminute. These are angular subdivisions; their familiar minute and second names do not make them interchangeable with elapsed-time units.
Can I enter a negative angle?
Yes. The converter preserves its sign, so −90 degrees becomes −0.25 turns. It does not choose a physical direction or coordinate convention for you. Keep the meaning of positive and negative rotation consistent in the system using the result.
Does the tool normalize angles into 0 to 360 degrees?
No. It converts the supplied magnitude without wrapping. A 450-degree angle becomes 1.25 turns rather than 90 degrees. Normalizing can be useful for orientation, but would remove accumulated-rotation information, so it is not performed automatically.
Can I enter degrees, minutes and seconds together?
The Value field accepts one decimal number, not a compound notation. Convert the parts to decimal degrees separately, such as degrees plus minutes/60 plus seconds/3600. For negative compound values, apply the intended sign consistently to the complete angle.
Can this convert compass bearings or map coordinates?
It can change the unit of a known angular value, but it does not interpret north references, magnetic variation, latitude, longitude or coordinate systems. A bearing’s reference and direction convention must be supplied by the original context, outside this unit conversion.
How precise are the converted radians?
Results display up to 12 significant digits using floating-point arithmetic. Irrational π-based results cannot be completely written as finite decimals. Use symbolic mathematics or an appropriate precision method if the next calculation needs more than the displayed approximation.
Explore the topic in the blog
Sources and method
Use the references below to check definitions and platform guidance. The model’s scope and limits are explained above. Read our editorial standards.