Centroid Calculator (T-Section)
Centroid location and moment of inertia of a T-section by first moments of area.
INPUTS
mm
mm
mm
mm
RESULTS
Centroid from bottom ȳ
142.63 mm
Total area A
7,600 mm²
Moment of inertia Ix (centroidal)
28.801 ×10⁶ mm⁴
c (top / bottom fibre)
57.4 mm / 142.6 mm
Section modulus (weaker, bottom)
201.9 ×10³ mm³
How it works
The centroid is the area-weighted average position: ȳ = ΣAᵢyᵢ/ΣAᵢ. Split any composite shape into rectangles, take first moments about a common datum, and divide by total area. The centroid fixes the neutral axis of bending — for unsymmetric sections like a T, the extreme fibre distances differ top and bottom, so bending stresses differ too.
Worked example
Flange 200×20 on a web 20×180: A₁ = 4000 mm² at ȳ₁ = 190 mm, A₂ = 3600 mm² at ȳ₂ = 90 mm. ȳ = (4000·190 + 3600·90)/7600 = 142.6 mm from the bottom — the centroid sits close to the flange because that's where the area is.
Frequently asked questions
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