01
Formula
Allowable load = 8 × Fb × S ÷ L².
S = b × d² ÷ 6. Deflection = 5 w L⁴ ÷ (384 E I). The span calculator solves L = square root of (8 × Fb × S ÷ w). L is in inches inside the formula and in feet on the form.
Apply for financingBeam span
Beam calculator for load, stress, and span
This beam calculator treats a rectangular section as a simply supported beam with a uniform load. It reports the allowable load from a bending stress you allow, the bending stress at the load you typed, midspan deflection, and a span calculator length for that load. It ignores shear, bearing, and lateral bracing. It is not a code design.
Allowable uniform load
142.60lb/ft
Bending stress at your load280 psi
Midspan deflection0.057 in
Span at this load18.88 ft
Planning estimate from the numbers you enter. Coverage, density, waste and price are assumptions, not a supplier quote or an engineering specification.
How it works
Allowable moment is bending stress times the section modulus.
Section modulus of a rectangle is width times depth squared, divided by 6. Moment of inertia is width times depth cubed, divided by 12. For a simple span, allowable pounds per inch equal 8 times allowable moment divided by span squared. Deflection in inches is 5 times the load per inch times span to the fourth, divided by 384 times the modulus of elasticity times the moment of inertia. A 1.5 by 9.25 inch section, 10 feet long, with 1,000 psi allowed and a modulus of 1,600,000 psi, can carry about 142.60 pounds per foot in bending. At 40 pounds per foot the bending stress is about 280 psi and the midspan deflection is a few hundredths of an inch. The span line is how long that section can run at 40 pounds per foot before it reaches 1,000 psi. You supply the allowable stress. The page does not look up a grade of lumber.
02
Example
1.5 by 9.25 inches, 10 foot span, 1,000 psi, 40 pounds per foot.
Allowable uniform load is about 142.60 pounds per foot. The 40 pound load is under that bending limit. Read the stress and the deflection on the card. If your species and grade allow a different Fb, type that Fb. Do not leave 1,000 psi in a design.
03
Tips
Bending is only one check.
A short, heavily loaded beam can fail in shear before it fails in bending. This beam calculator does not compute shear. Deflection limits such as span over 360 are yours to compare with the deflection line. Bracing and bearing length are not modeled.
04
Equipment
The saw that cuts the timber is the equipment.
Dengaro arranges financing for shop equipment. The beam result is not a loan amount and not a stamped drawing.
Important questions
Know what to expect.
What does simply supported mean?+
The beam is free to rotate at each end and is held against falling. A cantilever or a fixed-end beam uses a different moment. Do not use this span calculator for those.
Why is the allowable stress a field?+
Species, grade, and duration change it. The page will not pretend one psi fits every board. Type the value you are allowed to use.
Are the dimensions actual or nominal?+
Use the actual size. A nominal 2 by 10 is often 1.5 by 9.25, which is why those numbers are the default. A nominal size overstates the section.
Can I check a steel beam?+
Only if it is a solid rectangle and you type steel's modulus and an allowable stress. A wide-flange shape has its own section modulus. This form does not have a shape table.
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