The wood beam span calculator above runs the three checks that decide how far a simply supported wood beam can carry a uniform load: bending, horizontal shear and deflection. It reports a maximum span for each one, names the check that governs, and prints the L/360 and L/240 deflection limits alongside the deflection you would actually get, so you can see the margin rather than a bare pass or fail.
Before anything else. This is a preliminary sizing and teaching tool. It is not a structural design, it is not stamped, and it does not replace a licensed engineer or architect. A wood beam holds up a floor or a roof, and a beam that is wrong does not fail politely. Arb Digital publishes this as one of a set of free construction calculators so that the arithmetic behind a span table is visible and checkable, not so that anyone builds from the output. Have the member and its connections designed and reviewed by a qualified professional, and approved by your building department.
What This Wood Beam Span Calculator Does
It works in allowable stress design, the format used by the National Design Specification for Wood Construction. The 2018 edition of the NDS is published by the American Wood Council, approved by ANSI as an American National Standard, and referenced by the 2018 International Building Code. The structural requirements that actually bind you are in your adopted building code — an International Code Council model code as amended by your state, province or municipality — and those amendments differ from place to place. This tool implements the mechanics; it does not implement any code.
It publishes no design value table. Fb, Fv and E are inputs, and the defaults are deliberately round placeholder numbers that belong to no species and no grade. That is a considered choice, and the same one behind our breaker size calculator, which publishes no ampacity table and explains why: a number reproduced from memory into a safety-critical calculation is worse than no number at all, because it looks authoritative. Reference design values live in the NDS Supplement for sawn lumber and in the manufacturer's evaluation report for engineered products, and they change with grading agency, size and edition.
The boundary against the adjacent tool on this site is worth being precise about. Our beam load calculator solves the statics of a beam you already have — reactions, shear and moment for a given loading. This page asks the sizing question in the other direction: given a section, a set of design values and a load, how far can it reach before one of the three checks runs out?
How to Use It
- Enter the actual section. Dressed width and depth, and the number of plies. Nominal names will over-estimate the beam badly.
- Replace the design values. Type in the Fb, Fv and E for your species and grade from the NDS Supplement, or from the product's evaluation report.
- Enter your adjustment factors. They start at 1.00 so nothing is applied behind your back. Multiply the applicable NDS factors together and enter the product.
- Set the load. Tributary width multiplied by load per square foot gives the uniform line load, and the live load portion drives the L/360 check.
- Read which check governs, then switch to check mode to test a specific span and see actual deflection against both limits.
The Formula and How It's Calculated
Three checks, all for a simply supported beam carrying a uniformly distributed load — the assumptions matter more than the algebra and are covered in their own section below. Section properties come first: with total width b and depth d, section modulus is S = bd² ÷ 6, moment of inertia is I = bd³ ÷ 12, and area is A = bd.
Bending: maximum moment is M = wL² ÷ 8, and the beam is adequate while M does not exceed Fb' × S. Rearranged for span, L = √(8 Fb' S ÷ w). Shear: maximum shear in a uniformly loaded simple span is V = wL ÷ 2, and the allowable is (2 ÷ 3) × Fv' × A, which gives L = 4 Fv' A ÷ (3w). Deflection: midspan deflection is Δ = 5wL⁴ ÷ (384 E' I), and setting that equal to L divided by the limit ratio k gives L = ∛(384 E' I ÷ (5wk)).
A worked example, using the placeholder values so the arithmetic can be followed. Two plies of 1.5 by 9.25 inch stock give b = 3.0 in, so S = 42.78 in³, I = 197.9 in⁴ and A = 27.75 in². A 6 ft tributary width at 50 psf gives w = 300 lb/ft, or 25 lb per inch. Bending allows √(8 × 1000 × 42.78 ÷ 25) = 117.0 in, which is 9.75 ft. Shear allows 4 × 150 × 27.75 ÷ 75 = 222 in, or 18.5 ft. Deflection at L/240 on total load allows 156.0 in, and at L/360 on the 40 psf live portion allows 147.0 in. Bending governs at 9.75 ft, by a wide margin over shear — which is the usual outcome for a slender wood beam and precisely why running only one check is dangerous.
The Assumptions Every One of These Numbers Rests On
Most wrong answers come from a valid formula applied to the wrong case, so here is the full list. The beam is simply supported — free to rotate at both ends, with no continuity over an intermediate support and no fixity. It carries a uniformly distributed load only; a point load from a post above, a girder framing in, or a concentrated load anywhere on the span changes the moment and shear diagrams completely and none of these formulas apply.
Further: the beam is assumed laterally braced so it cannot buckle sideways; if it is not, the NDS beam stability factor CL applies and belongs in your adjustment factor. It is assumed un-notched — a notch on the tension face near a support is one of the most damaging things you can do to a wood beam. Multiple plies are assumed fastened together so they act as one member, which requires a specific nailing or bolting pattern. Bearing at the supports is not checked, nor is the connection, and nothing here accounts for creep, fire resistance, vibration or long-term deflection under sustained load.
Why Deflection So Often Wins
Bending strength scales with d², but stiffness scales with d³, while the deflection check compares against a span-proportional limit. Short, heavily loaded beams therefore tend to be governed by bending or shear, and long, lightly loaded beams almost always by deflection. Increase depth by 20 percent and bending capacity rises about 44 percent while stiffness rises about 73 percent — which is why depth is nearly always the cheapest way to fix a bouncy floor.
Both S and I scale only linearly with b, so going from two plies to three raises capacity by 50 percent. Going from a 9.25 inch depth to an 11.25 inch depth raises S by 48 percent and I by 80 percent — same extra timber, better outcome, subject to headroom. The section modulus calculator works through those section properties on their own, and the beam deflection calculator handles other load cases.
L/360 and L/240 Are Serviceability, Not Strength
These ratios do not describe collapse. They describe whether a floor feels solid, whether a plaster ceiling below it cracks, and whether doors keep closing. L/360 means the beam may sag by its span divided by 360 — on a 12 ft span, 144 ÷ 360 = 0.40 inches. L/240 allows 0.60 inches. Both appear in code deflection tables, conventionally L/360 against live load and L/240 against total load, with different values for roofs and for members supporting plaster.
The tool prints the limit and the actual figure together on purpose, because a beam at 99 percent of L/360 and one at 40 percent both read as "pass" and are entirely different floors. Meeting L/360 also does not guarantee a floor that feels good underfoot: perceived bounce is a vibration problem driven by frequency and damping, and a long-span floor can satisfy every deflection limit and still be unpleasant. For the joists rather than the beam, our floor joist calculator covers the repetitive-member case.
Where the Load Actually Comes From
The tool multiplies tributary width by load per square foot, the standard simplification for a beam picking up floor or roof on both sides. Tributary width is half the span of what frames in on each side, added together — a beam with 12 ft of joist on one side and nothing on the other carries 6 ft.
The load values themselves come from your adopted code and nowhere else. Occupancy live loads, roof live loads, snow and dead load allowances are code quantities that vary by use and location, and ground snow load in particular varies enormously across short distances. This page does not publish them and cannot guess them. Nor does it combine them: load combinations are a code procedure, and for wood the load duration factor CD interacts with which combination governs — one reason the adjustment factors are left in your hands.
Arb Digital builds free tools that earn search traffic for construction, timber and engineering businesses. Browse the library, or tell us what your customers keep working out by hand.
Browse Free Tools Talk To Arb DigitalCommon Mistakes to Avoid
- Using nominal dimensions — a 2x10 is 1.5 by 9.25 inches, and using 2 by 10 overstates section modulus by about 44 percent.
- Checking bending only — deflection governs most long spans and shear governs some short deep ones. The smallest of the three is the answer.
- Applying a point load to these formulas — a post landing mid-span is a different problem entirely, and this tool models uniform load only.
- Leaving the adjustment factors at 1.00 without checking — wet service, load duration, size and lateral stability can move the allowable stress substantially in either direction.
- Assuming plies share load automatically — multi-ply beams need a specified fastening pattern, and side-loaded plies need particular attention.
Related Free Tools From Arb Digital
Use the beam load calculator for statics on a given beam, the beam deflection calculator for other load cases, the section modulus calculator for section properties, the floor joist calculator for repetitive framing and the board foot calculator for pricing the timber. The full free online tools hub lists every calculator we publish.
Frequently Asked Questions
It depends on the section, the species and grade design values, the adjustment factors and the load — there is no universal answer. The tool runs bending, shear and deflection for the numbers you enter and reports the smallest of the three, which is the span that governs.
Because reference design values belong to the NDS Supplement and to manufacturers' evaluation reports, they vary by grading agency, size and edition, and a figure reproduced from memory into a structural calculation is more dangerous than no figure at all. Fb, Fv and E are inputs, and the defaults are round placeholders belonging to no species.
Deflection governs most long, lightly loaded spans, because stiffness scales with depth cubed while the limit scales with span. Bending governs many shorter or heavily loaded beams. Shear rarely governs sawn lumber but can control short, deep members. Run all three.
They are serviceability deflection limits, not strength limits. L/360 permits a sag of the span divided by 360 — 0.40 inches over 12 feet — and is conventionally checked against live load. L/240 permits 0.60 inches over the same span and is conventionally checked against total load.
It works in allowable stress design, so the margin is already inside the Fb, Fv and E values you enter and the adjustment factors you apply. Nothing further is added or removed silently, and every adjustment factor starts at 1.00 so you can see exactly what is being applied.
No. Every formula here assumes a simply supported beam under a uniformly distributed load. A post landing on the beam, a girder framing in, or any concentrated load produces different moment and shear, and needs the appropriate analysis instead.
In the arithmetic, yes — section modulus and moment of inertia both scale linearly with total width. In reality the plies must be fastened together to a specified pattern so they act as one member and share the load, and a ply loaded only from one side may not participate as assumed.
No. It is a preliminary sizing and teaching tool, it is not stamped, it checks nothing about bearing, connections, notching, fire or lateral stability, and it does not implement any building code. Structural members must be designed by a qualified professional and approved by the authority having jurisdiction.
This tool performs preliminary structural arithmetic only. It is not a structural design, it applies no building code, and it must not be built from. Wood beams, their connections and their bearing must be designed and reviewed by a licensed engineer or architect and approved by the authority having jurisdiction.
