Wood Beam Span Calculator — Max Joist & Rafter Span
Select the lumber size and species, enter the total load (live + dead) and joist spacing, and get the maximum safe span — governed by either bending stress or deflection, whichever is more limiting.
Nominal lumber size
Wood species / grade
psf
in
Deflection limit
ft
Governed by bending (bending limit 14.6 ft, deflection limit 769.6 ft)
- 1
Linear load (lbs/in)
50 × (16 ÷ 12) ÷ 12 = 5.556 - 2
Bending span limit (ft)
√(8 × 990 × 21.39 ÷ 5.556) ÷ 12 = 14.6 - 3
Deflection span limit (ft)
∛(384 × 1,600,000 × 98.93 × 360 ÷ (5 × 5.556)) ÷ 12 = 769.6 - 4
Maximum safe span
min(14.6, 769.6) = 14.6Governed by bending — the more restrictive of the two limits controls.
How does this calculator work?
Max span = min[√(8·Fb·CF·S / w), ∛(384·E·I·Δratio / (5·w))], where all quantities are in inches and lbs. Fb and E come from NDS 2018 No. 2 design values; w = load_psf × spacing_ft / 12 lbs/in. Results are approximate — consult an engineer for structural applications.
Formula
How this is calculated
A uniformly loaded simple beam fails first by either bending (the fibre stress exceeds the allowable value Fb) or by deflecting too much. The bending limit gives L ≤ √(8·Fb·S / w), where S = b·h²/6 is the section modulus. The deflection limit (e.g. L/360 for stiff floors) gives L ≤ ∛(384·E·I·ratio / (5·w)), where I = b·h³/12 is the moment of inertia and ratio is the denominator (360, 240 or 180). The more restrictive of the two governs. All calculations use consistent inch-pound units; the linear load w = total_psf × spacing_ft / 12 in lbs/in.
Design values (Fb and E) are taken from the 2018 NDS Supplement for No. 2 grade, visually graded Dimension Lumber, adjusted by the NDS size factor CF (1.5 for 2×4 up to 1.0 for 2×12 and deeper). Actual lumber dimensions use the standard dressed sizes: a 2×10 is 1½″ × 9¼″ actual, for example. The same set of formulas underlies published residential span tables, so results should broadly agree with NDS Table F1 for matching inputs.
Important limitations: this calculator applies to simply-supported, uniformly loaded single-span members only. It does not apply to cantilevers, multi-span beams, point loads, non-rectangular cross-sections, glulam, LVL or I-joists, or situations where load duration factors, wet-service corrections or bearing-area checks are needed. For code-compliant structural design, consult a licensed structural engineer.
Frequently asked questions
The most common residential assumption is 40 psf live load (people and furniture) plus 10–15 psf dead load (framing, subfloor, flooring) for a total of 50–55 psf. Heavier applications like a bedroom over a garage or a tiled bathroom floor may use 50 psf live load. Check your local building code for the required live-load value.
L/360 is the standard floor joist limit — it prevents cracking of brittle finishes like plaster or tile and feels solid underfoot. L/240 is common for roofs and ceiling joists where there is no plaster. L/180 is a relaxed limit sometimes allowed for rafters carrying only roofing material.
Published span tables sometimes use slightly different load assumptions, include repetitive-member factors (Cr = 1.15 for joists spaced ≤ 24″ and loaded in parallel), or apply different duration-of-load adjustments. This calculator uses unadjusted No. 2 design values without the repetitive-member factor, so it is slightly conservative compared to most residential span tables.
Also known as
TG we-Calculate Editorial Team. (2026). Wood Beam Span Calculator — Max Joist & Rafter Span [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/wood-beam-span-calculator
TG we-Calculate Editorial Team. "Wood Beam Span Calculator — Max Joist & Rafter Span." TG we-Calculate. 2026. https://we-calculate.com/calculator/wood-beam-span-calculator.
TG we-Calculate Editorial Team, "Wood Beam Span Calculator — Max Joist & Rafter Span," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/wood-beam-span-calculator
@misc{wecalculate_wood_beam_span_calculator, title = {Wood Beam Span Calculator — Max Joist & Rafter Span}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/wood-beam-span-calculator}}, year = {2026}, note = {TG we-Calculate} }
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