How to calculate the area of an annular sector using outer radius and thickness?

Annular sector area = π × [outer radius² - (outer radius - thickness)²] × (angle / 360°) = π × thickness × (2 × outer radius - thickness) × (angle / 360°)

How to calculate the area of an annular sector using inner radius and thickness?

Annular sector area = π × [(inner radius + thickness)² - inner radius²] × (angle / 360°) = π × thickness × (2 × inner radius + thickness) × (angle / 360°)

How to calculate the area of an annular sector using outer and inner radius?

Annular sector area = π × (outer radius² - inner radius²) × (angle / 360°)

What is the relationship between annular sector area and annulus area?

Annular sector area = annulus area × angular ratio = annulus area × (angle / 360°)

Annular Sector Area Calculation

Enter the required parameters to calculate the area of an annular sector instantly, with unit conversion.

Input

Outer radius & Thickness

Inner radius & Thickness

Outer radius & Inner radius

Outer Radius O.R.

Thickness t

Angle θ

Area

Annular Sector Area Formulas

Area = π × [outer radius² - (outer radius - thickness)²] × (angle / 360°)
Area = π × [(inner radius + thickness)² - inner radius²] × (angle / 360°)
Area = π × (outer radius² - inner radius²) × (angle / 360°)
Area = annulus area × angular ratio

FAQ

What is an annular sector and where is it used?
An annular sector is a portion of a ring (annulus) defined by two radii and an angle. It's commonly used in mechanical engineering for calculating areas of flanges, washers, pipe sections, and gear segments. Applications include gasket design, material quantity estimation, and stress analysis.
How do I choose the right input method for my calculation?
Use "Outer radius & Thickness" for pipes and tubes where you know the outer dimension and wall thickness. Use "Inner radius & Thickness" for hollow shafts where the inner dimension is known. Use "Outer & Inner radius" when both dimensions are directly measurable.
What's the difference between degrees and radians for angle input?
Degrees are more intuitive (360° = full circle), while radians are mathematically natural (2π = full circle). For practical applications, degrees are usually preferred. The calculator automatically handles both units, so choose what's most convenient for your measurements.
How accurate are the area calculations for engineering applications?
The calculations use precise mathematical formulas with high accuracy suitable for engineering design. For material estimation, consider adding 5-10% margin for waste. For stress analysis, the geometric accuracy is typically sufficient for most engineering applications.
Can I use this calculator for partial pipe sections or curved beams?
Yes, this calculator is perfect for partial pipe sections, curved beam cross-sections, and segmented rings. Common applications include calculating areas for partial flanges, curved structural members, and sectioned pipe fittings in HVAC and piping systems.
What are typical applications and angle ranges for annular sectors?
Common applications: pipe elbows (90°), flange segments (30-60°), gear teeth (5-15°), valve seats (180-270°), and bearing races (full 360° or partial segments). The calculator handles any angle from 0° to 360° for complete flexibility.

Annular Sector Area Equations (LaTeX)

Using outer radius and thickness:

\[Area = \pi \times [OR^2 - (OR - t)^2] \times {\theta \over 360}\]

\[= \pi \times t(2 \times OR - t) \times {\theta \over 360}\]

Using inner radius and thickness:

\[Area = \pi \times [(IR + t)^2 - IR^2] \times {\theta \over 360}\]

\[= \pi \times t(2 \times IR + t) \times {\theta \over 360}\]

Using outer and inner radius:

\[Area = \pi \times (OR^2 - IR^2) \times {\theta \over 360}\]