Section Modulus Calculator
Calculate elastic and plastic section modulus for bending stress analysis and beam design.
Calculate S from I and c
S = I / c
S = section modulus, I = moment of inertia, c = distance to extreme fiber
S = section modulus, I = moment of inertia, c = distance to extreme fiber
Results
Section Modulus (S)
—
Moment of Inertia (I)
—
Extreme Fiber Distance (c)
—
Note: For asymmetric sections, calculate S for both top and bottom fibers using the respective c values.
Required Section Modulus
Sreq = M / Fb
M = bending moment, Fb = allowable bending stress
M = bending moment, Fb = allowable bending stress
Results
Required Section Modulus
—
Moment (converted)
—
Allowable Stress
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Next Step: Compare Sreq to the section modulus of your selected member. The member is adequate if Sactual ≥ Sreq.
Calculate Bending Stress
fb = M / S = Mc / I
fb = actual bending stress
fb = actual bending stress
Results
Actual Bending Stress (fb)
—
Moment
—
Section Modulus
—
Check: The beam is adequate for bending if fb ≤ Fb (allowable bending stress).
Complete Beam Bending Check
Enter beam properties and loading to check adequacy.
Results
Bending Check
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Max Moment (M)
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Actual Stress (fb)
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Allowable Stress (Fb)
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Utilization Ratio
—
Required Smin
—
Plastic Section Modulus (Z)
Z = Mp / Fy
Shape Factor = Z / S
Shape Factor = Z / S
Results
Plastic Section Modulus (Z)
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Elastic Section Modulus (S)
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Shape Factor (Z/S)
—
Moment of Inertia (I)
—
Shape Factors:
Rectangle: 1.5 | Circle: 1.7 | Wide Flange: ~1.1-1.2
Z is used for plastic design (LRFD) while S is for elastic (ASD).
Rectangle: 1.5 | Circle: 1.7 | Wide Flange: ~1.1-1.2
Z is used for plastic design (LRFD) while S is for elastic (ASD).
Common Lumber Section Properties
| Nominal Size | Actual (b × h) | Area (in²) | Ix (in⁴) | Sx (in³) | c (in) |
|---|---|---|---|---|---|
| 2×4 | 1.5 × 3.5 | 5.25 | 5.36 | 3.06 | 1.75 |
| 2×6 | 1.5 × 5.5 | 8.25 | 20.80 | 7.56 | 2.75 |
| 2×8 | 1.5 × 7.25 | 10.88 | 47.63 | 13.14 | 3.625 |
| 2×10 | 1.5 × 9.25 | 13.88 | 98.93 | 21.39 | 4.625 |
| 2×12 | 1.5 × 11.25 | 16.88 | 177.98 | 31.64 | 5.625 |
| 4×6 | 3.5 × 5.5 | 19.25 | 48.53 | 17.65 | 2.75 |
| 4×8 | 3.5 × 7.25 | 25.38 | 111.15 | 30.66 | 3.625 |
| 4×10 | 3.5 × 9.25 | 32.38 | 230.84 | 49.91 | 4.625 |
| 4×12 | 3.5 × 11.25 | 39.38 | 415.28 | 73.83 | 5.625 |
| 6×6 | 5.5 × 5.5 | 30.25 | 76.26 | 27.73 | 2.75 |
| 6×8 | 5.5 × 7.5 | 41.25 | 193.36 | 51.56 | 3.75 |
| 6×10 | 5.5 × 9.5 | 52.25 | 392.96 | 82.73 | 4.75 |
| 6×12 | 5.5 × 11.5 | 63.25 | 697.07 | 121.23 | 5.75 |