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Beam Deflection Calculator

Construction

Estimate maximum deflection of a simply-supported beam under a center point load from span, load, elastic modulus, and moment of inertia inputs.

10100,000
12600
500,00030,000,000
15,000

Max Deflection (in)

0.225
Span (in)
120

This calculator computes your Max Deflection (in), Span (in) from the values you enter.

Inputs
Center Point Load (lbs)Span (in)Elastic Modulus (psi)Moment of Inertia (in⁴)
Outputs
Max Deflection (in)Span (in)

What is a Beam Deflection?

A Beam Deflection Calculator estimates how much a simply supported beam will sag, or deflect, under a single point load applied at the center of its span. It uses the standard beam theory formula for this specific load case, taking the applied load, span length, the beam material's elastic modulus, and the cross-section's moment of inertia as inputs to compute maximum deflection in inches.

This tool is designed for quick, informational estimates during early planning or DIY project sizing — not as a substitute for a full structural engineering analysis, which must account for actual code-required load combinations, safety factors, and support conditions beyond the single center-load case modeled here.

How to use this Beam Deflection calculator

  1. Determine your point load in pounds — the concentrated weight or force applied at the center of the beam's span.

  2. Measure your beam's span in inches — the distance between the two supports.

  3. Find your material's elastic modulus in psi — approximately 1.6 million psi for typical softwood lumber, or around 29 million psi for structural steel; check span tables or manufacturer data for your specific material and grade.

  4. Find your cross-section's moment of inertia in inches to the fourth power — available from lumber span tables or structural steel shape references for standard sizes, or calculated directly for custom rectangular sections.

  5. Enter Center Point Load (lbs), Span (in), Elastic Modulus (psi), and Moment of Inertia (in⁴) using the sliders or number fields.

  6. Read your Max Deflection (in) in the highlighted result card — this is your estimated maximum sag at the center of the span.

  7. Compare against a deflection limit, such as span/360 for floors under brittle finishes, to gauge whether the beam size seems adequate — then confirm with a structural engineer before finalizing any real construction.

Formula & Methodology

The calculator uses the classic simply-supported beam formula for a single center point load:

> Δ = (P × L³) ÷ (48 × E × I)

Where:
- Δ = maximum deflection at center span, in inches
- P = point load, in pounds
- L = span length, in inches
- E = elastic modulus of the material, in psi
- I = moment of inertia of the cross-section, in inches to the fourth power

Worked example:

- Load = 1,000 lbs, Span = 120 in, E = 1,600,000 psi, I = 100 in⁴
- L³ = 120³ = 1,728,000
- Numerator = 1,000 × 1,728,000 = 1,728,000,000
- Denominator = 48 × 1,600,000 × 100 = 7,680,000,000
- Δ = 1,728,000,000 ÷ 7,680,000,000 = 0.225 in

This result means the beam is estimated to sag roughly a quarter inch at its center under the 1,000-pound load. This formula assumes a single concentrated load, uniform material properties, and a purely elastic response — real structures involve additional load cases and safety factors that require a structural engineer's full analysis. For related load estimation, see the Snow Load Calculator.

Frequently Asked Questions

A simply supported beam rests on two supports — one at each end — that allow the beam to rotate freely but not translate vertically, like a wood joist resting on two masonry walls or a steel beam sitting on two columns. This is the most common and simplest beam support condition, and the formula used here applies specifically to this case with a single point load at the center of the span.
No. This calculator provides a simplified single-load-case estimate for informational and preliminary planning purposes only. Final structural beam sizing must be verified by a licensed structural engineer using the actual applicable building code, load combinations, safety factors, and site-specific conditions, which this simplified formula does not include.
Moment of inertia (I) measures how a beam's cross-sectional shape resists bending — a taller, deeper beam has a much higher moment of inertia than a wider, shallower one of the same area. For standard dimensional lumber and steel shapes, moment of inertia values are published in span tables and structural steel manuals; for a rectangular wood beam, I = (width × depth³) ÷ 12 in inches.
Softwood lumber commonly used in residential framing has an elastic modulus (E) around 1.2 to 1.9 million psi depending on species and grade, with 1.6 million psi being a common average for reference. Structural steel has a much higher and more consistent elastic modulus of approximately 29 million psi, which is why steel beams deflect far less than wood beams of similar size under the same load.
A widely used residential guideline limits live-load deflection to span/360 for floors supporting brittle finishes like tile, meaning a 120-inch span should deflect no more than about 0.33 inches. Total load deflection limits are often more permissive, such as span/240. Always confirm the applicable deflection limit against your local building code rather than relying on a single rule of thumb.
Deflection is proportional to the cube of the span length in this formula, so doubling the span increases deflection by a factor of eight, all else being equal. This cubic relationship is why increasing span length has a far larger effect on beam sag than a proportional increase in load, and why longer spans typically require disproportionately deeper or stronger beams.
Live load refers to variable, temporary loads such as occupants, furniture, or snow, while dead load refers to the permanent weight of the structure itself. Total load deflection calculations, like the simplified center-point-load formula used here, combine both, while some building code deflection limits apply specifically to live load only — check which load type your governing code section addresses.
No, this calculator specifically models a single concentrated point load at the center of the span, which uses the formula PL³/48EI. A uniformly distributed load across the full span uses a different formula, 5wL⁴/384EI, and produces a different — typically somewhat lower — maximum deflection for an equivalent total load.
For a rectangular beam, moment of inertia scales with the cube of the depth but only linearly with the width, so increasing a beam's depth is far more effective at reducing deflection than increasing its width by the same proportion. This is why floor joists are installed on edge (deep, narrow orientation) rather than flat.
Load is entered in pounds (lbs), span in inches (in), elastic modulus in pounds per square inch (psi), and moment of inertia in inches to the fourth power (in⁴). Mixing units — such as entering span in feet instead of inches — will produce a significantly incorrect deflection result, so always convert to these specific units before entering values.
Since elastic modulus appears in the denominator of the deflection formula, a stiffer material with a higher E value produces proportionally less deflection for an identical load, span, and cross-sectional shape. Steel, with an elastic modulus roughly 18 times higher than typical softwood lumber, deflects about 18 times less than an equivalent wood beam of the same moment of inertia under the same load and span.
Deflection controls serviceability — preventing sag, bounce, or cracked finishes — but a beam must also be checked separately for bending stress and shear strength to ensure it won't fail structurally under load, even if deflection alone appears acceptable. A qualified structural engineer evaluates all of these failure modes together, not deflection in isolation.
Also known as
beam deflection formula calculatorsimply supported beam calculatorwood beam deflection calculatorsteel beam deflection calculatorpoint load deflection calculator