Beam Deflection Calculator
A free, browser-based calculator. Runs entirely in your browser — no sign up, nothing stored.
Enter Values
How to use this calculator
- Enter the span L, the material's Young's modulus E (steel ≈ 200 GPa) and the section's second moment of area I in cm⁴.
- Add a central point load and/or a uniform load.
- Read the maximum mid-span deflection and the span-to-deflection ratio.
How it works
The Beam Deflection Calculator estimates the maximum deflection of a simply supported beam from its stiffness (E·I) and load.
A central point load deflects the beam by PL³/48EI; a uniform load by 5wL⁴/384EI. The two are added at mid-span. The result is also shown as a span-to-deflection ratio (L/δ) so you can compare it against serviceability limits like L/250 or L/360.
Worked example
6 m steel beam, I = 5000 cm⁴, 5 kN/m. E·I = 200×10⁹ × 5000×10⁻⁸ = 10×10⁶ N·m². δ = 5×5000×6⁴ / (384×10×10⁶) ≈ 8.4 mm, about L/710 — comfortably within L/360.
Tips
- Deflection is very sensitive to span — it grows with L³ (point) and L⁴ (uniform). Halving the span cuts deflection dramatically.
- Stiffer (deeper) sections raise I quickly because I grows with depth cubed.
Frequently asked questions
Where do I find E and I?
Young's modulus E is a material property (steel ≈ 200 GPa, aluminium ≈ 69 GPa, timber ≈ 11 GPa). The second moment of area I comes from section tables for the shape/size you're using, or from the Second Moment of Area Calculator.
What deflection limit should I use?
It depends on the application and code — common serviceability limits are L/250 for total load and L/360 for live load on floors. Check the limit that applies to your project.
Can I use these results for final design?
No. These calculators are for first-pass sizing, checking and learning. They assume ideal supports, static loads and elastic behaviour, and they don't apply load factors, member capacity, buckling or connection checks. Always verify against the relevant design code (e.g. AS 4100, AS 1170, Eurocode) and have a qualified engineer sign off structural work.
Related tools
Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.