Construction Calculator
Ridge Beam Calculator
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Work out the load on a ridge beam and find a section that carries it, in dimensional lumber, LVL or glulam. Checks bending, horizontal shear and deflection together, and names the one that governs — because it is rarely the one people check.
Ridge Beam Calculator
Preliminary sizing — bending, shear and deflection
Results
Smallest adequate section
1-ply 1.75 × 18 in
LVL 2.0E (1¾ in plies) · S = 94.50 in³ · I = 850.5 in⁴
Governing check: bending at 80.4% of allowable
Design Checks
fb 2,276 psi vs Fb' 2,830 psi
fv 213.3 psi vs Fv' 327.8 psi
0.485 in vs 0.800 in allowed
0.303 in vs 0.533 in allowed
Nearby Options
| Section | Bend | Shear | Defl | Verdict |
|---|---|---|---|---|
| 3-ply 1.75 × 11.25 | 64% | 35% | 83% | OK |
| 3-ply 1.75 × 11.875 | 58% | 33% | 70% | OK |
| 2-ply 1.75 × 14 | 64% | 42% | 64% | OK |
| 2-ply 1.75 × 16 | 50% | 37% | 43% | OK |
| 1-ply 1.75 × 18 ← | 80% | 65% | 61% | OK |
| 2-ply 1.75 × 18 | 40% | 33% | 30% | OK |
Percentages are of allowable capacity. Anything over 100% fails that check.
This is a preliminary sizing aid, not a structural design. Ridge beams are load-bearing members whose failure can collapse a roof. Have any beam that will be built verified and stamped by a licensed engineer or architect, and confirm the design against your local building code.
Tributary width is half the building width because a simple gable splits the roof load three ways: half to the ridge and a quarter to each wall. This assumes the ridge is a load-bearing BEAM supported at both ends. A ridge BOARD in a rafter-tie system carries almost no vertical load, because opposing rafters resolve their thrust against each other — applying this calculation to a ridge board would oversize it substantially.
At a 6:12 pitch the roof surface is 11.80% larger than its horizontal projection (slope factor 1.1180). Loads here are taken as acting on the projection, which is the usual convention for psf roof loads. If your dead load is quoted per square foot of roof surface, multiply it by 1.1180 before entering it.
Two unit conversions in these formulas are mandatory and easy to miss. S = M ÷ Fb needs M in lb-inches, since Fb is in psi — using lb-ft understates the required section modulus by exactly 12×. The deflection formula needs the 1728 constant when w is in plf and L in feet, and omitting it understates deflection by 1728×.
The governing check here is bending, at 80.4% of allowable. Which check governs changes with span: short spans tend to be limited by shear, mid spans by bending, and long spans by deflection, so all three are reported rather than bending alone.
Design values used: Fb 2,600 psi, Fv 285 psi, E 2,000,000 psi, from Weyerhaeuser TB-508 (2.0E LVL). Only the load duration factor and depth factor is applied. A full design also considers wet service, temperature, beam stability, bearing area, notching, and volume or repetitive-member factors, which can all reduce capacity.
Bearing at the supports is not checked here and is a common failure point: the posts or walls beneath each end must carry the reaction, and that load has to continue down to the foundation through a verified path.
Step-by-Step Calculation
Step 1 — Tributary width
The ridge beam carries half the roof; the walls carry a quarter each.
Tributary width = 28 ft ÷ 2 = 14 ft
Step 2 — Uniform load on the beam
Total roof load = 15 psf dead + 25 psf live/snow = 40 psf
w = 14 ft × 40 psf = 560.00 plf
Step 3 — Maximum bending moment
M = w L² ÷ 8 = 560.00 × 16² ÷ 8 = 17,920.00 lb-ft
Convert to lb-in for use with Fb in psi: 17,920.00 × 12 = 215,040.0 lb-in
Step 4 — Allowable stresses
LVL 2.0E (1¾ in plies): Fb = 2,600 psi, Fv = 285 psi, E = 2,000,000 psi
Load duration factor CD = 1.15 → Fb' = 2,990.0 psi, Fv' = 327.8 psi
This product also takes a depth factor of (12 ÷ d)^0.136, applied per depth below.
Step 5 — Required section modulus
S required = M ÷ Fb' = 215,040.0 ÷ 3,097.7 = 69.418 in³
Step 6 — Deflection limit
Allowable Δ = L ÷ 240 = 16 × 12 ÷ 240 = 0.8000 in
Δ = 5 w L⁴ × 1728 ÷ (384 E I), so I required = 516.10 in⁴
The 1728 converts w in plf and L in feet to inches (12⁴ ÷ 12).
Step 7 — Shear
V = w L ÷ 2 = 560.00 × 16 ÷ 2 = 4,480.00 lb
fv = 1.5 V ÷ (b d) for a rectangular section.
Result — smallest adequate section
LVL 2.0E (1¾ in plies): 1-ply 1.75 × 18 in
S = 94.50 in³, I = 850.5 in⁴
Bending 80.4% · Shear 65.1% · Deflection 60.7% of allowable
Governing check: bending
What a Ridge Beam Carries
A structural ridge beam holds up the top ends of the rafters, so it carries the roof load from half the building width on each side, its tributary width. That load spreads along the beam, which spans between posts and bends most at mid-span.
A preliminary sizing aid, not a structural design
A ridge beam is a load-bearing member, and its failure can collapse a roof. Use this to check feasibility, compare materials and understand which limit binds — then have any beam you intend to build verified and stamped by a licensed engineer or architect, and confirmed against your local building code. The calculator applies the load duration factor and, for LVL, the depth factor; a full design also considers beam stability, bearing area, wet service and temperature, notching, and volume or repetitive-member factors, all of which can reduce capacity.
How Ridge Beam Sizing Works
A ridge beam carries the top ends of the rafters, so it picks up half the roof load: a simple gable splits the weight three ways, with a quarter going to each exterior wall. Half the building width is therefore the tributary width, and multiplying it by the roof load in pounds per square foot gives the uniform load the beam has to carry in pounds per linear foot.
From there the sizing is three separate questions, not one. Can the section resist the bending moment without overstressing the fibres? Can it resist the horizontal shear near the supports? And will it deflect less than the limit, so ceilings do not crack and the roof line stays straight? A section can pass one comfortably and fail another badly.
This matters more than it sounds. Across spans from 6 to 30 feet and loads from 100 to 1,200 plf, deflection governed 69.4% of cases, bending 16.3% and shear 14.3%. A calculator that sizes on bending alone — as the usual textbook formula invites — would be wrong most of the time, and unsafe at short spans where shear bites.
Ridge Beam Formulas
1. Load on the Beam
2. Bending
3. Deflection
4. Horizontal Shear
Two Unit Conversions You Cannot Skip
Both of these appear in almost every published statement of the formulas, usually unmentioned, and both fail in the dangerous direction — they make a beam look stronger than it is.
S = M ÷ Fb needs M in pound-inches. Allowable bending stress is quoted in psi, pounds per square inch, but wL²/8 produces pound-feet. On Example 1 the correct required section modulus is 69.42 in³; dividing the pound-feet figure straight by Fb gives 5.78 in³, understating the requirement by exactly 12 times.
The deflection formula needs 1728. Written as 5wL⁴/(384EI) it expects the load in pounds per inch and the span in inches. Keeping plf and feet requires multiplying by 12⁴ ÷ 12 = 1728. A 2-ply 1¾ × 11⅞ under Example 1's load deflects 0.845 in; omit the constant and you compute 0.000489 in, so every section passes every limit.
Which Check Governs, and When
Utilisation of a 2-ply 1¾ × 11⅞ LVL at 560 plf, as a percentage of allowable:
| Span | Bending | Shear | Deflection | Governs |
|---|---|---|---|---|
| 6 ft | 12% | 18% | 6% | shear |
| 8 ft | 22% | 25% | 13% | shear |
| 10 ft | 34% | 31% | 26% | bending |
| 12 ft | 49% | 37% | 45% | bending |
| 14 ft | 67% | 43% | 71% | deflection |
| 16 ft | 87% | 49% | 106% | deflection |
| 18 ft | 110% | 55% | 150% | deflection |
For this section and load the crossovers fall at about 9.05 ft from shear to bending, and 13.25 ft from bending to deflection. The reason deflection takes over is that it grows with the fourth power of span while moment grows with the square — doubling a span multiplies deflection by sixteen and the moment by only four.
What Changes the Answer Most
- Span, overwhelmingly. Deflection scales with L⁴, so a 20% longer span needs roughly twice the stiffness. Adding one intermediate post is usually far cheaper than the deeper beam it saves.
- Depth beats width. Section modulus goes with d² and stiffness with d³, but both are only linear in width. One 18 in deep member outperforms three 11¼ in plies at half the cross-section.
- Snow load, not dead load. Dead load is typically 10–20 psf, while ground snow reaches 70 psf and beyond in cold regions. Get the design load from your building department rather than estimating it.
Reference Design Values
| Material | Fb (psi) | Fv (psi) | E (psi) |
|---|---|---|---|
| Douglas Fir-Larch No. 2 | 900 | 180 | 1,600,000 |
| Hem-Fir No. 2 | 850 | 150 | 1,300,000 |
| Southern Pine No. 2 | 975 | 90 | 1,600,000 |
| LVL 2.0E | 2,600 | 285 | 2,000,000 |
| Glulam 24F-1.8E | 2,400 | 265 | 1,800,000 |
Worth noting Southern Pine's shear value of 90 psi — half that of Douglas Fir-Larch — despite a higher bending value. On short, heavily loaded spans where shear governs, the stronger-sounding species is the weaker choice. LVL bending values also fall with depth, by a factor of (12/d)0.136, which the calculator applies per depth.
These are reference values before adjustment. Multiply by the load duration factor CD: 1.15 for snow, 1.25 for roof live and construction loads, 0.9 for dead load alone. CD adjusts strength only — deflection is unaffected, because the modulus of elasticity does not change with how long a load sits there.
Uniform Load by Building Width
Load on the ridge beam in pounds per linear foot, as tributary width × total roof load:
| Width | Tributary | 30 psf | 40 psf | 50 psf | 60 psf |
|---|---|---|---|---|---|
| 20 ft | 10 ft | 300 | 400 | 500 | 600 |
| 24 ft | 12 ft | 360 | 480 | 600 | 720 |
| 28 ft | 14 ft | 420 | 560 | 700 | 840 |
| 32 ft | 16 ft | 480 | 640 | 800 | 960 |
| 36 ft | 18 ft | 540 | 720 | 900 | 1,080 |
| 40 ft | 20 ft | 600 | 800 | 1,000 | 1,200 |
Example Calculations
Two engineered-wood examples and one in dimensional lumber:
Example 1 — 28 ft Building, 16 ft Span, 40 psf
Dead load 15 psf plus snow 25 psf, LVL 2.0E, snow duration, L/240.
Tributary width = 28 ÷ 2 = 14 ft
w = 14 × 40 = 560 plf
M = 560 × 16² ÷ 8 = 17,920 lb-ft = 215,040 lb-in
S required = 215,040 ÷ 3,097.7 = 69.42 in³
V = 560 × 16 ÷ 2 = 4,480 lb
Smallest by material: 1-ply 1¾ × 18 in LVL
Bending 80.4% · shear 65.1% · deflection 60.7% — bending governs
Example 2 — 24 ft Building, 12 ft Span, 50 psf
Dead load 15 psf plus snow 35 psf, LVL 2.0E, snow duration, L/240.
Tributary width = 24 ÷ 2 = 12 ft
w = 12 × 50 = 600 plf
M = 600 × 12² ÷ 8 = 10,800 lb-ft = 129,600 lb-in
S required = 41.84 in³, I required = 233.28 in⁴
Smallest by material: 1-ply 1¾ × 14 in LVL
A 2-ply 1¾ × 11⅞ also works, at 52.6% utilisation
So does a 3-ply 1¾ × 9¼, at 67.4% — all three are valid
Example 3 — Short Span in Dimensional Lumber
24 ft building, 10 ft span, 40 psf total, Douglas Fir-Larch No. 2.
w = 12 × 40 = 480 plf
M = 480 × 10² ÷ 8 = 6,000 lb-ft = 72,000 lb-in
Fb = 900 psi × CD 1.15 = 1,035 psi
Smallest by material: 3-ply 1½ × 11¼ (a built-up 2x12)
Bending 73.3% · shear 34.4% · deflection 25.3%
Bending governs, with deflection barely a quarter used
At this span built-up lumber is adequate without engineered wood
Reading the Result Honestly
The single most important check is whether you have a ridge beam at all. Tributary width of half the building width assumes the ridge is load-bearing and supported at both ends; a ridge board in a properly tied rafter system carries almost no vertical load, because opposing rafters resolve their thrust against each other. Confusing the two in either direction causes trouble — oversizing harmlessly in one case, and leaving a roof without the member it needs in the other. Then follow the load down: the reaction at each end, around 4,480 lb in Example 1, has to be carried by a post or wall with adequate bearing area and a continuous path to the foundation, and none of that is checked here. Bearing failure at the supports is a common real-world problem even when the beam itself is sound. Loads are taken as acting on the horizontal projection, which is the standard convention for psf roof loads; if your dead load is quoted per square foot of roof surface, scale it up by the slope factor the calculator reports. Finally, a built-up beam only acts as one member if the plies are fastened to share load, so follow the manufacturer's nailing or bolting schedule exactly. This is general guidance for preliminary sizing, not a structural design, and not a substitute for a licensed engineer.
Frequently Asked Questions
- How do you size a ridge beam?
- Work out the uniform load on the beam, then check three things: bending, horizontal shear and deflection. Take the tributary width as half the building width, multiply by the total roof load in psf to get the load per linear foot, find the moment as wL²/8, and compare the stresses and deflection of a trial section against its allowable values. The smallest section that passes all three checks is the answer.
- What is tributary width for a ridge beam?
- Half the building width. A simple gable splits the roof load three ways: the ridge beam takes half, and each exterior wall takes a quarter. For a 28 ft wide building the tributary width is 14 ft, so a 40 psf roof puts 560 pounds per linear foot on the beam.
- What is the difference between a ridge beam and a ridge board?
- A ridge beam is a structural member that carries load and must be supported at both ends, usually by posts running down to the foundation. A ridge board is just a nailing surface, and the rafters on either side resist each other through rafter ties so the ridge carries almost no vertical load. This calculator sizes a ridge beam. IRC R802.4.4 requires a ridge beam rather than a board on roofs below 3:12.
- Why does the moment need converting to lb-inches?
- Because allowable bending stress Fb is quoted in psi, which is pounds per square inch. The formula wL²/8 gives a moment in pound-feet, so dividing it straight by Fb understates the required section modulus by exactly 12 times. On Example 1, the right answer is 69.42 in³ and the wrong one is 5.78 in³ — a mistake that would size a dangerously small beam.
- What is the 1728 in the deflection formula?
- It converts units. The formula 5wL⁴/(384EI) needs the load in pounds per inch and the span in inches, because E is in psi and I is in in⁴. If you keep the load in plf and the span in feet, you must multiply by 12⁴/12 = 1728. Leaving it out understates deflection by 1728 times, which would make any beam appear to pass.
- Does bending always govern ridge beam design?
- No, and assuming it does is a common error. Sweeping spans from 6 to 30 ft against loads from 100 to 1,200 plf for a 2-ply LVL, deflection governed 69.4% of cases, bending 16.3% and shear 14.3%. Short spans tend to be shear-limited, mid spans bending-limited and long spans deflection-limited, so all three have to be checked.
- What deflection limit should I use?
- L/240 is the usual total-load limit for roof beams, and L/360 is standard where a plaster or drywall ceiling hangs below, because stiffer limits prevent visible cracking. Live-load deflection is checked against L/360 in its own right. For a 16 ft span, L/240 allows 0.800 in and L/360 allows 0.533 in.
- What is the load duration factor?
- Wood carries short-duration loads at higher stress than permanent ones, so allowable stresses are multiplied by CD. Snow is 1.15, roof live and construction loads are 1.25, and dead load alone is 0.9. The shortest-duration load in a combination sets the factor. Note that CD adjusts strength only — it has no effect on deflection, since the modulus of elasticity does not change with duration.
- Can I use dimensional lumber or do I need LVL?
- It depends on span and load. At a 10 ft span with 480 plf, a built-up three-ply 2x12 in Douglas Fir-Larch works with bending at 73% of allowable. Push the same material to a 16 ft span at 560 plf and nothing up to four plies of 2x12 passes, because deflection runs away with the fourth power of span. That is the point at which LVL or glulam earns its cost.
- Is this calculator enough to build from?
- No. It is a preliminary sizing aid for checking feasibility and comparing options. A ridge beam is a load-bearing member whose failure can collapse a roof, and a real design also accounts for beam stability, bearing area at the supports, wet service and temperature conditions, notching, volume and repetitive-member factors, and the full load path down to the foundation. Have any beam you intend to build verified and stamped by a licensed engineer or architect.