Enter Circle Values
Formula Used
Arc and radius: θ = s ÷ r.
Chord and radius: θ = 2 sin⁻¹(c ÷ 2r).
Sector and radius: θ = 2A ÷ r².
Arc fraction: θ = 2π(s ÷ C).
Area fraction: θ = 2π(As ÷ Ac).
Related values: s = rθ, c = 2r sin(θ ÷ 2), and A = r²θ ÷ 2.
How to Use the Calculator
Select the required calculation mode first. Enter values using consistent units. Press Calculate to view detailed results.
Choose minor, major, or directed angles. Adjust precision for your report. Export results when calculations are complete.
Coordinate mode uses a centre and endpoints. Both endpoints need equal radii. Direction controls the measured rotation.
Example Data
| Calculation | Inputs | Central angle | Related result |
|---|---|---|---|
| Arc and radius | s = 15 m, r = 10 m | 85.9437° | Chord ≈ 13.6328 m |
| Chord and radius | c = 10 m, r = 10 m | 60° | Sector ≈ 52.3599 m² |
| Sector and radius | A = 50 m², r = 10 m | 57.2958° | Arc = 10 m |
| Circle fraction | 25% or 1/4 | 90° | Quarter circle |
| Equal sectors | n = 8 | 45° | 12.5% of circle |
About Central Angles
A central angle has its vertex at a circle’s centre. Its sides are two radii. The intercepted arc matches its degree measure.
An inscribed angle has its vertex on the circumference. It intercepts the same arc differently. Its measure equals half the central angle.
Minor angles stay at or below 180 degrees. Reflex angles exceed 180 degrees. Together they complete one full circle rotation.
Frequently Asked Questions
What is a central angle?
A central angle starts at the circle centre. Its rays are radii. Its measure determines the intercepted arc length.
Can the calculator return reflex angles?
Yes, select the reflex angle option. The calculator uses the complementary major rotation. Results remain below one complete revolution.
Why must chord length stay below diameter?
A chord connects two circle points. The diameter is the longest possible chord. Longer values cannot exist on that circle.
Does the calculator support radians?
Yes, radians are supported for inputs. Results also show degrees and gradians. Revolutions and DMS values appear automatically.
How are coordinate angles calculated?
The tool builds two radius vectors. Dot and cross products define rotation. Direction selects clockwise or counterclockwise measurement.
What is circular segment area?
A circular segment lies between chord and arc. It excludes the centre triangle. The calculator derives it from radians.
Can I enter a diameter instead?
Diameter is available for angle-based output modes. The calculator divides it by two. Leave radius empty when using diameter.
What happens with mixed units?
Selected units apply to every related field. Internal conversions use metres and square metres. Results return using your chosen units.
Can results be downloaded?
Yes, use CSV or PDF buttons. Copying and printing are also available. Exports include the displayed calculation summary.