Sector Area Calculator

Sector Area Calculator: Core Features and Principles

Tired of calculating sector areas by hand? This tool automatically applies geometric formulas to calculate the area based on the radius and central angle (supporting both degrees and radians). As a sector is a part of a circle, its area calculation follows specific mathematical principles: when entering degrees, it uses the formula (angle/360) × π × radius²; when entering radians, it uses 0.5 × radians × radius². The result is automatically converted to the squared value of the corresponding unit.

Why Choose Our Sector Area Calculator?

• Dual Input Modes: Supports both degrees (0-360°) and radians (0-2π) for the central angle.
• Dynamic Unit Adaptation: Freely enter the radius unit (e.g., cm, m, mm), and the result automatically converts to the corresponding square unit.
• Adjustable Precision: Customize the number of decimal places (default is 2) to meet different precision requirements.

How to Use

1. Select degrees or radians in the "Central Angle Type" option.
2. Enter the corresponding value in the "Central Angle Value" field.
3. Enter a positive number in the "Radius" field.
4. Specify the length unit (e.g., cm, m) in the "Unit" box.
5. Set the "Decimal Places" to control the precision of the result.
6. View the automatically generated area result (the unit is automatically converted to its squared form).

Frequently Asked Questions (FAQ)

• Q: What parameters are needed to calculate the area of a sector?
  A: You must provide both the radius and the central angle (in degrees or radians). Both are required.
• Q: If I enter the radius unit as cm, why does the result show m²?
  A: The tool automatically performs unit conversions; 1 cm² is actually equal to 0.0001 m². If you want the result to display in cm², please explicitly enter "cm" in the unit field.

Important Notes

The radius must be a positive number. The recommended range for the central angle is 0-360 degrees or 0-2π radians. Ensure consistency when entering units. Floating-point calculations may have extremely minor errors. Please do not enter real dimensional information if it involves sensitive or private data.

Technical Notes & Tips

For engineering drafting scenarios, we recommend using the radian mode to improve calculation efficiency. A typical example: a sector with a radius of 5 meters and an angle of 60 degrees has an area of approximately 13.09 square meters (Formula: (60/360) × π × 5²). Note that practical applications must consider the precision of π; this tool uses a 15-digit precision value for π in its calculations.