How to calculate the area of a sector using radius and angle in degrees?

Sector area = π × radius² × (angle in degrees / 360°)

How to calculate the area of a sector using radius and angle in radians?

Sector area = (radius² / 2) × angle in radians

What is the relationship between sector area and circle area?

Sector area = circle area × angular ratio = π × radius² × (angle / 360°)

How to convert between degrees and radians?

Degrees to radians: multiply by π/180. Radians to degrees: multiply by 180/π

Sector Area Calculation

Quickly calculate the area of a sector online. Enter radius and angle (degrees or radians), and get the area instantly with unit conversion.

Input

Radius R

Angle θ

Area

Sector Area Formulas

Area = π × radius² × (angle in degrees / 360°)
Area = (radius² / 2) × angle in radians
Area = circle area × angular ratio

FAQ

What is a sector and where is it commonly used?
A sector is a "slice" of a circle bounded by two radii and an arc. It's commonly used in engineering for calculating areas of fan blades, gear teeth, pie charts, radar coverage areas, and sprinkler irrigation patterns. The sector represents a portion of the total circular area.
How do I measure the angle of a sector accurately?
Use a protractor for physical measurements, or calculate from arc length (angle in radians = arc length / radius). For engineering drawings, angles are typically specified. Digital angle finders and CAD software can provide precise angle measurements for complex geometries.
When should I use degrees vs radians for angle input?
Use degrees for practical applications and engineering drawings (more intuitive). Use radians for mathematical calculations and when working with trigonometric functions. The calculator handles both units automatically, so choose what matches your available measurements.
What are typical sector applications in engineering?
Common applications include: fan blade areas for airflow calculations, gear tooth profiles, valve disc segments, antenna radiation patterns, cutting tool geometries, and land surveying for pie-shaped plots. Each application may have specific angle ranges and precision requirements.
How do I calculate material requirements for sector-shaped parts?
Calculate the sector area, then multiply by material thickness and density for weight. Add material waste factors (typically 5-15%) for manufacturing. Consider grain direction for materials like wood or composites, as sector cuts may not align with optimal grain orientation.
Can I use this calculator for multiple sectors or complex shapes?
This calculator handles single sectors. For multiple sectors, calculate each separately and sum the results. For complex shapes with both sectors and other geometries, break the shape into individual components and calculate each area separately before combining.

Sector Area Equations (LaTeX)

\[Sector\, area = circle\, area \times angular\, ratio\]

\[= \pi \times radius^2 \times {\theta(°) \over 360}\]

\[= \pi \, R^2 \times {\theta(°) \over 360}\]

\[Sector\, area = {radius^2 \over 2} \times \theta_{rad}\]

\[= {R^2 \over 2} \times \theta_{rad}\]