What an angle converter solves and why units differ
This tool lets you quickly find out the size of an angle in ten different units which are following, Degrees (°), Radians (rad), Gradians (gon), Minutes ('), Seconds ("), Turns (revolution), Milliradians (mrad), Octant, Sextant, Quadrant, Gon, Mil
If you want to learn how to change degrees to radians and radians to degrees, read on. Then read on! We will also talk about sharp and obtuse angles and answer the question of the hour: what is an angle?
What Is Angle & What Does It Mean?
An angle is defined as the measure of the amount of rotation required to align one line or plane with another, either by bringing them into coincidence or establishing parallelism.In other terms, an angle represents the degree to which one line or plane is rotated relative to another.
Angles play a crucial role in various fields such as geometry, trigonometry, geography, mapping, and construction. Therefore, acquiring a solid understanding of angle manipulation is essential. A protractor is a widely used instrument designed to measure the angle formed between two lines.
Two prevalent units for measuring angles are degrees and radians. A complete circle encompasses 360 degrees, indicating that a line is positioned at 360 degrees relative to itself, equivalent to 2π radians.
Angle Unit Conversion
Conversion factors execute conversions. With the conversion factor, unit conversion is straightforward multiplication:
Conversion formula: 1 radian = 1 degree / 0.01745329 radians = 57.29578 degrees.
For radians to revolutions, multiply by 57.29578 and divide by 360. Multiply by 57.29578/360 = 0.1591549. To convert radians to revolutions, multiply by 0.1591549.
This example shows how to convert units. Convert radians to degrees. Since you can multiply anything by 1 and keep the original value in other units, cancel out radian to get degree.
Types of angles and their measurements
Angles fall into six categories based on size. Each category has specific ranges measured in degrees, radians, turns, and gradians.
Acute angles measure less than 90 degrees. Right angles measure exactly 90 degrees. Obtuse angles measure between 90 and 180 degrees. Straight angles measure exactly 180 degrees. Reflex angles measure between 180 and 360 degrees. Full angles measure exactly 360 degrees.
Angle conversion reference table
To discover the conversion factors, use this table. To obtain degrees, multiply your initial value by the factor in the right column. Simply divide or multiply the component by its reciprocal to get the inverse of the conversion.
| From Unit | Multiply By | To Get Degrees |
|---|---|---|
| Degrees (°) | 1 | 1 degree |
| Radians (rad) | 57.29578 | 1 radian = 57.29578 degrees |
| Gradians (gon) | 0.9 | 1 gradian = 0.9 degrees |
| Minutes (') | 0.0166667 | 1 minute = 0.0166667 degrees |
| Seconds (") | 0.000277778 | 1 second = 0.000277778 degrees |
| Turns (revolution) | 360 | 1 turn = 360 degrees |
| Milliradians (mrad) | 0.0572958 | 1 milliradian = 0.0572958 degrees |
| Octant | 45 | 1 octant = 45 degrees |
| Sextant | 60 | 1 sextant = 60 degrees |
| Quadrant | 90 | 1 quadrant = 90 degrees |
| Gon | 0.9 | 1 gon = 0.9 degrees |
| Mil | 0.05625 | 1 mil = 0.05625 degrees |
The mathematical correlations between the units of angle provide the basis for these elements. A complete turn, 360 degrees, 2π radians, or 400 gradians is equivalent to one full circle. The factors maintain these connections.
Rounding impacts accuracy. When it comes to precision, the table presents factors with six decimal places. Utilize the utmost accuracy when doing technical tasks. Rounded numbers are useful for making fast estimations.
There are two stages to converting between units that do not have a degree. Start by converting to degrees using the table. Then, divide the result by your desired unit. To convert 2 radians to gradians, for instance, one might multiply 2 by 57.29578 to obtain 114.59156 degrees, and then divide by 0.9 to obtain 127.32396 gradians.
A number of units have common conversion factors. Since gon and gradians both stand for the same unit of measurement, they share the same factor. A gon is equal to one gradian. Rather of dividing a circle into 360 equal segments, both methods use 400.
The function of millimeters differs in military and surveying contexts. North American Mils break a circle into 6,400 pieces. There are 6,300 components in a Swedish mil. Every circle in this table is 6400 mils in diameter, according to NATO standards. Find out what the mil definition is that your application needs.
