Floor joist span calculator
A span table is the answer to four separate checks — bending, shear, live-load deflection and total-load deflection — with the smallest one printed. This works all four out from the section and the design values you enter, so you can see which one is actually governing your joist.
Actual, not nominal: a 2x is 38 mm (1.5 in).
A 2x10 is 235 mm (9.25 in).
Residential floors are usually 1.9 kPa (40 psf).
Joists, subfloor and finish. 0.5 kPa is about 10 psf.
No.2 SPF is about 6.03 MPa (875 psi). Read yours off the grade stamp and the code table.
About 0.93 MPa (135 psi) for SPF.
About 9650 MPa (1,400,000 psi) for No.2 SPF.
- Allowable clear span
- 14.75 ft
- Limit from bending
- 4496
- Limit from shear
- 11 535
- Limit from live-load deflection
- 4811
- Limit from total-load deflection
- 5094
- Deflection at that span, total load
- 12.88
- Bending capacity used at that span
- 100.0 %
- Line load on one joist
- 0.9600 kN/m
- Section modulus
- 349 758 mm3
- Second moment of area
- 41 096 604 mm4
Show the working
- Joist breadth (actual) = 38
- Joist depth (actual) = 235
- Joist spacing, centre to centre = 400
- Live load = 1.9
- Dead load = 0.5
- Bending design value Fb = 6.03
- Shear design value Fv = 0.93
- Modulus of elasticity E = 9650
- Repetitive member factor = 1.15
- Live-load deflection limit = 360
- Total-load deflection limit = 240
- Section modulus = 38 * 235^2 / 6 = 349 758
- Second moment of area = 38 * 235^3 / 12 = 41 096 600
- w_live = 1.9 * 400 / 1000 = 0.76
- w_dead = 0.5 * 400 / 1000 = 0.2
- Line load on one joist = 0.76 + 0.2 = 0.96
- fb_adj = 6.03 * 1.15 = 6.9345
- moment_capacity = 6.9345 * 349 758 = 2 425 400
- Limit from bending = sqrt(8 * 2 425 400 / 0.96) = 4495.74
- Limit from shear = 4 * 0.93 * 38 * 235 / (3 * 0.96) = 11 534.6
- Limit from live-load deflection = (384 * 9650 * 41 096 600 / (5 * 360 * 0.76))^(1/3) = 4810.53
- Limit from total-load deflection = (384 * 9650 * 41 096 600 / (5 * 240 * 0.96))^(1/3) = 5094.14
- Allowable clear span = min(4495.74, 11 534.6, 4810.53, 5094.14) = 4495.74
- Allowable clear span = 4495.74 / 304.8 = 14.7498
- Deflection at that span, total load = 5 * 0.96 * 4495.74^4 / (384 * 9650 * 41 096 600) = 12.876
- Bending capacity used at that span = 0.96 * 4495.74^2 / 8 / 2 425 400 * 100 = 100
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- section modulus S = b d^2 / 6, second moment I = b d^3 / 12
- line load w = pressure x joist spacing
- bending: w L^2 / 8 = Fb Cr S, so L = sqrt(8 Fb Cr S / w)
- shear: w L / 2 = (2/3) Fv b d, so L = 4 Fv b d / (3 w)
- deflection: 5 w L^4 / (384 E I) = L / k, so L = cube root of 384 E I / (5 k w)
- allowable span = the smallest of the four
This is an engineering check, not a code table. It uses the design values you enter and ignores load duration, wet service, size, incising, temperature and notching factors, any one of which your code may require.
Bending and deflection here assume a simple span carrying a uniform load. A continuous joist over a mid-span beam, a point load, or a notch at the bearing all change the answer.
Shear is checked at the support rather than at a depth d away from it, which is what most codes actually permit, so the shear figure is on the conservative side.
Have anything structural checked by an engineer or your building department. Nothing computed here is an approval.
Frequently asked
How far can a 2x10 joist span?
With the defaults here — No.2 SPF at 400 mm (16 in) centres carrying 1.9 kPa live and 0.5 kPa dead — the answer is a little under 4.5 m (about 14 ft 9 in), and bending is what limits it, not deflection.
Why is my span shorter than the table in the code book?
Usually the design values. Code tables assume a specific species, grade and load duration; change Fb or E to match your grade stamp and the numbers line up. This page also checks shear at the support rather than a depth away from it, which shortens the shear limit slightly.
What does L/360 mean?
The joist may sag no more than its span divided by 360 under live load alone. Over a 4 m span that is 11 mm. L/480 is a stiffer floor, which tile and stone need so the grout does not crack.