Free Online Angle Converter

Angles are geometric figures composed of two intersecting lines with a common point of intersection. As the angle vertex and lines are the sides, the common point is the vertex. Many interesting properties are associated with angles. In parallelograms, all angles add up to 360 degrees, whereas in triangles, they add up to 180 degrees.

Types of Angles


A right angle is one that equals 90°, an acute angle is one that is less than 90°, and an obtuse angle is one that exceeds 90°. The same angle is called a straight angle if it measures 180°, a 360° angle if it measures 360°, and Reflex Angles if they measure greater than 180° but less than 360°. The magnitudes of two angles are equal when one of them is congruent with the other.

In geometry, Complementary Angles are two angles that, when combined, make a 90° angle. The Supplementary Angle forms 180°, and the Supplementary or conjugate angle forms 360°.

Vertical or opposite angles are angles that are formed by intersecting two lines and are opposite from one another rather than supplementary. Both are congruent.

Measuring Angles

Measuring Angles

By measuring the circular arc formed by the sides of the angle, and extending one side from the vertex to the intersection point with the circle, an angle can be measured with a protractor, or its magnitude can be calculated with formula, by calculating the angle’s size using the formula. Degrees and radians are the most common units of measurement for angles, although other units are also available.

In addition to straight lines, angles can also be measured between curves. When measuring at the point of intersection, they are measured between the tangents of each of the curves.

How to Convert Units of Angles

A conversion factor is used to perform conversions. The conversion between units becomes a simple multiplication problem when you know the conversion factor:

S multiplied by C = E

Where S is our starting value, C represents our conversion factor, and E represents our final convert result.

In the following table, multiply by the right column the value in any unit to convert it to degrees, for example, from 5 radians.

5 Radians * 57.29578 [Degrees / Radian] = 286.4789 Degrees

Divide the degree value in the right column by its reciprocal or multiply by 1/x to get back to degrees.

286.4789 Degrees / 57.29578  [Degrees / Radian] = 5 Radians

You can multiply A by the factor for A to convert it into degrees, and then divide B by the factor for B to convert it back to degrees if you want to convert between any units in the left column.  It is possible to determine the one factor that you need by dividing the A factor by the B factor.

The radian to revolution conversion requires multiplying by 57.29578 and dividing by 360.  You can also multiply by 57.29578/360, which equals 0.1591549. Therefore, you multiply 0.1591549 by the radian value to convert directly to revolutions.

The following example demonstrates how to convert unit conversions as well. Say that you would like the radians converted to degrees. The ratio of 1 to anything can still be kept, but you get the value in different scales, so you can set it up this way so that radian cancels out, leaving you with the degree.


1 Degree = 0.01745329 Radians, 1 Degree / 0.01745329 Radians = 1

We can write the conversion as:

1 Radian = 1 Radian * (1 Degree / 0.01745329 Radians) = 57.29578 degrees

And we now have our factor for conversion from radians to degrees since 1 * 57.29578 = 57.29578.  Note that there are rounding errors in these values.

Having determined that one radian is equal to 57.29578 degrees, we can calculate the conversion factor for converting back to radians.  When we divide both sides in this equation by 57.29578, the result is 0.01745329 radians per degree.  By multiplying by 0.01745329 when converting degrees to radians, we obtain the conversion factor of 0.01745329.

Table of Angular Conversion

Units, Symbols, and Conversion values used in Angular Conversion to Degrees

[table id=7 /]

Units, Symbols, and Conversion values used in Angular Conversion to Radians

[table id=8 /]

What is an Angle? Angles acute, obtuse

A vertex is a starting point along which two rays flow, forming an angle. How can angles be useful? Knowing the distance between you and a tower, along with its angle from the ground, will let you estimate its height. 

You can use the same technique for measuring the moon’s size or our planet’s circumference with the right equipment. When you throw something, you need to know the angle at which you throw it if you want to know how far the ball will travel. 

In many other fields, angles also serve as a valuable tool, but let’s stick to common geometry for now. An angle can be divided into two parts based on its size:
[table id=6 /]

How do you Convert Degrees Minutes Seconds to Decimal Degrees?

Angles are sometimes counted in minutes or seconds as well as degrees. These are frequently used as coordinates, for instance. How else would you describe the conversion from DMS (Degrees Minutes Seconds) to decimal degrees, then? Think of degrees like hours, and you’ll see the answer is straightforward. For every hour, there are 60 minutes, and for every degree, there are 60 minutes. A minute consists of sixty seconds in both cases. 3600 seconds equal 1 degree:

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°.

Popular Angle Unit Conversions

  • Radians to Degrees
  • Degrees to Radians

Complete List of Angle Units for Conversion

  • Degree [°]
  • 1 Radian [Rad] = 57.2957795131 Degree [°]
    Radian to Degree,   Degree to Radian
  • 1 Grad [^g] = 0.9 Degree [°]
    Grad to Degree,   Degree to Grad
  • 1 Minute [‘] = 0.0166666667 Degree [°]
    Minute to Degree,   Degree to Minute
  • 1 Second [“] = 0.0002777778 Degree [°]
    Second to Degree,   Degree to Second
  • 1 Gon = 0.9 Degree [°]
    Gon to Degree,   Degree to Gon
  • 1 Sign = 30 Degree [°]
    Sign to Degree,   Degree to Sign
  • 1 Mil = 0.05625 Degree [°]
    Mil to Degree,   Degree to Mil
  • 1 Revolution [r] = 360 Degree [°]
    Revolution to Degree,   Degree to Revolution
  • 1 Circle = 360 Degree [°]
    Circle to Degree,   Degree to Circle
  • 1 Turn = 360 Degree [°]
    Turn to Degree,   Degree to Turn
  • 1 Quadrant = 90 Degree [°]
    Quadrant to Degree,   Degree to Quadrant
  • 1 Right Angle = 90 Degree [°]
    Right angle to Degree,   Degree to Right Angle
  • 1 Sextant = 60 Degree [°]
    Sextant to Degree,   Degree to Sextant


How do you Convert Angles into Degrees?

It always seems that people ask me what I mean by angles when I discuss them. Changing an angle is as simple as changing the angle between the two endpoints of your setup (i.e., what you are working on). One of the easiest ways to convert from one angle to another is to simply change the orientation of how your object is set up. For example, if you are working on a sphere, all you have to do is rotate it around an axis (like x or y) so you can see the effects of your work. You simply need to find the z-axis, place your object relative to it, and then rotate it until you see the effect.

How do you Convert Angle to Slope?

You need to understand basic hydraulic engineering concepts in order to make a canal. It might seem simple at first. In addition to your design, you need to make sure it will work in practice. It is impossible for water to drain if you build a beach on top of a concrete pad. If you build a beach on a slope, make sure that it is not built on a concrete pad. Most of the beach’s fun activities would not be possible because the beach would be ruined. Taking one concept and practicing it as often as possible until you are satisfied that you can build a water level beach is the best way to know how to convert slope to water level.

How do you Convert Angles to Millimeters?

The question you have is: “How can you Convert Angles to Millimeters?” In this article, you will discover the basic steps to follow as you Convert Angles to Millimeters. Throughout this article, you’ll learn the simple step-by-step process for converting any angle into millimeters. Don’t hesitate to try it out and see the difference it can make in your work.

How do you Convert Angle Measures to Degrees Minutes and Seconds?

Degree measurements can be very challenging to convert to angles. Most of the programs I have come across that teach this are useless because they do not understand how to convert degrees minutes and seconds to degrees. When converting degrees to degrees, a calculator is the easiest method. If you want to learn how to convert degrees to other measuring units, the calculator is the most reliable tool since it can give you an exact conversion based on an accurate measurement. In addition to setting up your calculator correctly, ensure that all measurements that you are converting are accurate.

How do you Measure an Angle without a Protractor?

If you don’t have a protractor, how do you measure angles? It is not possible, but the process can be simplified. To begin with, a protractor that measures angles on a horizontal (or vertical) surface is your best option for working from a straight line. A straight edge or measuring tape can be found in hardware stores or art supply shops. It’s very easy to make one if you’re not good at it, and I’ll show you how below.

What Angle is 60 Degree?

60 Degrees is what angle? Is that something on the camera that makes it seem like the shot was taken from the sky? In photography, there are things, and angles, that are harder to master than others, however, everyone can create stunning photographs by using general angles. Several things you need to know about 60 degrees if you’re wondering what that angle means.