About the Beam Deflection Calculator
What is the Beam Deflection Calculator?
This beam deflection calculator covers the four most common cases: simply supported beams with a central point load or a uniform load, and cantilevers with an end load or a uniform load.
Enter the span, load, elastic modulus and moment of inertia – for example from a steel section table such as ISMB 300 – to get deflection, maximum moment and shear.
How to use the Beam Deflection Calculator
- Beam and Load (sample: Simply supported – point load at centre)
- Span (m) (sample: 5)
- Load (kN for point load, kN/m for uniform) (sample: 20)
- Elastic Modulus E (GPa) (sample: 200)
- Moment of Inertia I (cm⁴) (sample: 8,603.6)
- Press Calculate Beam Deflection (results also refresh as you type). The result card shows the Maximum Deflection, along with Maximum bending moment, Maximum shear force, Span ÷ deflection and Check against a typical limit (L/250).
Formula used
Simply supported, centre load: δ = PL³ ÷ 48EI; uniform load: δ = 5wL⁴ ÷ 384EI
- Cantilever = end load PL³ ÷ 3EI; uniform load wL⁴ ÷ 8EI
- Limits = span ÷ 250 for beams, span ÷ 125 for cantilevers (typical)
For preliminary sizing only. Structural designs must be prepared and checked by a qualified structural engineer to IS 456, IS 800 and IS 875.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Beam and Load | Simply supported – point load at centre |
| Span (m) | 5 |
| Load (kN for point load, kN/m for uniform) | 20 |
| Elastic Modulus E (GPa) | 200 |
| Moment of Inertia I (cm⁴) | 8,603.6 |
| Result | Value |
|---|---|
| Maximum Deflection | 3.027 mm |
| Maximum bending moment | 25 kN·m |
| Maximum shear force | 10 kN |
| Span ÷ deflection | L/1,652 |
| Check against a typical limit (L/250) | Within limit |
Tips for using the Beam Deflection Calculator
- Deflection rises with the cube or fourth power of span – a slightly shorter span helps a lot.
- Use the long-term (reduced) modulus for concrete and timber to allow for creep.