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Angle Converter

Convert between degrees, radians, and other units of angle.

Angle Converter

Convert between degrees, radians, and other units of angle.

Understanding the Converter

An angle is the figure formed by two rays sharing a common endpoint. This tool helps convert between different units used to measure angles, essential in geometry, trigonometry, navigation, and engineering.

All conversions use radians as a base reference to ensure mathematical accuracy.

Formula Used

Standardized Conversion Process

To ensure accuracy, all conversions use the radian (rad) as a common base unit.

  1. Convert to Radians: The input value is converted to radians by multiplying it by its conversion factor.
  2. Convert to Target Unit: The radian value is then converted to the desired final unit by dividing it by the target unit's conversion factor.

Related Converters

A Guide to Units of Angle

Angles are a fundamental concept in mathematics and the physical world, describing the amount of rotation between two lines.

Common Angle Units

UnitDefinition & Context
Degree (°)A full circle is divided into 360 degrees. This is the most common unit in everyday life and introductory geometry.
Radian (rad)The standard unit of angular measure in mathematics. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius. A full circle is 2π radians.
Gradian (grad)A unit where a right angle is divided into 100 gradians, making a full circle 400 gradians. Used in some surveying and civil engineering contexts.
Arcminute (′)1/60th of a degree. Used in astronomy and navigation for very small angles.
Arcsecond (″)1/60th of an arcminute or 1/3600th of a degree. Used for extremely precise astronomical measurements.

Common Conversions at a Glance

FromToEquivalent Value
360 DegreesRadians2π rad (~6.283 rad)
180 DegreesRadiansπ rad (~3.14159 rad)
1 RadianDegrees~57.3°
1 DegreeArcminutes60′
1 DegreeArcseconds3600″
Right AngleDegrees90°
Right AngleRadiansπ/2 rad

Frequently Asked Questions

Why use radians instead of degrees?

Radians are the natural unit for measuring angles in mathematics. They simplify many formulas in calculus and physics, such as those for derivatives of trigonometric functions and arc length. The 360 degrees in a circle is an arbitrary number inherited from ancient Babylonians.

What is a gradian?

The gradian is a unit of angle where a right angle is 100 grads and a full circle is 400 grads. It was introduced as part of the metric system's decimal-based approach but has not been widely adopted, though it is still used in some fields like surveying.

How small is an arcsecond?

An arcsecond is extremely small. It's 1/3600th of a degree. It's equivalent to the angle subtended by a US dime from a distance of about 2.5 miles (4 km).

What does 'subtend' mean?

In geometry, an angle subtends an arc or line segment if the angle's two rays pass through the endpoints of the arc or segment. It's the angle 'created' by looking at an object from a certain point.

Summary

The Angle Converter is a fundamental tool for students, mathematicians, engineers, and astronomers. It provides quick and accurate conversions between the various units used to measure angles.

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Angle Converter

Convert between degrees, radians, and other units of angle.

How to use Angle Converter

Step-by-step guide to using the Angle Converter:

  1. Enter your values. Input the required values in the calculator form
  2. Calculate. The calculator will automatically compute and display your results
  3. Review results. Review the calculated results and any additional information provided

Frequently asked questions

How do I use the Angle Converter?

Simply enter your values in the input fields and the calculator will automatically compute the results. The Angle Converter is designed to be user-friendly and provide instant calculations.

Is the Angle Converter free to use?

Yes, the Angle Converter is completely free to use. No registration or payment is required.

Can I use this calculator on mobile devices?

Yes, the Angle Converter is fully responsive and works perfectly on mobile phones, tablets, and desktop computers.

Are the results from Angle Converter accurate?

Yes, our calculators use standard formulas and are regularly tested for accuracy. However, results should be used for informational purposes and not as a substitute for professional advice.