Green = meets your target span · red = too short · ★ = lightest size that works at 16" o.c. Click any cell to inspect it. "o.c." = on-centre spacing.
Diagram
How a joist is sized — the four checks & the factors
A floor or deck joist is a simple beam: supported at two ends, carrying an even (uniform) load across its span. To pick a size you check it four ways and the worst one governs.
1 · Bending (does it break?)
Load bends the joist; the moment is greatest at mid-span: M = wL²/8. The bending
stress fb = M/S must stay under the wood's allowable Fb'.
S (section modulus) grows with the square of depth — which is why a 2x10 is far
stronger in bending than a 2x8, not just 2 inches taller.
2 · Shear (does it tear near the supports?)
Vertical shear peaks at the supports: V = wL/2, with fv = 1.5V/A.
For ordinary residential floor spans this rarely governs — but it does on short, heavily-loaded joists.
3 · Live-load deflection (does it bounce?)
Δ = 5wL⁴/(384EI), limited to L/360 for floors. Deflection scales with the
fourth power of span, so it usually governs longer, shallower joists — and it's what makes a
floor feel "stiff" or "springy." Note it uses E and I (stiffness), not strength,
so a stiffer species helps here even at the same grade.
4 · Total-load deflection
Same formula with live + dead load, limited to L/240 — guards against long-term sag.
The adjustment factors
- CF — size factor: deeper sawn members get a small bending penalty (2x6 → 1.3, 2x8 → 1.2, 2x10 → 1.1, 2x12 → 1.0). Southern Pine bakes this into size-specific values instead.
- Cr — repetitive member: +15% to bending when ≥3 joists at ≤24" o.c. share load through sheathing. On by default — it's why joisted floors out-perform a lone beam.
- CM — wet service: exterior/damp lumber loses strength & stiffness (Fb ×0.85, E ×0.9). Turned on automatically for decks.
- CD — load duration: 1.0 for normal floor occupancy (this tool's default).