Beam Deflection Calculator
This beam deflection calculator finds how far a simply supported beam sags under a central point load, using the beam deflection formula. Enter the load, span, and section, and the beam deflection calculator returns the maximum deflection in millimeters.
Results
The Beam Deflection Calculator is part of our Force & Motion collection. Browse more force & motion to size, convert, and check your work alongside this tool.
What the beam deflection calculator does
The beam deflection calculator shows how much a beam bends under load, which decides whether a design feels solid or springy. For a simply supported beam with a central point load, this deflection in a beam calculator applies the beam deflection formula to find the maximum sag at midspan. Checking deflection matters because a beam can be strong enough yet still deflect more than looks or function allows.
Beam deflection formula
The beam deflection calculator uses the standard beam deflection formula for a simply supported beam with a central point load:
F is the load, L the span, E the modulus, and I the moment of inertia. The cubed span term in this deflection formula for a simply supported beam is why length dominates the result. A cantilever beam deflection formula differs, using L³ ÷ (3EI) for an end load.
Beam deflection calculator example
A 1000 N load at the center of a 2 m steel beam with E = 200 GPa and I = 1000 cm⁴, run through the beam deflection formula:
That small deflection shows the section is comfortably stiff for the load.
How to use the beam deflection calculator
Enter the central point load in newtons, the span in meters, the material stiffness (Young's modulus) in GPa, and the moment of inertia in cm⁴. The beam deflection calculator applies the beam deflection formula and returns the maximum deflection. Steel has a modulus near 200 GPa, which you enter directly.
Reading the beam deflection result
Compare the deflection to a limit, often the span divided by 250 or 360 for floors. If the beam deflection calculator result exceeds that, the beam is too flexible even if it is strong enough not to break. Deeper sections raise the moment of inertia fast, so they cut deflection more effectively than stronger material, a point the beam deflection formula makes clear.
When to use the beam deflection calculator
- Checking a beam feels stiff, not just strong, with the beam deflection formula
- Comparing sections by their deflection
- Sizing a lintel, shelf, or joist with a deflection in a beam calculator
- Verifying deflection against a span-over-limit rule
Common beam deflection mistakes
- Confusing strength with stiffness. The beam deflection formula checks movement, not failure.
- Wrong units for I. Enter moment of inertia in cm⁴ as the beam deflection calculator expects.
- Using the simply supported formula for a cantilever. A cantilever beam deflection formula is different.
Tips for accurate beam deflection results
- Use a deeper section to cut deflection faster than a stronger grade.
- Check the result against a span-over-limit rule.
- Pick the right beam deflection formula for your support type.
Why span dominates the beam deflection formula
The most striking thing the beam deflection calculator reveals is the power of span. In the beam deflection formula, deflection grows with the cube of the length, so doubling the span multiplies the sag by eight for the same load and section. This is why a shelf that holds fine at half a meter sags at a full meter, and why long spans demand much deeper beams. Seeing that cubed relationship in the deflection formula for a simply supported beam reshapes how you think about where to add support.
Stiffness versus strength
The beam deflection calculator answers a different question from a strength check, and confusing the two is a classic error. Strength asks whether a beam breaks; stiffness, which the beam deflection formula measures, asks whether it moves too much first. Many beams satisfy strength yet fail a deflection limit, feeling bouncy or cracking finishes. Because deflection depends on the moment of inertia, choosing a deeper section rather than a stronger grade is usually the efficient fix, and the deflection in a beam calculator lets you test that in seconds.
Reference Table
| Material | E (GPa) |
|---|---|
| Steel | 200 |
| Aluminum | 69 |
| Timber | ~11 |
Beam Deflection Calculator FAQ
What is the beam deflection formula?
For a simply supported beam with a central point load, deflection is F × L³ ÷ (48 × E × I). The beam deflection calculator applies this beam deflection formula and returns the deflection in millimeters.
What is the deflection formula for a simply supported beam?
The same δ = FL³/(48EI) for a central point load. A cantilever beam deflection formula is different, using FL³/(3EI) for a load at the free end. The calculator covers the simply supported case.
What deflection is acceptable?
A common limit is the span divided by 250 to 360. If the beam deflection calculator result exceeds that, the beam is too flexible even when it is strong enough.
What is moment of inertia?
It measures how a section resists bending, larger for deeper shapes. The beam deflection formula uses it as I in cm⁴, and increasing it cuts deflection quickly.