What a joist span is, and what limits it
The span is the clear distance between the faces of the supports — from the inside face of the sill plate to the inside face of the girder, not the overall length of the stick you cut. A 2×10 that runs 15 ft 5 in clear will be cut at 16 ft or more so it can bear on the plate at each end. Every span table in every code book is written in clear span, and the single most common way to fail an inspection is to read the table in overall length.
Two separate things limit that distance. The first is strength: bend the joist far enough and the extreme fibres at the bottom reach their allowable stress. The second is stiffness: long before a floor is anywhere near breaking, it becomes unpleasant. Dishes rattle, a crack opens along a tile grout line, and people describe the floor as bouncy. Building codes control that with a deflection limit written as a fraction of the span — L/360 means the floor may sag no more than the span divided by 360 under live load, which is about half an inch over a 15 ft span.
Which of the two governs is not a fixed property of the lumber. Shallow joists at wide spacing usually run out of bending capacity first; deep, tightly spaced joists in a stiff species usually hit the deflection limit first. This calculator solves both and tells you which one is doing the work, because the two respond to completely different fixes.
The two equations, and where each factor comes from
A floor joist is a simply supported beam carrying a uniform load. The maximum bending moment is M = wL² ÷ 8 at mid-span, and the maximum deflection is Δ = 5wL⁴ ÷ (384EI). Setting each equal to its limit and solving for L gives the two expressions above.
The load w is per joist, not per square foot. Each joist carries a strip of floor one spacing wide, so a 40 psf live load at 16 in on centre puts 40 × (16/12) = 53.3 pounds on every foot of joist. Divide by 12 again to get pounds per inch, which is what you need when E is in psi and lengths are in inches. That is where the 144 in the calculator's load step comes from.
Section properties come from the dressed size. A 2×10 measures 1½ in by 9¼ in, so its section modulus is 1.5 × 9.25² ÷ 6 = 21.39 in³ and its moment of inertia is 1.5 × 9.25³ ÷ 12 = 98.93 in⁴. Notice the exponents: bending capacity grows with depth squared, and stiffness with depth cubed. Doubling the number of joists halves the load on each and buys you 41% more bending span; going one size deeper buys far more than that.
Fb gets adjusted before you use it. The tabulated bending value in the NDS Supplement is multiplied by the repetitive-member factor Cr = 1.15, which applies to three or more members not more than 4 in thick spaced no more than 24 in apart and joined by a load-distributing sheathing — that is, an ordinary floor. It is also multiplied by the size factor CF, which rewards shallow members: 1.3 for a 2×6, 1.2 for a 2×8, 1.1 for a 2×10 and 1.0 for a 2×12 in the common visually graded grades. The load-duration factor is 1.0 for floor live load, so it does not appear.
Deflection is checked against live load alone. That is the convention the published span tables are built on: dead load causes an initial set that gets levelled out during construction, while live load is what moves under your feet. E is not adjusted by Cr or CF.
Worked example: a 2×10 SPF joist at 16 in on centre
You are framing a living room floor with Spruce-Pine-Fir No.1/No.2 2×10s at 16 in on centre, 40 psf live and 10 psf dead, checked at L/360.
- Section properties. b = 1.5 in, d = 9.25 in. S = 1.5 × 9.25² ÷ 6 = 21.391 in³. I = 1.5 × 9.25³ ÷ 12 = 98.932 in⁴.
- Adjusted bending value. Fb = 875 psi. Fb′ = 875 × 1.15 × 1.1 = 1,106.9 psi.
- Load per joist. Total: (40 + 10) × 16 ÷ 144 = 5.5556 lb/in. Live only: 40 × 16 ÷ 144 = 4.4444 lb/in.
- Bending span. L = √(8 × 1,106.9 × 21.391 ÷ 5.5556) = √34,094 = 184.65 in = 15.39 ft.
- Deflection span. L = ∛(384 × 1,400,000 × 98.932 ÷ (5 × 360 × 4.4444)) = ∛6,648,215 = 188.03 in = 15.67 ft.
- Allowable span. The smaller of the two: 15.39 ft, or 15 ft 4⅝ in. Bending governs, by about three inches.
Now check the floor you actually intend to build. At a 14 ft clear span, L = 168 in, and the live-load deflection is 5 × 4.4444 × 168⁴ ÷ (384 × 1,400,000 × 98.932) = 0.333 in. As a ratio that is 168 ÷ 0.333 = L/505, comfortably stiffer than the L/360 minimum and stiff enough for most tile installations. The span is 14 ÷ 15.39 = 91% of allowable.
The bay is 12 ft wide, so the layout is ⌊144 ÷ 16⌋ + 1 = 10 joists, 140 lineal feet of 2×10. Add two 12 ft rim boards and one row of blocking — nine pieces at 14½ in — for another 34.9 lineal feet.
How to read the result
Treat the allowable span as a ceiling, not a target. A floor built at 99% of its allowable span meets code and will still feel livelier than most clients expect, because L/360 was chosen to protect finishes rather than to guarantee comfort. If you want a floor that feels solid underfoot, design to L/480. Because the deflection span varies with the cube root of the limit, tightening from L/360 to L/480 costs at most (360 ÷ 480)^⅓ = 9% of the span, and less than that whenever bending is the governing check.
Use the governing check to choose your fix. If bending governs, more depth, a higher grade or tighter spacing all help. If deflection governs, only depth, stiffness and spacing help — paying for a No.1 grade instead of No.2 buys you a higher Fb and almost no extra E, so the span barely moves. That single distinction saves a lot of money on lumber orders.
Where the finish is brittle, tighten the limit. The Tile Council of North America handbook calls for L/360 under ceramic tile and L/720 under natural stone, both measured under live load — and L/720 is a demanding number that usually needs engineered joists or a much tighter layout. Sistering, adding a mid-span beam, or switching to I-joists are the usual answers.
Finally, remember that this calculator sizes a joist. The girder or beam that the joists land on carries half of every joist it supports and must be sized separately — start with the beam section modulus calculator and check its movement with the beam deflection calculator. Openings in the floor need trimmers and headers, which the header size calculator covers.
Allowable clear spans, Spruce-Pine-Fir No.1/No.2
| Joist | 12 in o.c. | 16 in o.c. | 19.2 in o.c. | 24 in o.c. |
|---|---|---|---|---|
| 2×6 | 10′ 3″ (d) | 9′ 3″ (d) | 8′ 9″ (d) | 8′ 1″ (b) |
| 2×8 | 13′ 6″ (d) | 12′ 3″ (d) | 11′ 5″ (b) | 10′ 3″ (b) |
| 2×10 | 17′ 2″ (d) | 15′ 4″ (b) | 14′ 0″ (b) | 12′ 6″ (b) |
| 2×12 | 20′ 7″ (b) | 17′ 10″ (b) | 16′ 3″ (b) | 14′ 6″ (b) |
(b) bending governs, (d) deflection governs. Published code span tables are generated from the same equations; where a table and a calculation disagree by an inch or two, the table in the code adopted by your jurisdiction is what the inspector will use.
This is a design aid, not a stamped design
The equations here are the standard mechanics used in the AWC National Design Specification for Wood Construction and the reference design values are those published in the NDS Supplement. They check bending and live-load deflection only. A complete design also checks horizontal shear, bearing area at the supports, notches and bored holes, concentrated and partition loads, cantilevers, and connections. Where a floor carries a bearing wall, a hot tub, a masonry hearth or a stair landing, or where the joists are cut or drilled, have the design confirmed by an engineer and check it against the code edition your jurisdiction has adopted.
Assumptions and common mistakes
- Reading overall length instead of clear span. The span is between support faces. Cut the joist longer.
- Using a single span table for a continuous joist. A joist running over a centre girder is two spans, not one. Each span is checked separately, and the negative moment over the support changes the picture.
- Ignoring the dead load of the finish. Ten psf covers framing, subfloor and carpet. A mortar bed and stone tile can double it, and dead load feeds the bending check directly.
- Assuming a higher grade fixes a deflection problem. Grade mostly raises Fb, not E. If deflection governs, go deeper or closer.
- Forgetting bearing. Most codes want at least 1½ in of bearing on wood or metal and 3 in on masonry. A joist can be strong enough and still crush at the end.
- Notching or drilling in the wrong place. Holes near the top or bottom edge, or notches in the middle third, remove capacity the calculation assumes is there.
- Applying dry-service values to a wet location. Joists that stay above 19% moisture content — over a crawl space with no vapour retarder, or in an open deck — need wet-service adjustment factors this calculator does not apply.
- Building at 100% of allowable and expecting a quiet floor. Code minimum protects the finishes, not your comfort.
Sawn lumber, engineered joists and the code tables
Solid sawn joists are only one option, and they are the one with the shortest spans. Wood I-joists and open-web floor trusses reach much further at the same depth because they put material where the stresses are, and their manufacturers publish span tables tied to specific products; those tables replace this calculation entirely, since the flange and web properties are proprietary. Laminated veneer lumber sits between the two.
Prescriptive code span tables exist so that a builder does not have to run these equations for every floor. They are generated from exactly the arithmetic on this page, then rounded and constrained to a set of standard load cases. Because they bake in assumptions about grade, moisture, spacing and load, they are conservative for some situations and simply unavailable for others — a 50 psf commercial live load, an unusual species, or an L/480 target. That is when calculating directly earns its keep.
Once the joists are settled, the rest of the floor follows: subfloor sheeting from the plywood sheet calculator, the lumber volume from the board foot calculator, and the walls that sit on the deck from the wall stud count calculator.