One sector with radii, arc, chord, sagitta, and dimension linesLive current inputs
Math & Statistics
Circle Solver Calculator
Solve a complete circle-and-sector geometry from radius and central angle, including diameter, circumference, arc length, chord, sagitta, sector area, and circular-segment area.
Diameter-
Full circumference-
Full circle area-
Selected arc length-
Chord length-
Sagitta-
Sector area-
Minor segment area-
CIRCLE GEOMETRY BLUEPRINT
One sector with radii, arc, chord, sagitta, and dimension lines
The live drawing preserves the entered angle, labels every derived length, and shades the circular segment separately from the sector.
QUANTITY LEDGER
Circle, sector, and segment quantities without conflating them
The ledger identifies which measure uses the full circle and which uses only the entered central angle.
| Quantity | Formula | Substitution basis | Value | Unit dimension |
|---|
GEOMETRY ENTRY
Identify whether the drawing calls for an arc, sector, or segment
- Enter the actual radius, not diameter.
- Enter the central angle in degrees.
- Use arc length for curved boundary distance.
- Use sector area for the wedge from the center.
- Use segment area for the cap between chord and arc.
THREE DIFFERENT REGIONS
A sector includes the center; a segment does not
The chord joins the two arc endpoints. The sector is bounded by two radii and the arc, while the circular segment is bounded by the chord and the arc.
Sagitta measures the maximum perpendicular gap from the chord to the arc. It is useful in arches, tanks, lenses, and fabrication layouts.
CENTRAL-ANGLE SOLUTION
Convert the angle to radians before using arc and segment formulas
Full-circle measures depend only on radius. Arc, chord, sagitta, sector, and segment depend on the selected central angle; segment area subtracts the isosceles triangle from the sector.
Detailed calculation process and general formulas
θᵣ = θπ/180C = 2πrL = rθᵣq = 2r sin(θᵣ/2)Kseg = r²(θᵣ-sin θᵣ)/2Symbols, meanings, and units
- r
- circle radiuslength
- θ
- entered central angledegrees
- θᵣ
- central angle in radiansradians
- L
- selected arc lengthlength
- q
- chord lengthlength
- Kseg
- minor circular-segment arealength²
DRAWING INTERPRETATION
Match each result to a physical decision
The annotated blueprint turns similar-sounding quantities into distinct geometry.
Curved edge
-Arc length is the material or travel distance along the circumference.
Straight span
-Chord length is the direct endpoint-to-endpoint distance.
Cap depth
-Sagitta is the rise from chord midpoint to the arc.
Decision takeaway: Choose the boundary and region first; using sector area when the problem asks for a segment is a common major error.
Applied decisions
Where one circle creates several valid answers
Curved window head
A fabricator knows the radius and included angle of an arch.
What the result clarifies: Chord and sagitta define the opening while arc length estimates curved trim.
Rotating sprinkler sector
A sprinkler covers only part of a full circle.
What the result clarifies: Sector area estimates nominal coverage and arc length describes the outer sweep.
Worked default scenario
Current-input substitution and reconciliation
Method references
References for this calculator's specific method
Scope and limitations
The segment formula shown is for the minor segment associated with an angle below 360 degrees. Real material takeoffs may require thickness, kerf, overlap, and manufacturing tolerances that are not included.
Circle Solver Calculator | Radius, Sector, Chord, Arc, and Segment FAQ
Is arc length the same as chord length?
No. Arc length follows the curve; chord length is the straight line between endpoints.
Why convert degrees to radians?
The formulas L=rθ and Ksector=r²θ/2 require θ in radians.
What is sagitta used for?
It gives the height of a circular arc above its chord.
Does the full circle area depend on angle?
No. Only the sector and segment measures depend on the selected angle.