DIY Cost Tools
Circular Sector Calculator
MATH & GEOMETRY CALCULATOR
Find circular sector area, arc length, and boundary length.
Use the same length unit throughout. All fields are required. Enter an angle above zero and below 360 degrees. For a complete disk, use the circle calculator. A circular segment uses a different formula.
How to use this calculator
Enter your dimensions and select Calculate. Length results use your input unit, areas use its square, and volumes use its cube. Retain measurement precision until the final answer.
Formula and explanation
Area = θπr²/360; arc = θ2πr/360; boundary = arc + 2r
A sector is a wedge bounded by two radii and an arc.
Worked example
For Radius (units) = 6, Central angle (degrees) = 60, results are Sector area (square units): 18.849556; Arc length (units): 6.2831853; Boundary length (units): 18.283185.
Important limitations
Enter an angle above zero and below 360 degrees. For a complete disk, use the circle calculator. A circular segment uses a different formula.
Ideal geometry does not account for manufacturing tolerances or measurement uncertainty. This is a calculation aid, not a structural design or building-code approval. Absolute inputs must not exceed one trillion.
Frequently asked questions
Degrees or radians?
Enter the central angle in degrees.
What is boundary length?
The arc plus the two straight radii.
Can I mix inches and centimeters?
Convert all lengths to one unit first. Mixed units produce incorrect results.
Why did my result disappear?
Blank, invalid, or out-of-range inputs clear the previous result and display an instruction.
Review notes
Reviewed October 1, 2026. Default results were checked against the displayed formulas. Script tests covered blank, negative, nonfinite, and excessive inputs. Results run locally in your browser.