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Minor Circular Segment Area — result sheet
Calculate the area between a circle chord and its minor arc from radius and included central angle.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: A = (r^2/2)(theta - sin(theta)), where theta is the minor central angle in radians.
The minor segment is the circular sector minus the isosceles triangle formed by its two radii and chord. The angle is entered in degrees and converted to radians before the formula is evaluated.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Circle radius — length units; Positive radius of the circle containing the chord and arc.; minimum 1.0E-6; maximum 1000000
- Minor central angle — degrees; Included minor central angle from 0 through 180 degrees.; minimum 0; maximum 180
Worked example
| Input | Value |
|---|---|
| Circle radius | 5 |
| Minor central angle | 60 |
theta = pi/3 radians, so A = 1/2 x 25 x (pi/3 - sin(pi/3)) = about 2.26465 square length units.
Assumptions and limits
- The result is the minor circular segment bounded by one chord and its minor arc, with central angle from 0 through 180 degrees.
- The radius is positive and the radius and area use compatible length units.
- The circle is ideal; thickness, measurement uncertainty, major segments, and noncircular boundaries are outside the calculation.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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