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Floor Joist Specifications

Material Properties

⚠️ CODE ALERT: FAIL: Joist exceeds L/360 deflection limits. The floor will sag and bounce, cracking tile and drywall. Decrease span or increase joist depth.

Actual Deflection

0.502″
Calculated joist sag.

L/360 Allowable Limit

0.467″
Maximum permitted deflection.
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What is The Physics of JoistDeflection?

The technical foundation and mathematics behind the JoistDeflectionCalc tool.

Mathematical Foundation

Core Equation
Δmax=5⋅w⋅L4384⋅E⋅I\Delta_{max} = \frac{5 \cdot w \cdot L^4}{384 \cdot E \cdot I}
Δmax\Delta_{max}= Maximum mid-span physical deflection sag (Inches).
ww= Uniformly distributed line load across the entire joist (Pounds per Linear Inch).
LL= Total unsupported clear span of the joist (Inches).
E,IE, I= Modulus of Elasticity (wood stiffness multiplier) and Moment of Inertia (geometric shape strength).

Laws & Principles

  • Because the span length (L) is mathematically raised to the 4th power, span dictates catastrophic failure more than any other factor. Doubling a floor span doesn't double the sag; it multiplies the deflection by sixteen times.
  • The International Residential Code (IRC) strictly limits live-load floor deflection to L/360. A 15-foot span mathematically cannot sag more than a half-inch before drywall cracks and tile pops.

Step-by-Step Example Walkthrough

" A 14-foot Douglas Fir simply-supported 2x10 joist (E=1,600,000 psi, I=53.8 in⁴) carries a 50 PLF live+dead load. "

  1. 1. Convert load to PLI: 50 PLF / 12 = 4.167 Pounds per Linear Inch.
  2. 2. Convert span to inches: 14 feet * 12 = 168 Inches.
  3. 3. Calculate the span to the 4th power: 168^4 = 796,594,176.
  4. 4. Calculate numerator: 5 * 4.167 * 796,594,176 = 1.659 × 10¹⁰.
  5. 5. Calculate denominator: 384 * 1,600,000 * 53.8 = 3.305 × 10¹⁰.
  6. 6. Divide to find absolute sag: 1.659 / 3.305 = 0.502 inches.
Final Result: 0.502" Sag (Fails L/360 Code)

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  1. 1.Enter your values into the input fields above. All inputs are labelled with the expected unit of measurement.
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Pro Tips

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Common Mistakes

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