Best for
Area and mass estimates
Use A with material density and length to estimate weight, axial stress, and section efficiency.
Engineering formula reference
Cross Section Formula Sheet
Search cross-sectional area formulas for common engineering shapes, with variables explained for rectangles, circles, tubes, I-beams, channels, angles, and box sections.
Section properties
Search cross section formula sheet
Filter the formula table by shape, variable, symbol, expression, or engineering use case.
Watch out
Thin-wall approximations
Approximate rows ignore details such as corner radii, flange taper, welds, and manufacturing tolerances.
Formula reference
Cross-sectional area formulas with variables
| Shape | Area formula | Variables and notes |
|---|---|---|
| Rectangle | A = b h | b = width, h = height |
| Circle | A = π r2 | r = radius |
| Hollow circle | A = π(R2 - r2) | R = outer radius, r = inner radius |
| Triangle | A = b h / 2 | b = base, h = perpendicular height |
| Thin-walled tube | A ≈ 2 π r t | Approximation for t much smaller than r |
| I-beam simplified | A = b h - bi hi | Outer rectangle minus inner void approximation |
| C-channel simplified | A ≈ 2 b t + (h - 2t)t | b = flange width, h = depth, t = thickness |
| T-beam | A = bf tf + bw hw | Flange area plus web area |
| L-angle simplified | A ≈ a t + b t - t2 | Subtract overlap at the corner |
| Box section | A = b h - (b - 2t)(h - 2t) | Outer rectangle minus inner rectangle |
| Square | A = a2 | a = side length |
| Regular hexagon | A = (3√3 / 2) a2 | a = side length |
How to use
Practical engineering checks
Axial stress
σ = P / A
P is axial load and A is cross-sectional area.
Mass estimate
m = ρ A L
rho is material density, A is area, and L is member length.
Hollow section check
A = Aouter - Ainner
Subtract the void area from the outside shape area.
Units
in2, mm2, m2
Area units are squared, so unit conversions must also be squared.
Definitions
Symbols and variables explained
A
Cross-sectional area of the shape.
b
Base or width dimension.
h
Height or depth dimension.
t
Wall thickness for thin-walled or built-up sections.
FAQ
Cross Section Formula Sheet questions
How do I use this formula sheet?
Find the shape or identity, confirm each variable definition, keep units consistent, then substitute values into the formula.
Are these formulas exact?
The basic geometry formulas are exact for ideal shapes. Rows marked approximate depend on simplified geometry, thin-wall assumptions, or ignoring radii and fillets.
Can I use these formulas for final engineering design?
Use them as calculation references. Final design should also check loads, materials, tolerances, safety factors, and any governing standards.
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