数学
已验证计算器，公式透明
Area of a Sector Calculator.
Calculates the area of a sector of a circle given the radius and the central angle in degrees or radians.
您的输入
工作原理
- 1
Measure the radius of the circle.
- 2
Measure the central angle of the sector in degrees.
- 3
Square the radius and multiply by pi.
- 4
Multiply by the angle and divide by 360 to get the area.
(pi * radius^2 * angle) / 360常见问题
What if the angle is given in radians?
Convert radians to degrees by multiplying by 180/pi, then use the calculator.
Can the angle be greater than 360 degrees?
The calculator allows up to 360 degrees, but for angles beyond 360, the sector would overlap; the formula still works mathematically.
What units should I use for radius?
Any unit of length (e.g., cm, m, inches). The area will be in square units of that length.
工作原理
Calculates the area of a sector of a circle given the radius and the central angle in degrees or radians.
- Measure the radius of the circle.
- Measure the central angle of the sector in degrees.
- Square the radius and multiply by pi.
- Multiply by the angle and divide by 360 to get the area.
公式
此计算器背后的数学公式，供您核对结果。
Area of a Sector
The area of a sector is a fraction of the circle's area, proportional to the central angle θ out of 360°.
Example:
Input: r = 5, θ = 60°
Calculation: (60/360) × π × 5² = (1/6) × π × 25
Result: ≈ 13.09 square units
实际应用场景
此计算在日常生活中的应用。
Pizza slice size
Find the area of a slice of pizza given its radius and the angle at the tip.
Example: A 12-inch pizza cut into 8 slices: each slice has angle 45°, area ≈ 14.14 sq in.
Land measurement
Calculate the area of a pie-shaped plot of land.
Example: A plot with radius 100 m and angle 30° has area ≈ 2618 m².
Design and fabrication
Determine material needed for a sector-shaped piece.
Example: A metal sheet sector with radius 2 m and angle 90° requires ≈ 3.14 m².
提示与常见错误
Tips
- Ensure the angle is in degrees; if it's in radians, convert first.
- Use consistent units for radius and area.
- For a full circle (angle=360°), the formula gives πr², the circle's area.
- Round the result to a reasonable number of decimal places for practical use.
Common Mistakes to Avoid
- Forgetting to convert radians to degrees.
- Using diameter instead of radius.
- Not dividing by 360 when using degrees.
假设与限制
- Use the stated inputs and units.
- Results are estimates for planning and education.
- Check measurements and source data before making an important decision.