angle Converter

Degree (°)

• Degree (°)
• Radian (rad)
• Gradian (gon)
• Minute (′)
• Second (″)
• Turn
• Milliradian (mrad)
• Revolution (r)
• Circle
• Quadrant
• Right angle
• Binary Degree (brad)

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Radian (rad)

• Degree (°)
• Radian (rad)
• Gradian (gon)
• Minute (′)
• Second (″)
• Turn
• Milliradian (mrad)
• Revolution (r)
• Circle
• Quadrant
• Right angle
• Binary Degree (brad)

Decimal places

0 1 2 3 4 5

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Conversion History

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About Angle Conversion, Units, and Formulas

Angle conversions are crucial for tasks like solving trigonometric problems, designing structures, or navigating routes. The most common angle units include degrees, radians, gradians, and revolutions. Degrees are widely used in everyday applications, radians are standard in mathematics and physics, gradians are used in some engineering contexts, and revolutions are helpful in rotational mechanics. To convert between these units, use the formulas provided in the sections below.

Instantly convert between all major angle units like degrees (°), radians (rad), gradians (gon), revolutions (rev), and more. Try conversions such as degrees to radians, radians to degrees, gradians to degrees, and revolutions to degrees below!

Degrees and Radians Conversion

Degrees and radians are the most frequently used angle units. Degrees are intuitive for general use, while radians are preferred in calculus and physics due to their mathematical properties.

Conversion Formulas

• Degrees to Radians: radians = degrees × (π / 180)
• Radians to Degrees: degrees = radians × (180 / π)

Example Calculation

• Convert 10 degrees to radians: 10 × (π / 180) ≈ 0.1745 rad
• Convert 5 radians to degrees: 5 × (180 / π) ≈ 286.4789°

Use our online converter for instant degrees to radians or radians to degrees conversions!

Degrees and Gradians Conversion

Gradians, also known as gons, are used in some engineering and surveying applications, where 400 gradians equal a full circle (360 degrees).

Conversion Formulas

• Degrees to Gradians: gradians = degrees × (10 / 9)
• Gradians to Degrees: degrees = gradians × (9 / 10)

Example Calculation

• Convert 20 degrees to gradians: 20 × (10 / 9) ≈ 22.2222 gon
• Convert 10 gradians to degrees: 10 × (9 / 10) = 9°

Try our degrees to gradians and gradians to degrees converter now!

Radians and Gradians Conversion

Converting between radians and gradians is less common but useful in specific technical fields like surveying.

Conversion Formulas

• Radians to Gradians: gradians = radians × (200 / π)
• Gradians to Radians: radians = gradians × (π / 200)

Example Calculation

• Convert 5 radians to gradians: 5 × (200 / π) ≈ 318.3099 gon
• Convert 10 gradians to radians: 10 × (π / 200) ≈ 0.1571 rad

Use our radians to gradians and gradians to radians converter today!

About Angle Units and Systems

Degrees are the most familiar unit, forming the basis of the sexagesimal system (360° in a circle). Radians, based on the circle’s radius, are fundamental in mathematics (2π radians in a circle). Gradians, part of the metric system, define 400 gons in a circle, often used in European engineering. Revolutions simplify rotational measurements, with 1 rev equaling a full 360° turn. Our online converter supports all these units for seamless conversions.

Why Use an Online Angle Converter?

An online angle converter saves time, eliminates calculation errors, and provides instant, exact results. It’s perfect for students, engineers, mathematicians, or navigators needing quick conversions between degrees, radians, gradians, and revolutions. Try conversions like degrees to radians, radians to degrees, gradians to degrees, and more below!

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