CarpentryBeam Calculator

Beam Calculator

Size a beam by span, tributary width and species, then see whether bending or deflection governs.

Beam Details

Common jobs

Beam span (ft)

Tributary width (ft)

What the beam carries

Beam material

Before you order

Tributary width is half the distance to the support on each side, not the full joist span. It is the input people get wrong, and it scales every figure here.

Estimates only. Not professional advice.

Beam size to specify

2x12doubled

floor beam in Douglas Fir #2, spanning 8 ft and carrying 400 plf.

400load plf
3,200moment ft-lb
28.4modulus needed in³
11.25beam depth in
Load assumed
10 psf dead + 40 psf live
Bending stress used
1,350 psi
Deflection check
Pass (L/360)
Beam weight
9 lb/ft
Beam material
$32 – $64

Uniform load on a simply supported span, checked against L/360. Material only, with no hangers, shoring, posts or footings in the figure.

Serviceability

Beam size margins: bending against deflection, size by size

A span table hands you one size and hides the two tests behind it. Strength decides whether a beam breaks, stiffness decides whether the floor above it bounces, and they run out at different spans. Every size this calculator carries is scored below against both, at your load. Nothing here changes the size above.

6 of the 8 sizes below clear both checks at 8 ft carrying 400 plf. Bending is the binding check on every row here. 2 sizes hold the L/360 line and still fail on strength, so stiffness alone is not the test either.

400 plf2x12 (doubled)L/360 = 0.27 insag 0.06 in11.25 in deep8 ft clear span
Span and depth share one scale. The sag and the dashed allowance are both stretched 15 times, because at true scale the curve would be thinner than the line drawing it.

At 8 ft this section runs out of strength before it runs out of stiffness. Past 29.6 ft that reverses and sag becomes the limit.

Behind the curve

Size drawn
2x12 (doubled)
Grade assumed
Douglas Fir #2
Bending stress, Fb
1,350 psi
Stiffness, E
1,600,000 psi
Section modulus, S
31.64 in³
Moment of inertia, I
356 in⁴
Modulus needed here
28.4 in³
Sag at midspan
0.06 in
Allowed at L/360
0.27 in
Binding check
Bending strength
Deflection wins past
29.6 ft
SizeDepthBendingL/360GovernsDeflection wins past
Doubled dimensional lumberDouglas Fir #2 · Fb 1,350 psi · E 1,600,000 psi
2x8 (doubled)7.25 in0.46×1.10×Bending19.1 ft
2x10 (doubled)9.25 in0.75×2.29×Bending24.4 ft
2x12 (doubled)yours11.25 in1.11×4.12×Bending29.6 ft
Laminated veneer lumberLVL (Laminated Veneer) · Fb 2,600 psi · E 1,900,000 psi
3-1/2"x9-1/4" LVL9.25 in1.69×3.17×Bending15.0 ft
3-1/2"x11-7/8" LVL11.875 in2.79×6.71×Bending19.3 ft
3-1/2"x14" LVL14 in3.87×11.00×Bending22.7 ft
Glue-laminated timberGlulam Beam · Fb 2,400 psi · E 1,800,000 psi
5-1/8"x12" Glulam12 in3.84×9.61×Bending20 ft
5-1/8"x15" Glulam15 in6.01×18.77×Bending25.0 ft

A margin under 1.00× fails. Both columns use the same Fb, E and section properties as the recommendation above, so the two can never disagree. The last column is a property of the section alone: past that span, stiffness runs out before strength does, whatever the load.

Doubled dimensional rows are scored as Douglas Fir #2, LVL and glulam as their own products. Steel is not scored here, because this calculator refers steel sizing to an engineer.

Specifying

Beam sizing decisions, in the order you make them

Numbered because each one closes off the next. Tributary width sets the load, the load sets the moment, and by the time you are choosing a depth the answer is already mostly decided.

  1. 01

    Measure the tributary width before anything else. It is half the distance to the support on each side, so a beam with joists spanning 16 ft either way carries 16 ft of floor, not 8. Getting this wrong scales every number that follows.

  2. 02

    Settle the load case next. A floor beam is checked at 50 psf and a roof beam at 35 psf, and our rafter calculator works out which roof loads actually reach a ridge beam or header.

  3. 03

    Pick the species and grade before you pick a size. Douglas Fir #2 is rated at 1,350 psi in bending and SPF #2 at 1,000 psi, so the same doubled 2x12 is a third weaker in one than the other.

  4. 04

    Check strength and stiffness as two separate tests, because they fail at different spans. A section can clear the bending check with room to spare and still bounce past L/360, and the table above shows which of the two is binding on every size.

  5. 05

    Size the bearing at each end at the same time as the beam. Minimum bearing is 1.5 inches on wood and 3 inches on masonry, and a post that carries the reaction has to land on a footing, not on a joist.

  6. 06

    Through-bolt a built-up beam every 24 inches with 1/2 inch carriage bolts. Nailing two plies together does not make them act as one member, and a nailed pair is not what the doubled figures assume.

  7. 07

    Lay out the framing around the pocket before you order, because the beam changes the studs and plates that carry it. Our framing calculator covers that side.

  8. 08

    Have a licensed engineer stamp anything load bearing. This page runs a uniform load through simplified span tables, and it cannot see point loads, notches, holes, fire ratings or your local amendments.

Written and reviewed by

What this page assumes

Grade
Douglas Fir #2
Bending, Fb
1,350 psi
Stiffness, E
1,600,000 psi
Sag limit
L/360, every load case
Bearing, wood
1.5 in minimum
Bearing, masonry
3 in minimum

Roofs are allowed L/240 in most codes. This page holds them to the tighter floor limit instead, so a roof beam it passes has margin in hand.

Headers and girders

Beam size by span and load: four framing jobs

Four jobs with their inputs stated. Every size, margin and price below is what this calculator returns for them, not a figure typed in beside it.

Basement girder under first-floor joists

8 ft span · 8 ft tributary · Floor Beam · Douglas Fir #2

2x12 (doubled)

400 plf · 1.11× bending · 4.12× L/360 · $32–$64

Joists land on the girder from both sides, so 8 ft of tributary width is the whole first floor above it. Post spacing is the variable here, not the beam: stretch the same girder to 10 ft and no doubled dimensional size in this table reaches the strength it needs.

Patio door header

6 ft span · 4 ft tributary · Wall Header · Douglas Fir #2

2x8 (doubled)

160 plf · 2.05× bending · 6.53× L/360 · $24–$48

A header only carries what sits above the opening, which is why the tributary width is small even in a wide wall. Jack studs at each end have to be there before the header is cut, and the king studs run full height either side of them.

Vaulted ceiling ridge beam

16 ft span · 10 ft tributary · Roof Beam/Ridge · LVL (Laminated Veneer)

3-1/2"x14" LVL

350 plf · 1.11× bending · 1.57× L/360 · $128–$240

Rafters bear from both sides, so half of each slope reaches the ridge. LVL earns its price here because it removes the post the room was opened up to avoid, and it is the depth rather than the width that does the work.

Deck girder between posts

12 ft span · 6 ft tributary · Deck Beam · Glulam Beam

5-1/8"x12" Glulam

300 plf · 2.28× bending · 3.80× L/360 · $120–$240

Decks take the same 50 psf a floor does, and the joists usually run one way only, so the tributary width is roughly half the joist span. Glulam is worth pricing against LVL outdoors because it is manufactured for exposure in the treated grades.

Margins are the same two ratios as the scorecard above: provided over required in bending, allowed over actual in deflection. Prices are the beam only.

At the lumber desk

Beam span and sizing questions

The ten things people ask before they order a beam, answered against the same Fb, E and section properties this calculator runs on.

How far can a doubled 2x12 span?

About 8 ft as a Douglas Fir #2 floor beam carrying 8 ft of tributary width. That load is 400 plf, which needs 64 in³ of section modulus, and a doubled 2x12 offers 31.6 in³. Halve the tributary width and the same beam reaches roughly 12 ft, because required strength climbs with the square of the span.

Does bending or deflection govern a residential beam?

For the sizes and grades this calculator carries, bending governs first and deflection takes over at longer spans. The crossover is a property of the section, not of the load: it lands near 15 ft on the shallowest LVL and near 25 to 30 ft on doubled dimensional lumber. Below that span, strength is the binding check.

What is deflection and why does it matter?

Deflection is how far a beam sags under load. Building codes cap it at L/360 for floors, meaning span divided by 360, and L/240 for roofs. On a 12 ft span L/360 is 0.4 inches, which is invisible to the eye and still enough to crack drywall and make a floor feel bouncy.

How do I calculate the load on a beam?

Multiply the total load in psf by the tributary width in feet to get pounds per linear foot. A floor at 50 psf with 8 ft of tributary width is 400 plf. Maximum bending moment for a uniform load is that figure times span squared, divided by 8.

LVL or doubled dimensional lumber: which should I use?

LVL when the span is past about 10 to 12 ft, dimensional lumber below that. LVL is rated at 2,600 psi in bending against 1,350 psi for Douglas Fir #2, so it carries roughly twice as much at the same depth and removes the mid-span post. It costs 8 to 15 dollars per linear foot against 4 to 8.

How much does a structural beam cost per linear foot?

SPF runs 3 to 6 dollars per linear foot, Douglas Fir #2 4 to 8, LVL 8 to 15, glulam 10 to 20 and steel 15 to 35. Those are material only. Steel also carries fabrication, and any beam that replaces a bearing wall carries temporary shoring on top.

How do I size a header over a window or door?

Headers carry the load above the opening, so the tributary width is what sits above the header, not the width of the room. For standard residential headers up to 6 ft wide, doubled 2x10s or 2x12s usually work. Wider openings need LVL or an engineered header.

Do I need posts under beam ends?

Yes. Every beam needs adequate bearing at each end, typically a post or column sized to carry the beam reaction force down to the foundation. Minimum bearing length is 1.5 inches on wood, 3 inches on masonry.

When should I use a steel beam?

Steel handles very long spans over about 20 ft and heavy point loads that wood cannot support. It needs an engineer for sizing and a crane or a crew for installation, which is why this calculator returns an engineer referral rather than a size when you pick it.

What are span tables and what do they leave out?

Span tables are published by lumber associations and in the IRC, and they list maximum allowable spans for a given size, species and load case. They assume a uniform load on a simply supported member. Point loads, cantilevers, notches, holes and continuous spans all fall outside them.

Sagging floors

What goes wrong when a beam is undersized, and what to do instead

None of these show up on the day the beam goes in. They show up as a door that stops latching, a crack over the opening, or a floor that moves when somebody walks past.

01

Undersizing for the load that is actually there

A beam sized off a guess at the tributary width is sized off a guess at the load, and load scales the moment directly while span scales it squared.

Measure half the distance to the support on each side, add the dead and live load for the real use, and size from that. Doubling the tributary width doubles the moment.

02

Stopping once the bending check passes

Strength and stiffness are different tests with different limits. A section can carry the load and still sag past L/360, and nothing about the bending result tells you which way it went.

Read both margins on the scorecard above, and look at which check is binding. On the deeper engineered sizes deflection takes over somewhere between 15 and 30 ft.

03

Sizing the beam and forgetting what holds it up

A correctly sized beam is only as good as its bearing. The reaction at each end has to land on something that reaches the footing.

Give every end 1.5 inches of bearing on wood or 3 inches on masonry, and put a post under it that carries the reaction down to a footing below frost.

04

Nailing a built-up beam instead of bolting it

Two plies nailed together do not act as one member, and the doubled figures on this page assume they do.

Through-bolt every 24 inches with 1/2 inch carriage bolts, staggered top and bottom. Nailing is for holding the plies while you drill.

05

Using the wrong grade in the calculation

Not all 2x12s are the same beam. Douglas Fir #2 is rated at 1,350 psi in bending and SPF #2 at 1,000 psi, a third less.

Read the grade stamp on the lumber you are actually buying, then set the species on this page to match before you read a size off it.

06

Feeding a point load into a uniform load calculation

Another beam or a post landing mid-span concentrates the moment at that spot, and a uniform-load formula spreads it out instead.

Anything with a point load goes to an engineer. That includes a girder truss bearing on a header and a post from the floor above landing between supports.

Load path

How load reaches a beam, and what carries it after that

A beam is one link in a chain that ends at the footing. Sizing the beam and ignoring the rest of the chain is the most common way a job that calculates fine still fails, because the weakest link is usually the bearing rather than the member.

Tributary width
Half the distance to the support on each side. Joists spanning 16 ft that land on the beam from both directions give it 16 ft of tributary width, not 8. This is the one input worth measuring twice.
Dead load and live load
Dead load is the structure itself, live load is what you put on it. A floor is checked at 10 psf dead plus 40 psf live, a roof at 15 plus 20, and a header at 10 plus 30. Both are already in the load case you pick.
Moment, then modulus
The uniform load and the span give a bending moment, and dividing that by the grade's allowable stress gives the section modulus you need. Section modulus is the only strength number you compare beams on.
Deflection, separately
Stiffness depends on the moment of inertia and the modulus of elasticity, not on the allowable stress, which is why the two checks disagree. Floors are limited to L/360, roofs to L/240, and this calculator holds everything to the tighter floor limit.
Bearing at each end
1.5 inches minimum on wood, 3 inches on masonry. Crushing at the bearing is a compression failure perpendicular to the grain and it happens under beams that are perfectly adequate in bending.
Posts and footings
Each end reaction goes into a post sized for it and a footing below the frost line. A post that lands on a joist or on a slab with no footing beneath is where the load path stops.
Built-up plies
Doubled sizes on this page assume the plies act together. That takes 1/2 inch carriage bolts every 24 inches, not nails, and the bolts are staggered so no single row of holes runs through the tension edge.
What falls outside all of it
Point loads, cantilevers, notches, holes drilled through the depth and continuous spans over more than two supports. Every one of those needs a stamped design, not a span table.

Buying the beam

Beam cost per linear foot, and what each material buys you

Material only, on one axis so the steps between them are readable. The jump from dimensional lumber to LVL is roughly double, and it buys about double the allowable bending stress at the same depth.

MaterialRange, $per LF
SPF (Spruce-Pine-Fir)
$3 – $6
Douglas Fir #2yours
$4 – $8
LVL (Laminated Veneer)
$8 – $15
Glulam Beam
$10 – $20
Steel I-Beam
$15 – $35
$0$9$18$26$35

Steel includes fabrication and nothing else: no crane, no shoring, no bearing plates. Any beam replacing a bearing wall also carries temporary support for the floor above while it goes in, which is usually the largest line on the job.

Moment and modulus

How this beam calculator sizes a beam

The load case gives a pressure in pounds per square foot. Multiplying by the tributary width turns it into a line load along the beam, and a uniform line load on a simply supported span peaks in the middle at wL² over 8. Dividing that moment by the grade’s allowable bending stress gives the section modulus the beam has to have, and the smallest listed size that reaches it is the recommendation.

That size is then checked a second time for sag, using the moment of inertia rather than the section modulus, and held to L/360. What the calculator cannot see: point loads, cantilevers, holes and notches, continuous spans, snow and wind beyond the load cases listed, fire ratings and local amendments. It is a screening tool for ordering and budgeting, not a design.

The formulas

w = psf × tributary widthM = w × L² ÷ 8S needed = M × 12 ÷ FbI = b × d³ ÷ 12sag = 5wL⁴ ÷ 384EIallowed = L ÷ 360

Span and load in feet and pounds for the moment, converted to inches and pounds per inch for the sag. Cost is span times a per-foot material rate.

Section properties

Beam sizes this calculator matches, and the two numbers behind each

Section modulus decides strength, moment of inertia decides stiffness, and the gap between the two columns is why the two checks fail at different spans. Depth is the lever on both.

SizeDepthSection modulus SMoment of inertia I
2x8 (doubled)7.25 in13.14 in³95 in⁴
2x10 (doubled)9.25 in21.39 in³198 in⁴
2x12 (doubled)11.25 in31.64 in³356 in⁴
3-1/2"x9-1/4" LVL9.25 in24.95 in³231 in⁴
3-1/2"x11-7/8" LVL11.875 in41.18 in³488 in⁴
3-1/2"x14" LVL14 in57.17 in³800 in⁴
5-1/8"x12" Glulam12 in61.5 in³738 in⁴
5-1/8"x15" Glulam15 in96.1 in³1,441 in⁴

Section modulus values are the ones this calculator matches against. Moment of inertia is width times depth cubed over twelve, the same expression the deflection check uses.

Load caseDeadLive
Floor Beamyours10 psf40 psf
Roof Beam/Ridge15 psf20 psf
Deck Beam10 psf40 psf
Wall Header10 psf30 psf

Dead plus live is the pressure multiplied by your tributary width. Snow country and tiled roofs sit above the roof case listed here.

GradeFbE
SPF (Spruce-Pine-Fir)1,000 psi1,400,000 psi
Douglas Fir #2yours1,350 psi1,600,000 psi
LVL (Laminated Veneer)2,600 psi1,900,000 psi
Glulam Beam2,400 psi1,800,000 psi
Steel I-Beam

Fb is allowable bending stress, E is stiffness. Steel carries neither here, because steel sizing goes to an engineer rather than to a table.

Disclaimer

These estimates are for planning purposes only. Actual costs vary by location, material availability, and project complexity. Always get at least 3 local quotes. This calculator does not replace professional advice.