Angle Converter  

Converting between various angle units—like degrees, radians, or revolutions—can be confusing and error-prone, especially in fields like mathematics, engineering, navigation, or geometry. Manual conversion not only takes time but also increases the chance of mistakes. That’s why our online Angle Converter tool is designed to provide fast, precise, and hassle-free conversions across all major angle units.

Whether you’re a student working on trigonometry, a developer coding geometric transformations, or a pilot navigating routes, our Angle Converter gives you accurate conversions instantly. Just enter a value in any supported unit, and it will convert it into all other relevant angle units—quickly and accurately.

This Angle Converter supports conversions between the following 8 angle measurement units:

• Arc Second
• Minute of Arc
• Degrees (°)
• Radians (rad)
• Gradians (gon)
• Revolutions (rev)
• Circles
• Mils

What is an Angle?

An angle is a measure of rotation between two rays or line segments that share a common endpoint (called the vertex). Angles are fundamental in fields like geometry, physics, astronomy, navigation, and engineering. Measuring angles correctly is crucial for understanding direction, constructing shapes, calculating trajectories, and more.

The most commonly used unit for angles is the Degree (°), but other units like Radians, Gradians, Minutes of Arc, Arc Seconds, and Revolutions are widely used depending on context—scientific, industrial, or navigational.

Here’s a quick overview of how these units relate to one another:

• 1 Degree = 60 Minutes of Arc
• 1 Minute of Arc = 60 Arc Seconds
• 1 Revolution = 360 Degrees
• 1 Radian ≈ 57.2958 Degrees
• 1 Circle = 1 Revolution
• 1 Gradian = 0.9 Degree
• 1 Revolution = 6400 Mils (NATO standard)

Our Angle Converter handles all these conversions automatically and precisely—no formulas needed.

What Are the Supported Angle Units in Our Angle Converter?

Our Angle Converter supports a complete set of angular measurement units, allowing you to seamlessly switch between degrees, radians, revolutions, and other specialized units. These conversions are essential in fields such as mathematics, engineering, navigation, astronomy, and surveying.

Below is the complete list and explanation of the supported angle units available in our tool, helping you convert values quickly and accurately:

1. Arc Second (″)

Arc Second is equal to 1/60 of an arc minute or 1/3600 of a degree. It is used in astronomy, optics, and precise navigation systems for tiny angular measurements.

2. Minute of Arc (′)

Minute of Arc or arcminute equals 1/60 of a degree. Common in navigation, map reading, and measuring angles in the sky.

3. Degree (°)

Degree is a widely recognized unit of angle. A full circle has 360 degrees. It is used in geometry, trigonometry, and everyday applications.

4. Radian (rad)

Radian is the SI unit of angular measurement. One radian is the angle created when the arc length equals the radius of the circle. A full circle is 2π radians (~6.28319).

5. Gradian (gon)

Gradian, also known as gon or grad, is defined so that 100 gradians equal a right angle, and 400 gradians make a full circle. It’s used in surveying and civil engineering.

6. Revolution (rev)

Revolution is a complete turn around a circle. One revolution equals 360 degrees, 2π radians, or 400 gradians. Common in motors, cycles, and rotational systems.

7. Circle

Circle is used informally to represent one full turn, equivalent to one revolution or 360 degrees.

8. Mil

Mil is a unit used primarily in the military and artillery, especially for aiming and targeting. There are 6400 NATO mils or 6283.19 true mils (milliradians) in a circle.

Angle Conversion Formulas

How to Convert Angle Units? – Explained with Examples

Converting between different angle units is essential in fields like mathematics, physics, navigation, astronomy, and engineering. This guide clearly explains the most common angle conversions using step-by-step formulas and examples.

1. How to Convert Degrees to Radians?

To convert degrees to radians, you can use the following formula:

radians = degrees * (π / 180)

Here, π (pi) is a mathematical constant approximately equal to 3.14159, and 180 represents the total number of degrees in a circle.

To convert a specific angle from degrees to radians, you can simply multiply that angle by the conversion factor (π/180). For example, if you want to convert 45 degrees to radians:

radians = 45 * (π / 180)

Using the approximation for π, the calculation would be:

radians ≈ 45 * (3.14159 / 180)

Thus,

radians ≈ 0.7854

So, 45 degrees is approximately equal to 0.7854 radians.

Similarly, you can use this formula to convert any given angle from degrees to radians. Just multiply the degree measure by (π / 180) to obtain the equivalent value in radians.

To convert degrees to radians, multiply the degrees by π/180. Formula: radians = degrees × π ÷ 180 Example: 180° × π ÷ 180 = π radians

2. How to Convert Radians to Degrees?

To convert radians to degrees, you can use the following formula:

degrees = radians * (180 / π)

Here, π (pi) is a mathematical constant approximately equal to 3.14159, and 180 represents the total number of degrees in a circle.

To convert a specific angle from radians to degrees, you can multiply that angle by the conversion factor (180/π). For example, if you want to convert 1.5 radians to degrees:

degrees = 1.5 * (180 / π)

Using the approximation for π, the calculation would be:

degrees ≈ 1.5 * (180 / 3.14159)

Thus,

degrees ≈ 85.9437

So, 1.5 radians is approximately equal to 85.9437 degrees.

Similarly, you can use this formula to convert any given angle from radians to degrees. Just multiply the radian measure by (180/π) to obtain the equivalent value in degrees.

To convert radians to degrees, multiply by 180/π. Formula: degrees = radians × 180 ÷ π Example: π radians × 180 ÷ π = 180°

3. How to Convert Degrees to Gradians?

To convert degrees to gradians, multiply by 10/9. Formula: gradians = degrees × 10 ÷ 9 Example: 90° × 10 ÷ 9 = 100 gradians

4. How to Convert Gradians to Degrees?

To convert gradians to degrees, multiply by 9/10. Formula: degrees = gradians × 9 ÷ 10 Example: 100 gradians × 9 ÷ 10 = 90°

5. How to Convert Degrees to Minutes of Arc?

To convert degrees to arcminutes, multiply by 60. Formula: arcminutes = degrees × 60 Example: 2° × 60 = 120 arcminutes

6. How to Convert Minutes of Arc to Arc Seconds?

To convert arcminutes to arcseconds, multiply by 60. Formula: arcseconds = arcminutes × 60 Example: 5 arcminutes × 60 = 300 arcseconds

7. How to Convert Arc Seconds to Degrees?

To convert arcseconds to degrees, divide by 3600. Formula: degrees = arcseconds ÷ 3600 Example: 7200 arcseconds ÷ 3600 = 2°

8. How to Convert Degrees to Revolutions?

To convert degrees to revolutions, divide by 360. Formula: revolutions = degrees ÷ 360 Example: 720° ÷ 360 = 2 revolutions

9. How to Convert Revolutions to Radians?

To convert revolutions to radians, multiply by 2π. Formula: radians = revolutions × 2π Example: 1 revolution × 2π = 2π radians

10. How to Convert Mils to Degrees?

To convert mils to degrees, divide by 17.77778. Formula: degrees = mils ÷ 17.77778 Example: 1777.778 mils ÷ 17.77778 = 100°

How to Use the Angle Converter Tool – Step-by-Step Guide

Use the following steps to easily convert angle values using our Angle Converter tool:

Step 1: Choose Your Input Unit: Select your starting angle unit from the supported list:

• Arc Second (″)
• Minute of Arc (′)
• Degrees (°)
• Radians (rad)
• Gradians (gon)
• Revolutions (rev)
• Circles
• Mils

Step 2: Enter the Angle Value: Type the numeric value into the input box labeled “Enter Value”.

Step 3: Select the Output Unit: Choose the unit into which you wish to convert your value.

Step 4: Get Instant Results: The tool auto-calculates and displays all conversions across supported units in real time.

Frequently Asked Questions – Angle Converter

Q1: What is the SI unit for angles?
The SI unit for angles is the radian (rad).

Q2: How many degrees are in one revolution?
1 revolution = 360 degrees.

Q3: What are arcminutes and arcseconds?
1 degree = 60 arcminutes; 1 arcminute = 60 arcseconds.

Q4: What is a mil?
A mil is 1/6400 of a revolution (used in military and artillery).

Q5: How many radians are in a circle?
A full circle contains 2π radians.

Q6: Is this tool accurate for scientific and engineering use?
Yes, it supports precise calculations using floating-point values and standard formulas.

Q7: Can I convert radians to mils?
Yes, use this tool or the formula: mils = radians × (3200/π).

Q8: What is a gradian?
A gradian is a metric unit where a right angle = 100 gradians (400 gradians = 360 degrees).

Q9: Is this tool compatible with mobile devices?
Yes, the converter is optimized for desktops, tablets, and smartphones.

Q10: Can I use this for academic or technical projects?
Absolutely. It’s ideal for students, researchers, engineers, and professionals.

📚 Read More Useful Conversion Tools: If you found this converter helpful, you might also be interested in exploring our other unit converters. Check out these tools for more accurate and instant conversions:

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Conclusion: In fields like mathematics, physics, engineering, and navigation, precise angle conversions are essential. Our Angle Converter simplifies the process by supporting a wide range of units—including degrees, radians, gradians, arcminutes, arcseconds, revolutions, circles, and mils. Whether you’re solving geometry problems or configuring mechanical systems, this tool ensures fast, accurate, and hassle-free conversions. Try it today and take the guesswork out of angle measurements!

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