A Fractional Part Of A Circle Calculator is a geometric tool that determines what portion of a whole circle is represented by a specific angle. Since a complete circle contains 360 degrees, this calculator takes any given angle (known as the central angle) and expresses it as a simple fraction or decimal of that total. This calculation is the foundational first step for many other important geometric formulas, such as finding the area of a pie-shaped wedge (a sector) or the length of a curved section of the circle’s edge (an arc). Consequently, it is an essential tool for students, designers, and engineers who need to work with parts of a circle.
formula of Fractional Part Of A Circle Calculator
The primary formula for finding the fractional part of a circle is a simple ratio.
Fractional Part of a Circle = Central Angle / 360
Where:
- Central Angle is the angle of the sector or arc, measured in degrees.
- 360 represents the total number of degrees in a full circle.
This fractional value is then used in other important calculations:
To calculate Sector Area:
Sector Area = (Central Angle / 360) × π × r²
Where:
- r = the radius of the circle.
To calculate Arc Length:
Arc Length = (Central Angle / 360) × 2 × π × r
Common Angles and Their Fractional Parts
This table provides a quick reference for the fractional and decimal equivalents of common angles in a circle, which can be useful for quick estimations.
| Central Angle (Degrees) | Fractional Part of Circle (Simplified) | Decimal Equivalent |
| 30° | 1/12 | 0.083… |
| 45° | 1/8 | 0.125 |
| 60° | 1/6 | 0.166… |
| 90° | 1/4 | 0.25 |
| 120° | 1/3 | 0.333… |
| 180° | 1/2 | 0.5 |
| 270° | 3/4 | 0.75 |
Example of Fractional Part Of A Circle Calculator
Let’s find the fractional part of a circle represented by a central angle of 150°.
Step 1: Identify the central angle.
Central Angle = 150°
Step 2: Use the formula to create the fraction.
Fractional Part = Central Angle / 360
Fractional Part = 150 / 360
Step 3: Simplify the fraction to its lowest terms.
Both 150 and 360 can be divided by their greatest common divisor, which is 30.
150 ÷ 30 = 5
360 ÷ 30 = 12
The simplified fraction is 5/12.
Therefore, a 150° angle represents 5/12 of a full circle.
Most Common FAQs
A full circle is defined as having 360 degrees. By dividing the central angle of your specific section by 360, you are creating a ratio that directly compares the “part” (your angle) to the “whole” (the full circle), which gives you the fractional value.
This calculation is the key first step for many practical problems. For example, if you know a pizza is cut into 8 equal slices, you can calculate that each slice has a central angle of 45° (since 360/8 = 45). From there, you could find the area of one slice or the length of its crust. It is fundamental for any problem involving sectors or arcs of a circle.
If your angle is in radians, the principle is the same, but you divide by the radian equivalent of a full circle, which is 2π. The formula would be: Fractional Part = Angle in Radians / (2π).