Semicircle Area Calculator: Complete Guide to Half-Circle Properties (2026)
Calculate the area, perimeter, arc length, and diameter of a semicircle. Enter radius or diameter for instant results.
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Put these formulas into practice with our instant, step-by-step Semicircle Area Calculator.
A semicircle is exactly half of a circle, but its properties are not simply half of a full circle\'s properties. The area is halved, but the perimeter includes the straight diameter in addition to the curved arc. The semicircle area calculator computes all properties — area, perimeter, arc length, and diameter — from a single known dimension, with complete step-by-step derivations.
Key Takeaway
The semicircle area is exactly half the full circle area: A = πr²/2. However, the perimeter includes the diameter: P = πr + 2r, which is NOT half the full circumference.
Semicircle Formulas
How to Use the Calculator
- Enter the radius or diameter of the semicircle.
- Select which dimension you are entering.
- The calculator instantly shows area, arc length, and perimeter.
Real-World Applications
Semicircles appear in architecture (Roman arches), engineering (semicircular beams), and everyday objects (half-moon windows, arched doorways). The area determines the enclosed space, while the perimeter determines the material needed for the boundary.
Frequently Asked Questions
- What is the area formula for a semicircle?
- A = πr²/2, exactly half the area of a full circle with the same radius.
- Is the perimeter half the circumference?
- No. The perimeter is πr + 2r (arc + diameter), while half the circumference is just πr.
- What is the inscribed angle in a semicircle?
- Any angle inscribed in a semicircle is always 90° (Thales' theorem).
Conclusion
The semicircle is a fundamental geometric shape with unique properties. Use our free semicircle area calculator to compute all properties from a single dimension.