Wood Beam Span Calculator
Enter your beam species, grade, nominal size, span, and load to instantly check whether the beam passes deflection, bending stress, and shear stress requirements. Results follow the NDS (National Design Specification for Wood Construction) and include the actual stress values versus allowable limits, so you can see exactly how much capacity remains.
How to size a wood beam using this calculator
Select your wood species and lumber grade, then pick a nominal cross-section width and depth. Enter the clear span between supports and the total uniformly distributed load (UDL) the beam must carry - this should include both dead loads (beam self-weight, decking, framing) and live loads (occupants, furniture, snow). Choose a deflection limit criterion for your application: L/360 is standard for most floor beams, while roof purlins and rafters often use L/240. The calculator instantly checks three NDS criteria and shows how close each one is to its limit. If any check fails, increase the section depth (the most effective fix), upgrade the lumber grade, choose a stiffer species, or reduce the span.
Three checks the NDS requires: deflection, bending, and shear
A wood beam must satisfy all three limit states simultaneously. Deflection controls the stiffness of the floor or roof - excessive sag causes cracked plaster, stuck doors, and a bouncy feel underfoot. The standard check is that midspan deflection under live load does not exceed L/360, where L is the span length. Bending stress is the tension-compression couple that resists the sagging moment; the required stress fb = M/S must not exceed the adjusted allowable Fb'. Shear stress acts horizontally along the grain near the supports; the required value fv = 1.5V/(bd) must stay below the adjusted allowable Fv'. Deflection governs for long, lightly loaded spans; bending governs for typical floor beams; shear rarely governs except for very short, heavily loaded beams.
NDS adjustment factors: CD, CM, and CF
The NDS adjusts reference design values by several factors before comparing them to the required stress. The load duration factor CD accounts for the ability of wood to carry larger stresses over shorter periods - floor live loads (10-year duration) use CD = 1.0, while a short-term construction load uses CD = 1.25. The wet service factor CM reduces Fb and Fv when lumber is used in a wet environment such as an exposed deck or outdoor bridge; for most indoor framing CM = 1.0. The size factor CF reduces the bending design value for deeper sections - below 12" nominal depth CF = 1.0, so it only matters for large timbers. Multiplying the reference design value by all applicable factors gives the adjusted design value Fb' or Fv'. This calculator applies CD, CM, and CF automatically based on your selections.
Choosing the right deflection limit
The deflection limit L/n controls how stiff the beam must be. For roofs with no brittle finish below, L/120 or L/180 is often acceptable. For floor beams under ordinary occupancy, L/360 is the most common code requirement. Beams supporting tile, stone, or other crack-sensitive finishes should use L/480 or even L/600. Note that the deflection check normally applies only to live load deflection, not total load deflection, which includes dead load as well - this calculator uses the total UDL input you provide, so for a strict L/360 live-load-only check, enter only the live load portion. Always verify with the local building code, which may specify different limits for your application.
NDS reference design values by species group (dry service, No. 2 grade)
| Species | Fb (psi) | Fv (psi) | E (psi) |
|---|---|---|---|
| Douglas Fir-Larch | 900 | 180 | 1,900,000 |
| Hem-Fir | 850 | 150 | 1,600,000 |
| Spruce-Pine-Fir | 775 | 135 | 1,500,000 |
| Southern Pine | 1000 | 175 | 1,800,000 |
| Eastern Spruce | 700 | 120 | 1,400,000 |
| Alaska Cedar | 800 | 155 | 1,400,000 |
| Western Red Cedar | 600 | 110 | 1,100,000 |
| Ponderosa Pine | 675 | 120 | 1,300,000 |
Fb = allowable bending stress, Fv = allowable shear stress, E = modulus of elasticity. Values in psi.
Frequently asked questions
What is the maximum span for a 4x10 Douglas Fir No. 2 floor beam carrying 200 lb/ft?
A 4x10 Douglas Fir-Larch No. 2 beam carrying 200 lb/ft (16.7 lb/in) at L/360 deflection will pass at roughly 10-11 feet with a comfortable margin and begin to fail around 13-14 feet depending on the adjusted design values and load duration. Use this calculator with your specific inputs to get the exact utilization ratios for your situation.
Why does the calculator use nominal dimensions like 2x10 but actual dimensions like 1.5" x 9.25"?
Dimensional lumber is sold by nominal size but surfaced to a slightly smaller actual size. A 2x10 is actually 1.5 inches wide by 9.25 inches deep, and those are the dimensions that determine structural capacity. All NDS formulas use actual dimensions, so the calculator automatically converts nominal to actual for you.
What does L/360 mean?
L/360 means the maximum allowable deflection equals the span length divided by 360. For a 12-foot (144-inch) beam, L/360 = 0.4 inches. It is the most widely used deflection limit for residential floor systems. Stricter limits such as L/480 or L/600 are used where cracking of finishes or vibration is a concern. Roofs and non-brittle assemblies often allow L/240 or L/180.
Does this calculator work for point loads or cantilevers?
No - this calculator is designed for a simple span (two end supports) carrying a uniformly distributed load. Point loads and cantilevers have different moment and deflection formulas. For those cases, a structural engineering reference or a licensed structural engineer should be consulted. The concentrated-load version of the deflection formula is PL³/(48EI) at midspan, significantly different from the UDL formula used here.
How do I account for beam self-weight in the UDL?
Add the beam self-weight per linear foot to your applied loads. Douglas Fir-Larch weighs roughly 35 lb/ft³, so a 4x10 (actual 3.5" x 9.25") has a cross-section area of 32.4 in² = 0.225 ft² and weighs about 7.9 lb/ft. For most residential beams the self-weight is less than 5% of the total load, but it should still be included for accuracy.
What is the load duration factor (CD) and why does it matter?
Wood can carry higher stresses for shorter time periods without failure. The NDS captures this with the load duration factor CD. For dead loads that act permanently, CD = 0.9. For typical floor live loads (assumed 10-year occupancy), CD = 1.0. Snow loads (2-month average) use CD = 1.15, and short-term construction loads use CD = 1.25. Wind and seismic use CD = 1.6. Applying the correct CD can meaningfully increase the allowable stress and may be the difference between pass and fail for a time-limited load case.
When does shear stress govern beam design?
Horizontal shear stress governs primarily for short, heavily loaded beams - typically spans under 6 feet with large concentrated loads or very high UDL values. For most typical floor and roof beams (spans of 8-20 feet), bending or deflection will govern. Shear capacity can be improved by widening the beam or choosing a species with a higher Fv reference design value, such as Douglas Fir-Larch or Southern Pine.