How to use this calculator
- Identify the measurements labelled Radius r, Central angle θ. Check whether the figure satisfies the assumptions described below.
- Enter positive measurements in a common unit. Use the degree symbol convention for angles. Ratios such as eccentricity have no unit.
- Select Calculate. Inspect the result labels: lengths, areas and volumes have different dimensions. Copy the output or print the page if you need a record.
The formula
Radius r = 5; Central angle θ = 90
Worked example
For Radius r = 5 cm, Central angle θ = 90°, applying the displayed relationship gives sector area ≈ 19.634954 cm². The remaining related measurements appear in the result panel. The example uses ideal dimensions and rounds only for display.
Model and limitations
Every diameter divides the disk into two congruent halves. A tangent at a point is perpendicular to the radius ending at that point. Radius, diameter and circumference describe lengths, while area measures the enclosed region.
Do not enter the diameter in a field asking for radius. A sector boundary includes two radii as well as its arc. Inputs are limited to 10⁹ for lengths, 10¹⁸ for areas and 10²⁷ for volumes. Extremely thin or nearly degenerate figures may lose numerical accuracy; avoid treating displayed rounding as a measurement tolerance.