Circle Calculator with Sector and Chord Results
Enter one known circle measurement and calculate radius, diameter, circumference and area. Add a central angle to calculate arc length, sector area, chord length and sagitta.
Known circle value
Complete circle measurements
circle calculator: formulas, interpretation and worked use
This circle calculator avoids separate forms for radius, diameter, circumference and area. A single mode selector determines how the radius is recovered before all other quantities are solved.
Transparent calculation steps
The circle calculator displays the intermediate values used in the result so users can audit the calculation rather than receiving an unexplained answer.
Input validation and edge cases
Impossible, incomplete and non-finite inputs are rejected with a specific message. Boundary cases are handled explicitly instead of being silently rounded into a misleading result.
Units and precision
Where units apply, inputs are converted to a consistent internal basis before the formula is evaluated. Results retain enough precision for checking and are then formatted for practical reading.
Worked interpretation
The result panel separates the primary answer, supporting quantities and a formula trace. This makes the calculator suitable for checking homework, planning scenarios and comparing alternatives.
Complete circle relationships
The circle calculator accepts a defining radius, diameter, circumference or area and derives the remaining whole-circle measurements from π. Sector and arc results use the entered central angle, while chord length follows 2r sin(θ/2). Segment area subtracts the isosceles triangle from its sector, making it different from sector area even when both use the same angle.
Angle and precision guidance
The circle calculator interprets central angles in degrees and normalizes them for the displayed sector. A 360-degree sector equals the full circle; a zero-degree sector has zero arc and area. Chord and segment formulas assume the minor central angle unless the interface indicates otherwise. Keep the radius unit consistent: length outputs use that unit and area outputs use its square. Display precision affects formatting, not the internal value of π or the unrounded quantities used to derive related results.
Can I start from area?
Yes. The radius is recovered with the square root of area divided by π.
What is sagitta?
Sagitta is the maximum distance from the midpoint of a chord to the corresponding arc.
Does the angle affect the full-circle results?
No. Radius, diameter, circumference and area depend only on the known circle measure; the angle controls sector and chord results.