How to use the Beam Deflection Calculator
- 1. Choose the caseSimply supported, cantilever, fixed-fixed or propped cantilever with a point load, UDL or moment.
- 2. Enter load and sectionSpan in m, load in kN or kN/m, E in GPa and I in cm⁴.
- 3. Check the resultSee deflection in mm, slope, max moment and whether it is within span / limit.
Standard deflection formulas
For a linear elastic beam, deflection depends on load, span and the flexural rigidity EI. The common cases are:
- Simply supported, central point load: δ = PL³ / 48EI
- Simply supported, UDL: δ = 5wL⁴ / 384EI
- Cantilever, end load: δ = PL³ / 3EI
- Cantilever, UDL: δ = wL⁴ / 8EI
- Fixed at both ends, UDL: δ = wL⁴ / 384EI
- Propped cantilever, UDL: δ ≈ wL⁴ / 185EI at 0.4215L from the prop
The tool converts everything to N and mm, so 1 kN/m becomes 1 N/mm and 1 cm⁴ becomes 10⁴ mm⁴.
Worked example and exam tips
A 5 m simply supported steel beam (E = 200 GPa, I = 10,000 cm⁴ = 10⁸ mm⁴) carries 10 kN/m. δ = 5 × 10 × 5000⁴ / (384 × 2×10⁵ × 10⁸) = 4.07 mm. The span/250 limit is 20 mm, so the beam is fine.
- Units cause most mistakes: keep N and mm throughout.
- Fixing the ends cuts the UDL deflection to one fifth of the simply supported value.
- For a point load away from the centre, the maximum deflection is not under the load, it lies between the load and the centre.
Need I for your section? Use the moment of inertia calculator.
Frequently asked questions
What deflection limit should I use?
It depends on the code and member. IS 456 uses span/250 for the final deflection of RCC members. Steel codes give limits by member type, so enter the one from your code.
Does it include self-weight?
Only if you add it to the UDL. Self-weight in kN/m is the section's mass per metre × 9.81 / 1000.
Which method is used?
The closed-form results of Euler-Bernoulli beam theory, the same ones you get by double integration or Macaulay's method.
Is this calculator free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form. Everything is calculated in your browser.