Free Angle Converter

Angles are essential in countless fields—surveying, astronomy, navigation, physics, and even game development. Converting between different angle units quickly and accurately is a frequent task. This free online angle conversion calculator supports ten distinct units: degrees, radians, gradians (gon), turns, arcminutes, arcseconds, milliradians, microradians, and π radians. Whether you need a dedicated degrees to radians converter, a tool to handle gradians to degrees, or simply a versatile angle conversion calculator, this utility gives you instant results.

Using the tool is straightforward: select the input unit (e.g., degrees), type the numeric value, and the converter automatically displays the equivalent angle in every other supported unit. This lets you compare and switch between systems without manual calculations.

Angle Basics

An angle is formed when two rays share a common endpoint, known as the vertex. Angles can be grouped by their size, typically measured in degrees or radians. The table below outlines the standard angle classifications:

Beyond simple size, angles also appear in special relationships. Complementary angles sum to $90^\circ$, while supplementary angles add up to $180^\circ$. A reference angle is the acute version of any given angle, useful in trigonometry. A central angle has its vertex at the center of a circle, directly relating to arc length.

Radians – The Universal Unit

In the SI system, the radian is the standard unit of angle. One radian is the angle that subtends an arc equal in length to the radius of the circle; this works out to about $57.2958^\circ$. Because a full circumference equals $2\pi R$, a complete revolution is $2\pi$ radians. The following table lists common degree–radian equivalences:

To convert degrees to radians, use the formula:

For the reverse conversion:

For example, $300^\circ$ in radians is $\dfrac{\pi}{180^\circ} \times 300^\circ = \dfrac{5\pi}{3}\ \text{rad}$.

Degrees, Minutes & Seconds (DMS) to Decimal Degrees

Geographic coordinates and some technical fields express angles in degrees (°), minutes ('), and seconds ("). Because $1^\circ = 60' = 3600"$, the conversion to decimal degrees is:

Take $48^\circ 37' 52"$: it equals $48 + \frac{37}{60} + \frac{52}{3600} \approx 48.6311^\circ$. The converter can handle both directions (DMS to decimal and decimal to DMS) with ease.

Other Angle Units

• Turn: One complete rotation equals $1\ \text{turn} = 360^\circ = 2\pi\ \text{rad}$. Conversion formulas: $\text{turns} = \dfrac{\text{degrees}}{360^\circ}$ and $\text{turns} = \dfrac{\text{radians}}{2\pi}$.
• Gradian (Gon): A right angle is defined as $100$ gradians. Thus, degrees to gradians: $\text{gradians} = \dfrac{10}{9} \times \text{degrees}$. Radians to gradians: $\text{gradians} = \dfrac{200}{\pi} \times \text{radians}$. Also, $\text{gradians} = 400 \times \text{turns}$.

These relationships allow manual conversion, but this free angle unit converter automates the entire process. Simply choose your input unit, enter the value, and instantly see results across all ten units. Whether you’re solving a geometry problem or preparing engineering specifications, this online angle conversion calculator saves time and minimises errors.