Beam Deflection Calculator
Use this beam deflection calculator to estimate midspan or maximum deflection for simply supported and cantilever beams using the common load cases shown by Omni.
Result
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Quick Answer: Beam deflection depends on load type, span length, and flexural rigidity EI. Typical formulas include P L^3 / (48 E I) for a simply supported midspan point load and 5 w L^4 / (384 E I) for a simply supported uniform load.
How to Calculate
- Choose the beam type: Select either a simply supported beam or a cantilever beam.
- Choose the load case: Pick the appropriate point, distributed, varying, or moment load case.
- Enter span and stiffness: Supply the span, modulus of elasticity, and area moment of inertia or use their product EI.
- Read the deflection result: The calculator reports either the midspan deflection or the maximum deflection for the chosen case.
Formula
delta = coefficient x load term / (E x I)
| Variable | Meaning | Unit |
|---|---|---|
| delta | Beam deflection | length |
| E | Modulus of elasticity | pressure |
| I | Area moment of inertia | length^4 |
| L | Beam span length | length |
Worked Examples
Simply supported beam - Midspan point load
- P: 45,000 N
- L: 4,000 mm
- E: 240,000 N/mm^2
- I: 72,000,000 mm^4
Result: delta = 3.47 mm
This matches the standard P L^3 / (48 E I) relation from Omni's FAQ example.
Cantilever beam - End point load
- P: 2 kN
- L: 2 m
- E I: 15,000 kN m^2
Result: delta = 0.178 mm
Cantilever end loads produce larger deflection than comparable simply supported midspan loads.
Interpretation Table
| Range | Meaning | Action |
|---|---|---|
| Low deflection | Small movement relative to span | Compare against your serviceability limit such as L/240 or L/360. |
| Moderate deflection | Movement may be visible or noticeable | Check stiffness, section size, and support assumptions. |
| High deflection | Likely serviceability concern | Review load case, span, EI, and design code limits before finalizing. |
Frequently Asked Questions
Beam deflection is the movement of a beam away from its original unloaded position under load.
Span length has a very strong effect because many beam deflection formulas include L cubed or L to the fourth power.
The product E I describes how strongly the beam resists bending. Higher E or higher I reduces deflection.
No. Use it for quick estimates, then compare the result against the limits in your applicable structural design standard.
Note: This calculator is for estimation and educational use. Real structural design should use the exact support conditions, code load combinations, and serviceability limits required by the project.
References
Last reviewed: March 14, 2026