How to Convert Angle Values Between Units

When to use an angle conversion

The Angle Converter is useful when an angle is written in a unit that does not match the one needed for a calculation, lesson, specification, or technical reference. It converts a numeric angle among degrees, radians, gradians, arcminutes, arcseconds, and turns. This makes it possible to keep the original measurement while expressing it in a different angular unit for the next part of your work.

Before you begin, identify both sides of the conversion. The source unit describes the value you already have, while the target unit describes the form you want to receive. Checking those choices first helps prevent a numerically valid-looking result from being interpreted in the wrong unit. The same starting number can represent different angles depending on its source unit, so the labels matter as much as the number.

Convert an angle step by step

Enter the numeric angle you want to convert. Use the value from your exercise, calculation, drawing, specification, or other reference.
Select the source unit that matches the value you entered. The available supported units are degrees, radians, gradians, arcminutes, arcseconds, and turns.
Select the target unit in which you want the answer.
Run the conversion, then inspect the returned numeric result together with its target unit.

If you omit the numeric value, the tool uses 0. If you omit the source unit, it uses degrees, and if you omit the target unit, it uses radians. Those defaults can be convenient for a quick check, but selecting the units yourself is preferable when the original value comes from a document or another calculation.

For recognized source and target units, the tool converts the supplied numeric angle and reports a successful result. The converted numeric value is rounded to 10 decimal places. That rounding is useful when the mathematical conversion produces a long or repeating decimal, because the result is presented at a consistent precision. Keep the selected target unit visible when you copy or compare the answer so the number is not separated from its meaning.

Understand the converted value

Interpret the result as an angle expressed in the target unit you selected, not as a unit-free number. For instance, a result requested in radians needs to be used as radians in the following calculation, even if the starting value was supplied in degrees. Recording the target unit beside the number preserves that context when you move the result into notes or another calculation.

The displayed numeric result is rounded to 10 decimal places, so the shown value represents the conversion at that precision. A successful result depends on a recognized source unit and a recognized target unit. If the conversion does not succeed, review both unit selections and compare them with the supported choices before trying again.

This tool covers conversions among the six supported angle units. It does not establish how values outside the recognized unit choices should be interpreted, so do not substitute an unlisted label and expect it to be treated as an angle unit.

Worked example

You need to express a 180-degree angle in radians before using it in a calculation.

Enter 180, select degrees as the source unit, select radians as the target unit, and run the conversion.

The result is successful and contains a numeric angle in radians rounded to 10 decimal places.

Limitations

The described conversion applies to numeric angles paired with recognized source and target units; an unrecognized unit leads to an unsuccessful result, while other input situations are not covered here.

Common errors

Cause: one unit selection is not recognized. Correction: choose degrees, radians, gradians, arcminutes, arcseconds, or turns for both the source and target.

FAQ

Can I convert degrees to radians?

When the source is degrees and the target is radians, enter the angle, select those two units, and run the conversion to receive the numeric result in radians.

What happens when I leave the inputs blank?

When those fields are omitted, the numeric value is 0, the source unit is degrees, and the target unit is radians.

How many decimal places does the result use?

The converted numeric value is rounded to 10 decimal places before the result is reported.