What is section modulus (Z)?

Section modulus (elastic section modulus) relates bending stress to bending moment: σ = M / Z. It is computed as Z = I / c, where I is the second moment of area and c is the distance from the neutral axis to the extreme fiber.

Zxx is the section modulus about the x-x axis (bending about x), and Zyy is about the y-y axis. For non-symmetric shapes (channel/angle), Z differs for the two axes.

Is this elastic section modulus or plastic section modulus?

This calculator reports elastic section modulus (Z = I/c). Plastic section modulus depends on the plastic neutral axis and is not computed here.

AmesWeb

Section Modulus Calculator (Zxx / Zyy)

Use this section modulus calculator to compute the elastic section modulus (also searched as Zxx calculator) for common sections. The calculator uses Z = I / c and reports Zxx and Zyy with unit conversion.

Inputs

Section modulus calculator shape diagram

I‑beam dimensions: H, B, h, b

Cross‑section

Select a shape; inputs update automatically.

Unit system

Length unit

Section modulus unit

Tip: for rectangles/pipes you can swap orientation quickly.

Height (H)

Width (B)

Thickness (h)

Thickness (b)

Auto‑calculates as you type.

Results

Elastic section modulus

Z_xx = ---

Z_yy = ---

Quick notes

---

Intermediate values (for checking)
A	---	I_xx	---
I_yy	---	c_x, c_y	---
x̄, ȳ	---	Shape	---

Units shown for intermediate values use the selected length unit (converted internally to mm for calculation).

Definitions (section modulus equation)

Term	Definition
Z = I / c	Elastic section modulus (also written as S in some books).
I	Second moment of area (area moment of inertia) about the bending axis.
c	Distance from neutral axis to the extreme fiber (c = H/2 for a rectangle about x‑x).
Zxx, Zyy	Section modulus about x‑x and y‑y axes (often searched as zxx calculator / zyy calculator).

Looking for plastic section modulus? That is a different property (plastic neutral axis) and depends on yielding—this tool reports elastic Z = I / c.

Section modulus formulas for common shapes

Below are the most searched quick formulas (rectangle section modulus, circle section modulus, pipe section modulus). For built‑up shapes like I‑sections, channels and angles, this calculator uses composite‑area formulas for centroid and second moment of area and then applies Z = I/c.

Rectangle (B × H)

I_xx	B·H³ / 12
I_yy	H·B³ / 12
Z_xx	B·H² / 6
Z_yy	H·B² / 6

Also searched as section modulus of rectangle.

Circle (solid round bar)

Circle section modulus formula (round bar)

I	π·d⁴ / 64
Z	π·d³ / 32

Also searched as section modulus of circle.

Pipe / Hollow circle (CHS)

Pipe section modulus formula (hollow circle)

I	π·(D⁴ − d⁴) / 64
Z	π·(D⁴ − d⁴) / (32·D)

Also searched as pipe section modulus calculator.

Hollow rectangle (RHS)

Rectangular hollow section (RHS) section modulus formula

I_xx	B·H³/12 − b·h³/12
I_yy	H·B³/12 − h·b³/12
Z_xx	2·I_xx/H
Z_yy	2·I_yy/B

Also searched as rectangular hollow section elastic section modulus calculator.

How to use this section modulus calculator

Select a shape (rectangle, pipe/CHS, I‑section, channel, angle).
Enter dimensions in any supported length unit (mm/cm/m/in/ft).
Read Zxx and Zyy in mm³ or in³.

If you already know the second moment of area, you can still use the definition Z = I/c: for a rectangle about x‑x, c = H/2.

FAQ

How do I calculate section modulus?

Compute the second moment of area about the bending axis (I), find the extreme‑fiber distance (c), then Z = I / c. This page automates those steps for common shapes.

What is the difference between elastic and plastic section modulus?

Elastic section modulus uses Z = I / c and applies to linear‑elastic bending stress. Plastic section modulus is based on the fully yielded stress block and the plastic neutral axis.

Can I use this for I‑beam or channel section modulus?

Yes. Choose I‑beam or C channel and enter the shown dimensions. For non‑symmetric sections, Z differs by axis.