■ Moment of Inertia Calculator
Second moment of area, section modulus & radius of gyration
Results
Ix (strong axis)
—
mm⁴ ×10⁶
Sx Section Modulus
—
mm³ ×10³
rx Radius of Gyration
—
mm
Cross-Section Area
—
mm²
Formulas
Rectangle: I = bh³/12 | S = bh²/6 | r = h/√12
Circle: I = πD⁴/64 | Hollow: I = π(D⁴−d⁴)/64
I-Beam: I = bfH³/12 − (bf−tw)(H−2tf)³/12
📝 Worked Example
Rectangle: b = 100 mm, h = 200 mm.
I = 100 × 200³ / 12 = 66.67 × 10⁶ mm⁴
S = 100 × 200² / 6 = 666.7 × 10³ mm³ | r = 57.7 mm
I = 66.67 ×10⁶ mm⁴ | S = 666.7 ×10³ mm³ | r = 57.7 mm