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Angle converter.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. In physics, angle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc by its radius. In the case of an angle (figure), the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any point and its image by the rotation.

A degree , also a degree of arc, arc degree, usually denoted by the degree symbol °, is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians.

Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. Thus, one revolution is equal to 2π radians.

Using the Angle Converter Converter

This online unit converter allows quick and accurate conversion between many units of measure, from one system to another. The Unit Conversion page provides a solution for engineers, translators, and for anyone whose activities require working with quantities measured in different units.

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You can use this online converter to convert between several hundred units (including metric, British and American) in 76 categories, or several thousand pairs including acceleration, area, electrical, energy, force, length, light, mass, mass flow, density, specific volume, power, pressure, stress, temperature, time, torque, velocity, viscosity, volume and capacity, volume flow, and more. Note: Integers (numbers without a decimal period or exponent notation) are considered accurate up to 15 digits and the maximum number of digits after the decimal point is 10.

In this calculator, E notation is used to represent numbers that are too small or too large. E notation is an alternative format of the scientific notation a · 10 x . For example: 1,103,000 = 1.103 · 10 6 = 1.103E+6. Here E (from exponent) represents “· 10^”, that is “ times ten raised to the power of ”. E-notation is commonly used in calculators and by scientists, mathematicians and engineers.

• Select the unit to convert from in the left box containing the list of units.
• Select the unit to convert to in the right box containing the list of units.
• Enter the value (for example, “15”) into the left From box.
• The result will appear in the Result box and in the To box.
• Alternatively, you can enter the value into the right To box and read the result of conversion in the From and Result boxes.

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Degree Conversion Calculator

Enter a value in degrees below to convert to another unit of angle.

Do you want to convert degrees to radians ?

What Is a Degree?

Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. He holds several degrees and certifications.

A degree is a unit used to measure angle .

The degree is an SI accepted unit for angle for use with the metric system. A degree is sometimes also referred to as a degree of arc, arc degree, or arcdegree. Degrees can be abbreviated as ° , and are also sometimes abbreviated as deg . For example, 1 degree can be written as 1° or 1 deg.

Degrees can also be expressed using arcminutes and arcseconds as an alternative to using the decimal form. Arcminutes and arcseconds are expressed using the prime (′) and double-prime (″) characters, respectively, although a single-quote and double-quote are often used for convenience.

One arcminute is equal to 1/60th of a degree, and one arcsecond is equal to 1/60th of an arcminute.

Protractors are commonly used to measure angles in degrees. They are semi-circle or full-circle devices with degree markings allowing a user to measure an angle in degrees. Learn more about how to use a protractor or download a printable protractor .

Background and Origin

Although the true origin of the degree is not certain, it likely originated in Babylonian astronomy. Babylonian, and later Greek, astronomers observed that stars advance about 1/360th of their circular path in the sky every night. They also divided the ecliptic, or circle representing the path of the sun, into 360 parts.

Another common theory is that degrees originated out of the Persian calendar, which is made up of 360 days in the year. 360 is also very close to the 365 actual days in a year and 354 average number of days in the luni-solar year.

Regardless of the origin, the number 360 is an easy number to use mathematically, which makes it appealing to use. The appeal comes from the fact that the number 360 has 24 divisors.

Degrees are a very widely used unit of angular measure, and are used in managed fields. Though the degree is not an SI unit, it is accepted for use as a measure of angle.

How Much Is a Degree?

A degree is a measure of angle equal to 1/360th of a revolution , or circle. [1] The number 360 has 24 divisors, making it a fairly easy number to work with. There are also 360 days in the Persian calendar year, and many theorize that early astronomers used 1 degree per day.

How to Convert Degrees

To convert degrees to another unit of angle, you need to multiply the value by a conversion factor. A conversion factor is a numerical value used to change the units of a measurement without changing the value. [2]

You can find the conversion factors for degrees in the conversion table below .

Then, multiply the angle measurement by the conversion factor to find the equivalent value in the desired unit of measurement.

degrees × conversion factor = result

You can also use a calculator, such as one of the converters below , for the conversion.

Degree Conversion Table

Degree conversion calculators.

You can also convert angle using one of our degree converters below.

• degrees to radians converter
• degrees to milliradians converter
• degrees to minutes of arc converter
• degrees to seconds of arc converter
• degrees to gradians converter
• degrees to revolutions converter
• degrees to circles converter
• degrees to mils (NATO) converter
• degrees, minutes, and seconds to degrees decimal
• degrees decimal to degrees, minutes, and seconds
• Collins Dictionary, Definition of 'degree', https://www.collinsdictionary.com/us/dictionary/english/degree
• National Institute of Standards & Technology, Unit Conversion, https://www.nist.gov/pml/owm/metric-si/unit-conversion

Other Angle Units

• radian conversions
• milliradian conversions
• minute of arc conversions
• second of arc conversions
• gradian conversions
• revolution conversions
• circle conversions
• mil conversions

Degree Minutes Seconds Calculator

Degree Minutes Seconds Calculator is an online tool which converts decimal degrees to degrees (°), minutes ('), seconds (").

What is a Degree Minutes Seconds Calculator?

A Degree Minutes Seconds Calculator is an online tool which converts decimal degrees to degrees (°), minutes ('), seconds ("). You just need to enter the angle in degrees to get your answer in just a click.

How to Use the Degree Minutes Seconds Calculator?

The decimal degrees can be used by following a few simple steps:

• Step 1: Enter the angle in decimal degrees in the input box. 
• Step 2: Click on " Convert" to get the answer in Degrees, minutes, seconds.
• Step 3: Click on "Reset" to enter the new values.

How to Convert Decimal Degrees to Degree Minutes Seconds?

The conversion of degrees into degree-minute-seconds can be done with the help of the conversion factor of 60.This is because:

• 1 degree = 60 minutes (60')
• 1 minute = 60 seconds (60'')

The decimal part of a degree is first multiplied by 60 to get the measure in minutes. Then, the decimal part of the minutes is multiplied by 60 to get the measure in seconds.

Let us convert 12.72° into degrees-minutes-seconds.

For this, we first need to take the decimal part for the solution.

0.72° = 0.72 x 60'

= 43.2'

= 43' + (0.2 x 60")

=43'12"

Hence, the converted measure of the angle is 12°43'12"

Let us understand more on this, with the following example.

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Solved Example:

Convert 15.43° into degree-minutes-seonds.

15.43° = 15° + (0.43 x 60')

= 15° + 25.8'

=15° + 25' + (0.8 x 60")

= 15° + 25' + 48''

= 15° 25' 48''

Therefore, the angle in degree-minutes-seconds is 15° 25' 48''.

Now, try the calculator to convert to degree-minute-seconds, for the following values.

• 105.23°

Angle Conversion Calculator

What is an angle - acute, obtuse angles, what is a radian and how to convert degrees to radians, how to convert degrees minutes seconds to decimal degrees, other units.

With this angle converter, you can quickly check the size of an angle in ten different units:

• degrees, minutes of arc, and seconds of arc;
• degrees (deg);
• radians (rad);
• gradians (gon);
• turns (tr);
• π radians (*π rad);
• minutes of arc (arcmin);
• seconds of arc (arcsec);
• milliradians (mrad); and
• microradians (μrad).

Would you like to learn how to convert degrees to radians, and learn the radians to degrees formula? Then keep reading! We will also explain what an acute and obtuse angle is, and answer the question of the hour: what is an angle?

An angle is a figure formed by two rays that share a starting point, called a vertex . You may ask: why are angles useful? You can estimate the height of a tower if you know its distance from you, and the angle between the ground and the tower's top. Using the same technique, you can measure how big the moon is, or, with the right equipment, the circumference of our own planet. Also, if you throw something, and you want to know how far it will travel, you'll need to know the angle you throw it at. There are many other fields where angles are useful, but, for now, let's focus on basic geometry. We can divide angles by their size:

But there are other ways to group angles. Some of them are:

• Complementary angles — two angles that add up to a right angle (90°);
• Supplementary angles — combined angle pair equals 180° (straight angle);
• Reference angle — an acute angle that represents any other angle. Don't hesitate to learn more in the reference angle calculator ; and
• Central angle — an angle with a vertex at the center of a circle, whose arms extend to the cirlce's circumference.

The radian is the most universal unit for measuring angles. 1 radian is equal to about 57.2958 degrees , which is the angle that creates an arc equal to the length of the radius, R:

A full turn is equal to 2π radians, which is why the circumference is equal to 2πR . To make things easier for you, we created a table with the most common angles:

As you see, 180 degrees is equal to π radians, so the degrees to radians formula is:

radians = π/180° × degrees

That means the radians to degrees formula is predictable:

degrees = 180°/π × radians

Let's look at an example: What is a 300° angle in radians?

radians = π/180° × 300° = ⁵⁄₃π rad

And now you know how to convert degrees to radians!

Minutes of arc and seconds of arc are sometimes used alongside degrees. For example, they're often used to specify coordinates. How to convert DMS (degrees minutes seconds) to decimal degrees, then? The answer is straightforward, think about degrees like hours. One hour equals sixty minutes, and one degree equals sixty minutes. In both cases, each minute contains sixty seconds. So one degree equals 3600 seconds:

1 degree = 60 minutes of arc = 3600 seconds of arc

When you realize that, figuring out the formula is easy:

Decimal degrees = degrees + minutes/60 + seconds/3600

Let's say you want to figure out what 48°37'45" is in decimal degrees:

48°37'52" = 48 + 37/60 + 52/3600 = 48.6311°

So 48°37'45" is the same as 48.6311°.

To describe the size of an angle, you usually use degrees or radians. However, there are other units that you might come across. One of them is a turn . One turn equals 360 degrees, or 2π radians. To convert between these units, use one of the formulas below:

• Degrees to turns formula: turn = degrees / 360° ; and
• Radians to turns equation: turn = radians / 2π .

A less common unit is called a gradian , or a gon . In this case, one gradian is defined as one-hundredth of the right angle. The degrees to gradians formula is:

• gradians = ¹⁰⁄₉ × degrees

To convert radians to gradians, use this equation:

• gradians = 200/π × radians

And to switch turns into gradians:

• gradians = 400 × turns

Now you know how to convert between different angular units. To learn more about geometry, check out the triangle area calculator , or any of our other geometry calculators!

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• radians\:to\:degrees\:\pi
• radians\:to\:degrees\:2
• radians\:to\:degrees\:\frac{\pi}{3}
• radians\:to\:degrees\:2\pi
• How to convert radians to degrees?
• To convert radians to degrees, multiply the radian value by 180/π.
• What is a radian?
• A radian is a unit of measurement for angles. It measures the size of an angle as the ratio of the length of the arc cut out by the angle on a circle, to the radius of the circle. One radian is approximately equal to 57.3 degrees.
• Why do we convert Radians to degrees?
• We convert radians to degrees for the sake of convenience and compatibility with commonly used angular measurements and coordinate systems.
• What is the degrees of π radians?
• π radians is equal to 180 degrees.

radians-to-degrees-calculator

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