Angle Converter

Seven angle units in one place: degrees, radians, gradians, arcminutes, arcseconds, full turns, and NATO mils, with every unit shown at once beneath the main result.

What is the Angle Converter?

The Angle Converter routes every value through degrees, then divides into whichever unit you asked for. It knows seven of them: degrees, radians (1 rad = 57.2957795 degrees), gradians or gon (0.9 degrees each), arcminutes (1/60 of a degree), arcseconds (1/3600), full turns (360 degrees), and NATO mils at 6,400 to a circle. Load the page and it opens on the classic sanity check, 180 degrees into radians, which lands on pi.

Key Features

• Seven units: degrees, radians, gradians, arcminutes, arcseconds, turns, and NATO mils
• Quick Conversions grid restates your value in all seven units simultaneously
• Results carry six decimal places, enough to keep radians meaningful
• A swap button flips the from and to units in place
• The formula line spells out the conversion using proper unit symbols

Common Use Cases

• Feeding radians into sin and cos calls that reject degree input
• Reading survey bearings written as degrees, arcminutes, and arcseconds
• Translating gradian readings from continental European survey work back into degrees
• Turning artillery or rifle-scope mil figures into degrees for a spec sheet

How to Use the Angle Converter

1. Type the angle into the Value box, which opens on 180.
2. Pick your source unit under From, such as Degrees or NATO Mils.
3. Pick the target unit under To, such as Radians or Gradians.
4. Read the large result, its unit name, and the formula line underneath.
5. Scan the Quick Conversions grid to see the same angle in all seven units.

Tips for Best Results

• Radians make calculus clean: the derivative of sin x equals cos x only in radians.
• Watch for pi multiples: 3.14159 radians is a straight line, 6.28319 a full circle.
• Gradians split a right angle into a tidy 100, which is why surveyors liked them.
• Convert arcseconds before averaging them; mixing 1/60 and 1/3600 divisions by hand invites errors.

Why Use WiserWork's Angle Converter?

Angle units are the one place where a wrong answer still looks perfectly plausible: 1 radian and 1 degree are both small positive numbers, and nothing about the digits warns you. This converter keeps all seven units on screen together, so a value sitting in the wrong column is obvious immediately. Nothing is uploaded either, because the arithmetic runs inside the page you already loaded.

Who Uses the Angle Converter?

Students meeting radians in trigonometry and calculus for the first time, programmers whose math libraries expect radians while their design files store degrees, and surveyors handling bearings in degrees, arcminutes, and arcseconds. Machinists, animators, and optics buyers reach for the mil and turn conversions instead.

Frequently Asked Questions

Which angle units does this tool support?

Seven: degrees, radians, gradians (gon), arcminutes, arcseconds, turns (full revolutions), and NATO mils. Any one of them converts to any other.

Why do mathematicians prefer radians over degrees?

A radian is defined by the circle itself, the angle whose arc equals the radius, so no arbitrary constant sneaks in. That is why the derivatives of sine and cosine come out clean only when the input is in radians.

How many degrees is one radian?

About 57.2957795 degrees, which is the exact factor this tool uses. A full circle is 2 pi radians, roughly 6.28319.

What is a gradian and who still uses it?

A gradian, also written gon or grade, is 0.9 degrees, so a right angle is exactly 100 gradians and a full circle is 400. It survives mainly in continental European surveying.

What are arcminutes and arcseconds?

An arcminute is 1/60 of a degree and an arcsecond is 1/60 of an arcminute, or 1/3600 of a degree. Astronomy, navigation, and land surveying all use them for fine bearings.

How many NATO mils are in a circle?

6,400, which is what the 0.05625 degrees-per-mil factor here works out to. Artillery and rifle optics favor mils because one mil is close to a milliradian, making range estimates easy in the field.

What does the Turns unit mean?

One turn is one complete revolution, or 360 degrees. It is the natural unit for rotation counts in animation, gearing, and motor specifications.

How precise are the results?

The main result is rounded to six decimal places and the Quick Conversions grid to four. That is finer than most drawings, survey sheets, or math homework will ever need.

Can I convert in the other direction?

Yes. The circular button sitting between the two dropdowns trades your source and target units, then recalculates right away.

Does it handle negative angles?

Yes. The Value box accepts negative numbers and the factor applies the same way, so minus 90 degrees becomes minus 1.570796 radians.

Degrees, radians, and mils each answer to a different tradition, and mixing them quietly wrecks a calculation. Keep this page open beside your trig homework, survey notes, or shader code and read all seven side by side.