Use radius 2 and a 180° central angle
Input and settings
Radius: 2 / Central angle: 180 degrees
Expected result
Circle area ≈12.566370614359 / Circumference ≈12.566370614359 Sector area ≈6.28318530718 / Arc length ≈6.28318530718
Circle and Sector Calculator
Calculate circle area, circumference, sector area and arc length from radius and central angle. View approximate results using pi, then copy or save TXT and JSON.
How to use
- Enter the radius and a central angle from 0 to 360 degrees.
- Calculate and review circle/sector areas and lengths.
- Check the radius unit and squared area unit before using the result.
Calculation inputs
Radius must be nonnegative, angle from 0 to 360 degrees. At most 64 characters and 12 fractional digits each; radius up to 10^18. No exponents, commas, spaces or unit text. Write decimals as 0.5.
Results
Try a use case and check the result
Compare a semicircle and full circle of radius two to check areas, circumference and arc length.
Example buttons replace the inputs and settings above and calculate. Restore previous input steps back one example at a time. After trying multiple examples, repeat restore to return to your original input. This history is lost when the page closes.
At 360°, the sector covers the full circle
Input and settings
Radius: 2 / Central angle: 360 degrees
Expected result
Circle area = sector area ≈12.566370614359 Circumference = arc length ≈12.566370614359
How to read the result
Sector area and arc length equal the full-circle values multiplied by angle÷360; at 180° each is half. If radius is in cm, lengths are in cm and areas in cm². Matching numbers for this radius still have different units. Arc length is only the curved edge and excludes the sector’s two straight radii.
Scope and limits
Enter radius, not diameter. Radius is non-negative and angle is 0–360°. Each field allows 64 characters, twelve fractional digits and magnitude up to 10¹⁸; exponents, commas and outer spaces are rejected. Results are approximate: π is truncated at eighty decimal places and results rounded to twelve, with half ties away from zero. Chords, circular segments and solids are not calculated.
Verification: calculations check all four metrics for half/full circles, zero angle/radius and out-of-range rejection. Browser checks cover real Worker output, JSON downloads, invalidation on input edits and restoration.
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Details and limits
Circle area = pi × r²; circumference = 2 × pi × r; sector area = pi × r² × theta/360; arc length = 2 × pi × r × theta/360. r is radius and theta is the central angle in degrees.
For radius 3 and angle 90 degrees, circle area is approximately 28.274333882308, circumference 18.849555921539, sector area 7.068583470577 and arc length 4.712388980385.
At 0 degrees, sector area and arc length are zero. At 360 degrees they match the full circle. Radius zero is allowed and gives zero for all four results.
Length results use the radius unit; areas use its square. With radius in cm, circumference and arc length are in cm and areas in cm². No automatic unit conversion.
Inputs retain up to 12 fractional digits with integer-based arithmetic. Pi is a decimal constant truncated to 80 places. Results are rounded to 12 decimal places, halfway away from zero, with trailing zeros removed. Results involving pi are approximate.
TXT and JSON include radius, angle, four results and precision metadata. Numeric values remain strings. Saved UTF-8 files have no BOM or added trailing newline. Each report is limited to 4,000 bytes. Inputs and results are neither stored nor sent.
Editing inputs cancels work and clears old output. Cancel keeps inputs; reset clears inputs and results.
Frequently asked questions
Are angles degrees or radians?
Enter degrees from 0 to 360. Radian input is not supported.
Are zero radius and zero angle allowed?
Yes. Zero radius gives four zero results; zero angle gives zero sector area and arc length.
What units do results use?
Circumference and arc length use the radius unit; areas use its square. Results involving pi are approximate.
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