Beam Deflection Calculator

Calculator Input Form

Beam and load case

Span length

Span unit

Modulus of elasticity

Modulus unit

Moment of inertia

Inertia unit

Point load

Point load unit

Uniform load

Uniform load unit

Point load location from left

Location unit

Allowable deflection ratio

Service multiplier

Project note

Example Data Table

Case	Span	E	I	Load	Limit	Expected use
Simply supported uniform load	6 m	200 GPa	85,000,000 mm4	8 kN/m	L/360	Floor beam review
Cantilever end point load	2.4 m	200 GPa	42,000,000 mm4	12 kN	L/240	Canopy edge check
Fixed ended uniform load	5 m	25 GPa	0.018 m4	18 kN/m	L/480	Concrete member estimate

Formula Used

The calculator converts all inputs to base SI units. It then applies the chosen beam deflection equation.

Simply supported uniform load: δ = 5wL^4 / 384EI.
Simply supported center point load: δ = PL^3 / 48EI.
Simply supported eccentric point load: Macaulay equation with reactions R1 = Pb/L and R2 = Pa/L.
Cantilever end point load: δ = PL^3 / 3EI.
Cantilever uniform load: δ = wL^4 / 8EI.
Fixed ended uniform load: δ = wL^4 / 384EI.
Fixed ended center point load: δ = PL^3 / 192EI.
Service check: factored δ = calculated δ × service multiplier.
Allowable check: allowable δ = L / selected ratio.

Here, P is point load, w is line load, L is span, E is modulus, and I is moment of inertia.

How to Use This Calculator

Select the beam support and loading case.
Enter span length and choose the matching unit.
Enter material stiffness as modulus of elasticity.
Enter moment of inertia from the chosen beam section.
Enter point load, uniform load, or load location as needed.
Enter a deflection limit, such as 240, 360, or 480.
Use the service multiplier for long-term or conservative checks.
Press calculate, then export CSV or PDF when needed.

Construction Beam Deflection Guide

Why Deflection Matters

Beam deflection is the vertical movement that happens when a member carries load. It is not always a sign of failure. Yet it affects finishes, doors, windows, ceilings, cladding, and user comfort. A beam can be strong enough and still feel too flexible. That is why serviceability checks matter during construction planning.

Key Design Inputs

The main inputs are span, load, modulus of elasticity, and moment of inertia. Span has a large effect because many formulas use the third or fourth power of length. A small span change can create a large movement change. The modulus shows material stiffness. Steel has high stiffness. Timber and concrete vary by grade, age, and moisture. Moment of inertia describes section shape. Deep sections usually deflect less than shallow sections.

Load Case Selection

Different support and load cases create different deflection patterns. A simply supported beam under uniform load bends most near midspan. A cantilever with an end load moves most at the free end. Fixed ended beams are stiffer because the ends resist rotation. Selecting the closest case helps the estimate stay useful.

Allowable Limits

Many projects compare calculated deflection with a limit such as L/240, L/360, or L/480. The correct limit depends on codes, finishes, occupancy, and project requirements. Brittle finishes often need tighter limits. Temporary beams may allow larger movement. Always check the governing specification before approval.

Practical Use

This calculator is useful for early review, field checks, and option comparisons. It can compare beam depths, materials, loads, and support assumptions quickly. It also helps users see whether stiffness controls the design. Results should be reviewed by a qualified professional before final construction. Real beams may include holes, connections, composite action, cracked concrete, creep, and partial restraint. Those effects can change the final deflection.

Better Decisions

Use conservative inputs when information is uncertain. Check units carefully. Keep records of assumptions. Compare several sections before ordering material. A clear deflection check reduces rework, protects finishes, and supports safer construction decisions.

Field Notes

Measure actual spans between bearings, not overall beam length. Include wet concrete, stored materials, and construction loads when relevant. Recheck camber, bearing settlement, and vibration if the project has sensitive finishes or equipment.

FAQs

What is beam deflection?

Beam deflection is the displacement of a beam under load. It usually means vertical movement from the original unloaded position. Excessive deflection can damage finishes or reduce comfort, even when strength is acceptable.

Which deflection limit should I use?

Common limits include L/240, L/360, and L/480. The correct value depends on the project code, beam use, finishes, and owner requirements. Use the governing specification for final checks.

Why does span affect deflection so much?

Many formulas use span to the third or fourth power. Because of that, a small increase in span can cause a much larger increase in movement.

What is moment of inertia?

Moment of inertia describes how the cross section resists bending. Deeper sections usually have higher inertia. Higher inertia normally means lower deflection under the same span and load.

Can this calculator be used for timber beams?

Yes, if you enter the correct modulus of elasticity and section inertia. Timber properties vary by species, grade, moisture, and duration of load. Use approved design values.

Does this replace engineering design?

No. This tool gives calculation support for standard cases. Final construction decisions should be reviewed by a qualified engineer, especially for unusual supports, connections, or safety critical members.

What does the service multiplier do?

It multiplies the calculated deflection. You can use it for conservative checks, creep allowance, or long-term service effects when your project method requires adjustment.

Why is eccentric point load sampled?

The maximum location may not occur at midspan or at the load. The calculator evaluates the beam curve at many points and reports the largest deflection found.