Angle Unit Converter – Convert Degrees, Radians & Gradians Online

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Angle Unit Converter

Convert angle measurements quickly between degrees, radians, and gradians. Enter a value, choose the source and target units, and get the converted result instantly.

Degrees Radians Gradians Instant Results Mobile Friendly

Angle Unit Converter

Convert between common angular measurement units with one simple tool.

Value

From Degrees (°) Radians (rad) Gradians (gon)

Convert To Degrees (°) Radians (rad) Gradians (gon)

Please enter a valid numeric angle value.

Converted Result

0

What Is an Angle Unit Converter?

An angle unit converter changes an angular measurement from one unit into another equivalent unit. This is useful because different fields commonly use different ways to express angles.

Degrees are familiar in everyday geometry and navigation, radians are widely used in mathematics and calculus, and gradians can be found in surveying and some engineering applications. This converter lets you move between these units without performing the calculation manually.

How to Use the Angle Unit Converter

1. Enter the numerical angle in the Value field.
2. Select the unit of the number you entered in the From field.
3. Select the unit you want in the Convert To field.
4. Select Convert Angle to calculate the equivalent measurement.
5. Use Swap Units when you want to reverse the conversion direction.

Angle Conversion Formulas

All three units describe the same geometric quantity. The conversion process uses fixed relationships between degrees, radians, and gradians.

180° = π radians = 200 gradians

Degrees to Radians

radians = degrees × π ÷ 180

Radians to Degrees

degrees = radians × 180 ÷ π

Degrees to Gradians

gradians = degrees × 10 ÷ 9

Gradians to Degrees

degrees = gradians × 9 ÷ 10

Radians to Gradians

gradians = radians × 200 ÷ π

Gradians to Radians

radians = gradians × π ÷ 200

Common Angle Units

Degrees

A full circle contains 360 degrees. Degrees are commonly used in geometry, navigation, diagrams, and everyday descriptions of angles.

Radians

A full circle contains 2π radians. Radians are especially important in trigonometry, calculus, physics, and mathematical formulas.

Gradians

A full circle contains 400 gradians. Gradians are also called gon and are particularly associated with surveying and some technical work.

Angle Conversion Reference Table

Degrees	Radians	Gradians
0°	0 rad	0 gon
30°	π/6 rad	33.3333 gon
45°	π/4 rad	50 gon
90°	π/2 rad	100 gon
180°	π rad	200 gon
270°	3π/2 rad	300 gon
360°	2π rad	400 gon

Angle Conversion Examples

Example 1: Degrees to Radians
To convert 90 degrees to radians: 90 × π ÷ 180 = π/2 radians, which is approximately 1.570796 radians.

Example 2: Radians to Degrees
To convert π radians to degrees: π × 180 ÷ π = 180 degrees.

Example 3: Degrees to Gradians
To convert 90 degrees to gradians: 90 × 10 ÷ 9 = 100 gradians.

Example 4: Gradians to Degrees
To convert 200 gradians to degrees: 200 × 9 ÷ 10 = 180 degrees.

When Is Angle Conversion Useful?

Mathematics

Convert angles into the unit required for geometry, trigonometry, algebra, or calculus calculations.

Engineering

Switch between angular units when working with technical formulas, measurements, diagrams, and engineering calculations.

Science & Physics

Convert angular values when formulas or scientific calculations require a particular unit.

Surveying

Convert between degrees and gradians when working with angular measurements used in surveying.

Education

Check homework and practice problems involving different angle measurement systems.

Programming

Convert angular values when working with mathematical functions, graphics, simulations, or applications that use different units.

Common Mistakes When Converting Angles

• Confusing degrees and radians: Always check which unit a formula or application expects before entering an angle.
• Using the wrong conversion direction: The formula for degrees to radians is the reverse of radians to degrees.
• Forgetting the π relationship: Remember that 180 degrees equals π radians.
• Mixing gradians with degrees: A full circle contains 400 gradians but only 360 degrees.
• Rounding too early: Keep additional decimal places during intermediate calculations when precision matters.

Degrees, Radians, and Gradians: What Is the Difference?

Degrees divide a complete circle into 360 equal parts. Radians measure an angle in relation to the radius of a circle, with one complete circle equal to 2π radians. Gradians divide a complete circle into 400 equal parts.

None of these units changes the physical angle itself. They simply use different scales to represent the same angular measurement. For example, 90 degrees, π/2 radians, and 100 gradians all describe a right angle.

Related Angle Converters

Degrees to Gradians Convert degree measurements into gradians. Degrees to Radians Convert degrees into radians quickly. Radians to Degrees Convert radian measurements into degrees.

Frequently Asked Questions

How do I convert degrees to radians?

Multiply the degree value by π and divide by 180. For example, 180 degrees equals π radians.

How do I convert radians to degrees?

Multiply the radian value by 180 and divide by π. For example, π radians equals 180 degrees.

How many degrees are in a full circle?

A complete circle contains 360 degrees.

How many radians are in a full circle?

A complete circle contains 2π radians, approximately 6.283185 radians.

How many gradians are in a full circle?

A complete circle contains 400 gradians, also known as gon.

Is 90 degrees equal to π/2 radians?

Yes. 90 degrees is exactly equal to π/2 radians and 100 gradians.

What is the difference between degrees and gradians?

Degrees divide a full circle into 360 parts, while gradians divide it into 400 parts.

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