What Is Moment of Inertia?

The moment of inertia (I)—more precisely, the second moment of area—quantifies a pipe cross-section’s resistance to bending. A higher moment of inertia means the pipe deflects less under a given bending load. Together with the section modulus (Z = I/c, where c is the distance from the neutral axis to the outer fiber), these properties are fundamental inputs to every piping stress calculation per ASME B31.1 and B31.3.

Formulas for Hollow Circular Sections (Pipes)

Property	Formula	Units
Moment of inertia (I)	I = (pi/64) x (D_o^4 - D_i^4)	mm^4 or in^4
Section modulus (Z)	Z = I / (D_o/2) = (pi/32) x (D_o^4 - D_i^4) / D_o	mm^3 or in^3
Polar moment of inertia (J)	J = (pi/32) x (D_o^4 - D_i^4) = 2*I	mm^4 or in^4
Radius of gyration (r)	r = sqrt(I/A), where A = (pi/4)(D_o^2 - D_i^2)	mm or in

Where D_o = outside diameter, D_i = inside diameter (D_o - 2t), and t = wall thickness.

Moment of Inertia and Section Modulus for Standard Pipe Sizes

Values based on nominal dimensions per ASME B36.10:

NPS	Schedule	OD (mm)	Wall (mm)	I (cm^4)	Z (cm^3)
2 in.	Sch 40	60.3	3.91	18.8	6.24
4 in.	Sch 40	114.3	6.02	162	28.4
6 in.	Sch 40	168.3	7.11	562	66.8
8 in.	Sch 40	219.1	8.18	1,365	124.6
10 in.	Sch 40	273.0	9.27	3,012	220.7
12 in.	Sch 40	323.8	10.31	5,698	351.9
16 in.	Sch 30	406.4	9.53	10,630	523.2
20 in.	Sch 20	508.0	9.53	20,090	790.8
24 in.	Sch 20	609.6	9.53	34,440	1,130

Role in Piping Stress Analysis

Application	How I or Z Is Used
Bending stress	sigma_b = M / Z, where M = bending moment at the point of interest
Deflection calculation	delta = (5 x w x L^4) / (384 x E x I) for a uniformly loaded beam (simplified span model)
Support span	Maximum span depends on I—larger I allows longer spans between supports
Thermal expansion stress	Displacement stress range per ASME B31.3 Eq. 17 uses Z to convert moment to stress
Torsional stress	tau = T / (2*Z) for torsional moment T, using polar section modulus
Natural frequency	f_n proportional to sqrt(EI / (mL^4))—affects vibration analysis
Buckling resistance	Critical buckling load (Euler) = pi^2 * E * I / L^2

Thin-Wall Approximation

For standard piping (D/t > 10), the thin-wall approximation provides a quick estimate:

Property	Thin-Wall Formula	Accuracy
I (approx.)	I ~ (pi/8) x D_m^3 x t	Within 2-5% for Sch 40 and thinner
Z (approx.)	Z ~ (pi/4) x D_m^2 x t	Within 2-5% for Sch 40 and thinner

Where D_m = mean diameter = D_o - t.

Common Mistake

Using nominal pipe size instead of actual outside diameter for I and Z calculations. A “4-inch pipe” has an OD of 114.3 mm (4.500 in.), not 101.6 mm (4.000 in.). Always use OD and wall thickness from ASME B36.10/B36.19 for accurate section properties.

The moment of inertia is a direct input to piping stress software (CAESAR II, AutoPIPE) and is calculated automatically from the pipe size and schedule defined in the pipe class specification.

Read the full guide to pipe class specifications