About the Beam Deflection Calculator
When a beam carries a load it bends, and the amount it sags decides whether a floor feels bouncy or a shelf looks crooked. This calculator uses the standard textbook formulas for four common cases: a simply supported beam with a load in the middle or spread along its length, and a cantilever with a load at the free end or spread along its length. Enter the length, the load, the material and the second moment of area. It returns the maximum deflection, the span-to-deflection ratio with L/360 and L/250 checks, the maximum bending moment, the support reaction and the end slope. It is a learning aid, not a design tool.
Updated October 2026
How to use the Beam Deflection Calculator
- 1Pick the beam and load arrangement.
- 2Enter the length in metres and the load in kilonewtons, or kilonewtons per metre for a spread load.
- 3Choose the material or type your own Young's modulus.
- 4Enter the second moment of area I in cm⁴.
- 5Read the deflection, the L/ ratio and the bending moment.
The four cases
A simply supported beam rests on two supports with no restraint against rotation. With a single load in the middle, the sag is P L cubed over 48 E I. With a uniform load w along the length, it is 5 w L to the fourth over 384 E I. A cantilever is fixed at one end and free at the other. A load P at the tip gives P L cubed over 3 E I and a uniform load gives w L to the fourth over 8 E I.
Notice how strongly the span matters. Doubling the length of a simply supported beam under the same point load multiplies the deflection by eight, while doubling the depth of a rectangular section cuts it by a factor of eight.
Choosing the numbers
- Steel has E of about 200 GPa, aluminium 69 GPa, softwood timber around 11 GPa and normal concrete about 30 GPa.
- Convert a load in kilograms to newtons by multiplying by 9.81.
- 1 kN is about 102 kg of force.
- I for a steel section is listed in tables in cm⁴.
- Use the characteristic load, not a factored load, for deflection checks.
Related tools
To get I for a simple shape, use the Moment of Inertia Calculator. The Force Calculator converts mass and acceleration into newtons, the Torque Calculator handles twisting loads and the Spring Calculator (Hooke's Law) covers elastic stretch. All of these are simplified models and a professional should check any real structure.
Features
- Simply supported and cantilever beams
- Point load and spread load
- Preset materials: steel, aluminium, timber, concrete
- Deflection, slope, moment and reaction
- L/360 and L/250 checks
- SI units with clear labels
- Runs in your browser
Frequently asked questions
What is beam deflection?
It is how far a beam bends downward under load. The maximum deflection is usually at the middle of a simply supported beam and at the free end of a cantilever.
What is the formula for a centre load?
For a simply supported beam with a point load P in the middle, the maximum deflection is P times L cubed divided by 48 times E times I.
What is I, the second moment of area?
It describes how well the cross-section resists bending. It depends on the shape and the direction of bending. Deep sections have a much larger I than flat ones of the same area.
What does L/360 mean?
It is a common serviceability limit that says the deflection should not exceed the span divided by 360. L/250 is a looser limit for general use. Codes set the exact limits for your project.
Does it include the beam's own weight?
No. Add the self weight as part of a spread load if it matters, which it often does for long timber or concrete beams.
Can I use feet and pounds?
This page uses metres, kilonewtons and gigapascals. Convert your values first with a unit converter.
Is it safe to design from this?
No. Real design checks shear, bending stress, buckling, connections and code load factors. Use a qualified engineer for anything that carries people or property.