mathematics calculator
Cross Sectional Area Calculator
Calculate circle, rectangle, triangle, or annulus cross-sectional area with shape-specific dimensions.
Cross Sectional Area Calculator
Cross-sectional area
Select a shape and enter its dimensions.
This tool models ideal circle, rectangle, triangle, and annulus sections only.
Formula version 1.0.0
How to use this calculator
- Choose circle, rectangle, triangle, or annulus.
- Enter the positive dimensions shown for that shape.
- Use one length unit throughout.
- Calculate and read the ideal planar cross-sectional area.
Symbols and units
| Symbol | Meaning | Unit or domain |
|---|---|---|
A | Cross-sectional area | square length |
r | Circle radius | length |
w,h | Rectangle width and height | length |
R,r | Annulus outer and inner radii | length |
Checked examples
Three common sections
Inputs: Circle r=3; rectangle 4×5; triangle base 6 height 4
Calculation: πr²; wh; ½bh
Result: 9π, 20, and 12 square units
Each mode applies its own ideal planar formula.
Check: cross-sectional-area-core.test.ts
Annular section
Inputs: Outer radius 5, inner radius 3
Calculation: A=π(5²−3²)
Result: 16π square units
The central opening is subtracted from the outer circle.
Check: cross-sectional-area-core.test.ts
Assumptions, rounding, and limits
- Dimensions are finite and use one unit.
- Shapes are ideal and planar.
- Annulus inner radius is non-negative and smaller than outer radius.
- Manufacturing tolerances and irregular profiles are excluded.
Frequently asked questions
Can annulus inner radius be zero?
Yes. It then reduces to a solid circle.
Why must inner radius be smaller?
An equal or larger inner radius leaves no positive annular area.
Does this calculate structural strength?
No. It calculates geometry only, not stress or load capacity.
Sources and review
- OpenStax: Area — Planar area formulas
- OpenStax: Geometric Formulas — Common shape formulas
- Formula version
- cross-section.area@1.0.0
- Formula review
- Equatara formula review
- Editorial review
- Equatara editorial review
- Last verified
- 2026-10-25
- Applicability
- Ideal planar sections; no structural analysis.
- Next review
- On material formula/source change, or by 2028-10-25.
Related calculators
Found a problem?
Report a formula, result, example, source, or accessibility issue through the calculator correction process. Do not include sensitive input values.