The Partial Circle Area Calculator is a handy tool used to compute the area of a segment or partial circle. It simplifies the complex mathematical calculations involved in determining the area of a segment by taking input values such as the radius of the circle and the height of the segment, and then applying the appropriate formula to derive the result.
Formula of Partial Circle Area Calculator
The formula used by the Partial Circle Area Calculator is:
Formula: Area = 0.5 * π * r^2 * sin(θ)
Where:
- π (pi) is the mathematical constant approximately equal to 3.14159.
- r is the radius of the circle.
- θ (theta) can be calculated using the following formula: θ = 2 * arcsin(h / r)
- h is the height (sagitta) of the segment, which is the perpendicular distance from the base of the segment to the circle’s circumference.
Note: The area is calculated in square units (e.g., m²).
Table of General Terms
Here’s a table outlining the area of segments for various central angles (θ) assuming a radius of 1 unit:
| Central Angle (θ) | Area |
|---|---|
| 30° | 0.25 |
| 45° | 0.393 |
| 60° | 0.5 |
| 90° | 0.785 |
| 120° | 1.047 |
Example of Partial Circle Area Calculator
Suppose we have a partial circle with a radius (r) of 5 meters and a height (h) of 2 meters. To find the area of the segment, we can use the Partial Circle Area Calculator:
- Enter the radius (r) as 5 meters.
- Enter the height (h) as 2 meters.
- Click on the “Calculate” button.
- The calculator will display the area of the segment, which in this case, let’s assume is 7.85 m².
Most Common FAQs
The radius of a circle is the distance from the center of the circle to any point on its circumference.
The height (h) of a segment is measure as the perpendicular distance from the base of the segment to the circle’s circumference.
No, the Partial Circle Area Calculator is specifically design to calculate the area of partial circles or segments formed by a circle.
Yes, the calculation provide by the Partial Area Calculator is accurate for all valid input values of radius and height.
The area is present in square units, typically meters square (m²), representing the space enclose within the boundary of the segment.