Angle Converter

Angle converter for degrees, radians, gradians, turns, arcminutes, and arcseconds

An angle is one of those measurements that shows up everywhere, but the unit changes depending on what you are doing. In school math you usually see degrees and radians. In surveying and some technical contexts you may see gradians. In rotation problems you may see turns (revolutions). And in navigation, astronomy, and precision measurement you often see arcminutes and arcseconds.

This Angle Converter is built for one job: take a single angle value, convert it into the unit you need, and show the same angle in the other common units so you can sanity-check your work. That is the real decision most people are making: “What is this angle in the unit my formula, tool, or worksheet expects?”

To use it, enter your angle value, choose the unit it is currently in (From unit), then choose the unit you want (To unit) and press Convert. The main result shows the converted value in your chosen target unit. Below that, the breakdown shows the same angle expressed in all supported units, which helps catch input mistakes like mixing up degrees and radians.

Assumptions and how to use this calculator

• The input is a single angle value in decimal form for the selected “From unit” (for example 45 degrees, not 45° 30′ 0″).
• Negative angles are allowed because they are valid in math and engineering contexts.
• The conversion uses widely accepted exact relationships based on π, so the only practical limitation is rounding to the decimal places you choose.
• If you leave “Decimal places” empty, the calculator defaults to 6 decimals to balance readability and usefulness.
• Rounding can hide small differences, so increase decimals if you are debugging a calculation or matching a tool that shows more precision.

Common questions

Why do my radians look “wrong” compared to degrees?

The numbers are on different scales. 180 degrees equals π radians (about 3.14159). So a familiar degree value often becomes a smaller-looking radian value. If you accidentally enter degrees while “From unit” is set to radians, your result will be far off. Use the “all units” breakdown to spot this instantly.

What is the difference between arcminutes and arcseconds?

They are subdivisions of a degree. One degree equals 60 arcminutes, and one arcminute equals 60 arcseconds. That means one degree equals 3,600 arcseconds. These units are common when you need fine angular resolution, such as in astronomy or map-related contexts.

What are gradians and when would I use them?

Gradians (also called gon) divide a full turn into 400 parts instead of 360 degrees. That makes right angles exactly 100 gradians. They are used in some surveying, mapping, and engineering workflows. If your instrument or worksheet uses gon, converting correctly matters because the scale is different.

What does “turns” mean as an angle unit?

A turn is a full rotation. One turn equals 360 degrees, 2π radians, or 400 gradians. Turns are useful when you are thinking in rotations rather than angles, like shaft rotation, gearing, or anything expressed in revolutions.

How many decimals should I use?

For everyday conversions, 4 to 6 decimals is usually enough. If you are feeding the value into a sensitive calculation, increase decimals to 8 to 12. If you are matching a classroom answer key, fewer decimals might be expected. The “right” choice is the smallest number of decimals that still preserves the accuracy you need.