Cross-Sectional Area Calculator
Find the cross-sectional area of any standard shape — circular rods, rectangular beams, triangular sections, elliptical profiles, or hollow annular tubes — in whatever unit you prefer.
Cross-section shape
In square units of your chosen dimension (e.g. mm² if you entered mm)
- 1
Square the radius
5 × 5 = 25 - 2
Multiply by π
π × 25 = 78.5398
How does this calculator work?
Cross-sectional area is the area of a shape sliced perpendicular to its length. Formulas: circle πr², rectangle w·h, triangle ½bh, ellipse πab, hollow tube π(R²−r²). Pick your shape, enter dimensions in any consistent unit, and get the area instantly — used in stress, flow, and electrical calculations.
Formula
How this is calculated
The cross-sectional area is the area of the 2-D shape you would see if you sliced through an object perpendicular to its length. It appears in many engineering and physics formulas: stress σ = F/A (force divided by cross-section gives pressure), flow rate Q = A·v (area times velocity), and moment of inertia depend directly on which shape and dimensions you cut through.
For a solid circle (e.g. a round bar) use A = πr², where r is the radius. For a hollow circular tube (pipe), the net area is the outer circle minus the inner hole: A = π(R² − r²). Rectangular cross-sections (beams, planks) use A = w × h; triangular sections A = ½bh. Elliptical sections use A = π·a·b where a and b are the two semi-axes.
All formulas assume a simple, uniform cross-section with no fillets or tapers. For composite sections (I-beams, T-sections, channel sections), split the shape into rectangles, compute each area, and sum them. This calculator handles the five most common cross-section types; use consistent units throughout (e.g. all millimetres gives mm², all inches gives in²).
Frequently asked questions
Cross-sectional area directly determines structural capacity — a larger area carries more load for a given material stress (σ = F/A), conducts more current per unit resistivity, and allows greater flow through a pipe. Engineers choose cross-section shapes to maximise strength or flow while minimising material weight.
Use the annulus formula: A = π(R² − r²), where R is the outer radius and r is the inner radius (half the inner bore diameter). This gives the net solid material area — the area that carries the load or conducts the fluid wall thickness.
Use any consistent linear unit (mm, cm, m, inches). The area result will be in the corresponding square unit — e.g. entering dimensions in millimetres gives an area in mm². To convert, remember 1 cm² = 100 mm², 1 m² = 10,000 cm², 1 in² = 645.16 mm².
Also known as
TG we-Calculate Editorial Team. (2026). Cross-Sectional Area Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/cross-sectional-area-calculator
TG we-Calculate Editorial Team. "Cross-Sectional Area Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/cross-sectional-area-calculator.
TG we-Calculate Editorial Team, "Cross-Sectional Area Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/cross-sectional-area-calculator
@misc{wecalculate_cross_sectional_area_calculator, title = {Cross-Sectional Area Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/cross-sectional-area-calculator}}, year = {2026}, note = {TG we-Calculate} }
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