Moment of Inertia Calculator
Second moment of area I, area and section modulus for rectangle, circle and hollow circle.
INPUTS
mm
mm
mm
mm
RESULTS
I — 200×400 rectangle
1,066.667 ×10⁶ mm⁴
Area A
80,000 mm²
Section modulus S = I/c
5,333.3 ×10³ mm³
Radius of gyration r = √(I/A)
115.47 mm
How it works
The second moment of area I measures how far material sits from the bending axis — and it rewards depth cubed. Doubling a rectangle's depth multiplies I by 8 while doubling its width only doubles it. Every efficient section (I-beams, tubes, box girders) is an exercise in pushing area away from the neutral axis.
Worked example
A 200×400 mm rectangle: I = bh³/12 = 200·400³/12 = 1067×10⁶ mm⁴ about the strong axis. Rotate it 90° and I collapses to hb³/12 = 267×10⁶ mm⁴ — 4× weaker, which is why joists stand upright.
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