Beam Deflection Calculator
Sag of a simply supported beam with a central point load, and the span-to-deflection ratio.
Results
Deflection
0.6904
mm
Ratio
4346
Torque
3750.0
N·m
What this tool does
Deflection grows with the cube of the span, so doubling the length of a beam makes it sag eight times more under the same load. This covers one load case only — a single point load at mid-span on a simply supported beam.
Formula
δ = F × L³ ÷ (48 × E × I) (central load, simple support)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
f | Force | N |
l | Span | mm |
em | Young's modulus | MPa |
i | Second moment of area | cm⁴ |
D | Deflection | mm |
R | Ratio | — |
M | Torque | N·m |
Worked example
- Force5000 N
- Span3000 mm
- Young's modulus210,000 MPa
- Second moment of area1940 cm⁴
- Deflection0.6904 mm
- Ratio4346
- Torque3750.0 N·m
Limitations
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
Frequently asked questions
What does the span-to-deflection ratio mean?
It is the span divided by the sag, and it is how deflection limits are written in building codes — for example L/250 or L/360. A bigger number means a stiffer beam. Reading it this way lets you compare a short beam and a long one on the same scale.