The Floor Joist Span Calculator calculates how far a wood floor joist can span, based on the lumber size, joist spacing, floor loads and the wood’s strength and stiffness.
It finds two limits — bending strength, L = √(8 × Fb′ × S ÷ w), and deflection under live load, L = ∛(384 × E × I ÷ (5 × w_LL × limit)) — and reports the shorter one as the maximum span.
Floor Joist Span Calculator
Maximum span of a wood floor joist or beam from its size, spacing, wood strength and floor loads — checking bending and deflection.
Formula
- Section modulus: S = b × d² ÷ 6; moment of inertia: I = b × d³ ÷ 12
- Load per joist: w = (LL + DL) × spacing; live load only: w_LL = LL × spacing
- Bending limit: L_b = √(8 × Fb′ × S ÷ w)
- Deflection limit: L_d = ∛(384 × E × I ÷ (5 × w_LL × limit))
- Maximum span: min(L_b, L_d)
Where b, d = actual joist width and depth, LL and DL = live and dead loads, Fb′ = adjusted bending stress, E = modulus of elasticity, limit = 360 for L/360.
How the Calculation Works
Step 1: Convert the floor loads (psf) to a line load on each joist using the spacing.
Step 2: Solve the simple-beam formulas for the span at which bending stress reaches Fb′, and at which live-load deflection reaches span ÷ limit.
Step 3: The smaller span governs.
Variables Explained
| Input | Meaning |
|---|---|
| Joist size | Actual dimensions, e.g. a 2×10 is 1½ × 9¼ in |
| Spacing | On-center distance, e.g. 16 in |
| Live, dead load | Design loads in psf (from your code) |
| Fb′, E | Adjusted design values for your species and grade |
| Deflection limit | L/360 is common for floors; stiffer limits suit tile |
Example Calculation
Given: 2×10 (1.5 × 9.25 in) at 16 in o.c., 40 psf live + 10 psf dead, Fb′ = 1,138 psi, E = 1,600,000 psi, L/360
Bending limit ≈ 15.60 ft; deflection limit ≈ 16.38 ft
Result: maximum span ≈ 15.6 ft (bending governs)
Engineering Assumptions
- Simple span, uniform load, bending and deflection checks only (no shear, bearing or vibration check).
- Fb′ must already include the adjustment factors for your case (size, repetitive member, load duration, moisture).
- Building codes publish joist span tables for common species and grades; for permitted work, use those or an engineer’s design.
Formula Variations
Engineered I-joists and LVL use manufacturer span tables rather than these formulas. Continuous joists over a support, or point loads, need a different analysis.
Units and Dimensions
Enter inches, psf and psi, or metric units (mm, kPa, MPa); the result can be shown in feet or meters.
Frequently Asked Questions
How far can a 2×10 span?
It depends on species, grade, spacing and loads — enter your values, or check your code’s span table.
What does L/360 mean for joists?
Live-load deflection may not exceed the span divided by 360.
Does closer spacing increase span?
Yes — each joist carries less load.
Why does bending or deflection govern?
Shorter, deeper joists are often limited by bending; longer spans are often limited by deflection.
Can I use this for deck joists?
The method is the same, but decks have their own code requirements and wet-service adjustments.