A floor joist has to satisfy three separate limits, and which one controls changes with the span. Short joists are usually limited by shear, medium spans by bending, and long spans almost always by deflection — the floor bounces long before anything is close to breaking. The floor joist calculator above runs all three, prints the applied value against the allowable for each, names the one that governs, and separately gives you the joist count, blocking and rim length for the floor. It is a preliminary sizing and teaching tool. It is not a structural design, it is not stamped, and it does not replace a licensed engineer or the span tables your building official accepts.
Arb Digital publishes it as part of a free structural and construction library. Every material property it uses is an input, not a built-in table, and the reason is set out below. If you want the beam version of the same problem, our wood beam span calculator and beam deflection calculator cover single members rather than a repeating floor system.
Which Code This Follows, and What It Cannot Do
The checks here are allowable stress design for a simply supported, uniformly loaded sawn timber joist. That is the format used by the National Design Specification for Wood Construction, published by the American Wood Council and referenced by the International Building Code. Required live and dead loads, deflection limits, blocking and bridging requirements, notching and boring rules, bearing lengths and fire separation all come from the building code your jurisdiction has adopted — searchable through the ICC digital codes library — and adopted editions and amendments differ by state, province and country.
The tool applies no adjustment factors of its own. Design values for timber are modified for load duration, wet service, temperature, size, repetitive members, flat use, incising and more, and the correct combination depends on your species, grade, size and conditions. You enter values that are already adjusted, and the tool does the arithmetic. If you enter unadjusted tabulated values, the answer will be wrong in a direction you cannot predict. The American Wood Council's publications hub is where the standards and their span tables live.
How to Use It
- Enter the clear span, not the joist length. Face of support to face of support. A joist bearing 3 inches at each end on a 14 ft opening is a 14 ft clear span on a 14 ft 6 in piece of timber.
- Enter the actual joist dimensions. Dressed size, from your supplier. Depth matters enormously — it enters bending as a square and deflection as a cube.
- Enter adjusted design values for your species, grade and conditions, with the adjustment factors already applied.
- Enter the loads your code requires for the occupancy, and the deflection limits it specifies.
- Read the governing check, not the pass. The bar chart shows all three utilisations, and the largest one is the whole story.
The Formula / How It's Calculated
Load per joist is w = (live + dead) × spacing ÷ 12 pounds per linear foot. Then M = wL² ÷ 8, S = bd² ÷ 6 and the bending stress is fb = M ÷ S. Shear is V = wL ÷ 2 at the support and fv = 1.5V ÷ (bd) for a rectangular section. Deflection is Δ = 5wL⁴ ÷ (384 E I) with I = bd³ ÷ 12, computed twice — once on live load alone against the tighter limit, once on total load against the looser one.
Take the defaults: a 14 ft clear span, joists at 16 in on centre, actual section 1.5 by 9.25 in, 40 psf live and 10 psf dead. Load per joist is 50 × 16 ÷ 12 = 66.67 plf. The moment is 66.67 × 14² ÷ 8 = 1,633 lb-ft, the section modulus is 1.5 × 9.25² ÷ 6 = 21.39 in³, and the bending stress is 916 psi — 76.4 percent of the 1,200 psi entered. Shear works out at 466.7 lb and 50.4 psi, only 28.0 percent of the 180 psi allowable.
Deflection is where it gets interesting. With I = 98.93 in⁴ and E = 1,300,000 psi, the live load deflection is 0.358 in against an L/360 limit of 0.467 in — a utilisation of 76.8 percent, and an actual performance of L/469. Total load deflection is 0.448 in against an L/240 limit of 0.700 in, or 64.0 percent, giving L/375. So live load deflection governs this floor at 76.8 percent, narrowly ahead of bending at 76.4 percent. That closeness is typical, and it is exactly why running one check is not enough.
Why Depth Beats Everything Else
The three checks scale differently with the joist section, and the difference decides every real design. Shear capacity is proportional to the area, so it goes up linearly with depth. Bending capacity goes with the section modulus, bd² ÷ 6, so it goes up with the square. Stiffness goes with the second moment of area, bd³ ÷ 12, so it goes up with the cube.
Move from a 9.25 in deep joist to an 11.25 in one — nominal 2x10 to 2x12, a 22 percent increase in depth — and bending capacity rises 48 percent while stiffness rises 80 percent. Doubling the breadth instead, by sistering a second joist alongside, gives you exactly 100 percent more of all three, but it costs twice the timber and does far less per dollar than going deeper. Going deeper is almost always the efficient move, and it is why engineered joists are deep and thin rather than square.
Span works the other way and just as hard. Moment grows with the square of the span and deflection with the fourth power. Extending a 14 ft span to 16 ft — a 14 percent increase — raises the moment 31 percent and the deflection 71 percent. This is why a span that "nearly worked" almost never works after a small increase.
Deflection, Bounce and Why L/360 Is Not About Strength
Deflection limits are serviceability criteria, not strength criteria. A floor at exactly L/360 is nowhere near failing; it is simply at the point where the code judges the sag acceptable for a plastered ceiling underneath. The tighter live load limit exists because live load comes and goes and its deflection is visible as movement, while the looser total load limit accepts a permanent sag that includes creep under sustained dead load.
The complaint people actually make about floors is bounce, and bounce is not the same thing as deflection. It is a dynamic response governed by stiffness, mass and damping, and a floor can satisfy L/360 comfortably and still feel unpleasantly lively — particularly a long, lightly loaded span with no ceiling attached below. That is why many designers privately work to L/480 or tighter for residential floors, and why continuous blocking, a glued and screwed subfloor and a directly attached ceiling all improve the feel of a floor without changing a single number in this calculation.
Joist Count, Blocking and the Bits Around the Edges
The quantity side is arithmetic rather than analysis. The joist count is the floor width divided by the spacing, plus one, because a run of N spaces needs N+1 members. That count excludes the extras a real floor needs: doubled joists under parallel partitions, trimmers and headers around stair and chimney openings, and additional members where a bath or heavy fitting concentrates load. Each of those is a design decision, not a spacing decision.
Rim or band joists close the ends of the run and are counted as twice the floor width. Blocking or bridging rows run across the joists between them, and their total length is the floor width less the timber the joists themselves occupy. Whether blocking is required, and at what interval, comes from the code — but even where it is optional, a row at mid-span shares point loads between neighbouring joists and noticeably reduces bounce, which is a benefit this calculation does not capture.
What This Calculation Assumes, and When It Stops Being True
Every number above rests on a specific model: a single simply supported span, uniformly loaded, of a solid rectangular sawn section, laterally restrained along its compression edge by the subfloor, bearing adequately at both ends, dry, at normal temperature, and unnotched. Depart from any of those and the arithmetic no longer describes your floor.
The common departures are worth naming. A continuous joist over a mid-span beam has lower moments and much lower deflection than two separate spans, so treating it as simply supported is conservative but wasteful. A cantilever is a different calculation entirely. A point load — a bath, a stove, a partition running perpendicular — is not a uniform load and cannot be smeared into psf. A notch or a bored hole near a support removes shear capacity precisely where shear is highest, and codes restrict both tightly. An engineered I-joist or LVL is not a rectangular section and must be sized from the manufacturer's own tables, which account for web behaviour this formula knows nothing about. And a joist without lateral restraint to its compression edge can buckle sideways at a stress far below its bending capacity.
Arb Digital builds free, fast, search-friendly tools that bring builders, engineers and suppliers steady organic traffic. Browse the library or tell us what your customers keep asking you to work out.
Browse Free Tools Talk To Arb DigitalCommon Mistakes to Avoid
- Using the timber length as the span — clear span is face of support to face of support, and bearing length is not span.
- Entering nominal dimensions — a nominal 2x10 is 1.5 by 9.25 in, and using 2 by 10 overstates stiffness by more than half.
- Using unadjusted design values — tabulated figures must be modified for duration, service conditions, size and repetitive use before they mean anything.
- Checking bending only — deflection governs most residential floors, and a joist that passes bending can still produce a floor nobody wants to walk on.
- Notching or boring near a support — that is where shear is highest, and the codes restrict it for exactly that reason.
Related Free Tools From Arb Digital
For single members use the wood beam span calculator and the beam deflection calculator, for reactions the beam load calculator, and for section properties the section modulus calculator. Quantities come from the board foot calculator and the plywood sheet calculator, and the finished surface from the flooring calculator. Everything else is on the free online tools hub.
Frequently Asked Questions
That depends entirely on the species, grade, spacing, loads and deflection limit, which is why this tool takes all of them as inputs rather than answering from a table. With the defaults shown — 16 in centres, 40 psf live, 10 psf dead, an adjusted Fb of 1,200 psi and E of 1,300,000 psi — a 14 ft clear span works at 76.8 percent utilisation, governed by live load deflection.
Deflection, on most residential spans. Shear governs only very short heavily loaded spans, bending governs some medium ones, and once the span gets long the fourth-power growth of deflection overtakes everything. The tool runs all three and names the largest utilisation.
They are deflection limits expressed as a fraction of the span. L/360 is the tighter limit, normally applied to live load alone, and on a 14 ft span it allows 0.467 in. L/240 is looser, normally applied to total load, and allows 0.700 in on the same span. Both are serviceability criteria about appearance and feel, not about strength.
Deeper, almost always. Stiffness rises with the cube of depth but only linearly with breadth, so a 22 percent increase in depth buys 80 percent more stiffness while sistering a second joist buys 100 percent for twice the timber. Depth is far more efficient per dollar.
Divide the floor width by the spacing and add one, because a run of spaces needs one more member than it has gaps. A 20 ft wide floor at 16 in centres needs 16 joists. That count excludes doubled joists under partitions and trimmers around openings, which are separate decisions.
Because they depend on species, grade, size, moisture, temperature, load duration and repetitive use, and the correct combination of adjustment factors is specific to your situation. A value typed from memory into a free web page would be trusted and could be wrong, so it is an input with the source stated instead.
No. The formulas here describe a solid rectangular sawn section. An I-joist has a thin web and flanges that behave differently in shear and bending, and it must be sized from the manufacturer's own published tables for that specific product.
No. This is a preliminary check on a simplified model — one simply supported span, uniform load, no notches, adequate bearing and lateral restraint. Point loads, continuity, cantilevers, openings and connections all change the answer, and a licensed engineer or an accepted span table must confirm the design.
This tool performs preliminary structural checks for teaching and comparison only. It is not a structural design, it carries no engineering stamp, and it must not be used as a specification. Design values, adjustment factors, design loads, deflection limits and blocking requirements come from the standards and building code your jurisdiction has adopted, and a licensed structural engineer or an accepted span table must confirm any floor before it is built.
