Area Moment of Inertia with Definitions, Formulas & Calculator

Area Moment of Inertia (also known as Second Moment of Area) is a property of shape used to predict deflection, bending and stress in beams. This tool provides definitions, unit conversions, formulas, and calculators for various cross-sectional shapes.

Area Moment of Inertia Calculator

Area Moment of Inertia (I), also known as Second Moment of Area, is a property of shape used to predict deflection, bending and stress in beams.

Units

Imperial: inches⁴

Metric: mm⁴, cm⁴, m⁴

Unit Conversions

  • 1 cm⁴ = 10⁻⁸ m⁴ = 10⁴ mm⁴
  • 1 in⁴ = 4.16×10⁵ mm⁴ = 41.6 cm⁴
ShapeFormula for IxFormula for IyParameters
Solid SquareIx = a⁴ / 12Iy = a⁴ / 12a = side length
Solid RectangleIx = b h³ / 12Iy = b³ h / 12b = width, h = height
Solid CircleIx = π d⁴ / 64Iy = π d⁴ / 64d = diameter
Hollow CylinderIx = π (do⁴ - di⁴) / 64Iy = π (do⁴ - di⁴) / 64do = outer diameter, di = inner diameter
Square (Diagonal)Ix = Iy = a⁴ / 12Ix = Iy = a⁴ / 12a = side length
Rectangular (Oblique)Ix = (b h / 12)(h² cos²(a) + b² sin²(a))—b = width, h = height, a = angle
Symmetrical ShapeIx = (b H³ - h³(b - t)) / 12Iy = (a³ h / 12) + (b³ / 12)(H - h)t = (H - h) / 2
Non-symmetrical ShapeIx = 1/3 (B yb³ - B1 hb³ + b yt³ - b1 ht³)—Multiple parameters
Calculator

Inputs

Results

Area Moment of Inertia (Ix)-- mm⁴
Area Moment of Inertia (Iy)-- mm⁴
Area Moment of Inertia with Definitions, Formulas & Calculator | MEPKit Engineering Tools | MEPKit