The Floor Deflection Calculator calculates how much a wood floor joist sags under a uniform live load and whether that meets a deflection limit such as L/360.
It uses the simple-beam formula Δ = 5wL⁴ ÷ (384EI), where the load on each joist is the floor load times the joist spacing. The result is shown in inches, along with the span-to-deflection ratio (L/Δ) and a pass/fail check.
Floor Deflection Calculator
Deflection of a wood floor joist under a uniform load, the L/Δ ratio and whether it meets L/360 or your limit.
Formula
- Load per joist: w = q × spacing
- Moment of inertia: I = b × d³ ÷ 12
- Deflection: Δ = 5 × w × L⁴ ÷ (384 × E × I)
- Ratio: L ÷ Δ, compared with the limit (360, 480 or 720)
Where q = live load (psf), L = span, b and d = actual joist width and depth, E = modulus of elasticity.
How the Calculation Works
Step 1: Turn the floor load into a line load on one joist.
Step 2: Calculate the joist’s stiffness (E × I).
Step 3: Apply the deflection formula and compare L/Δ with the limit.
Variables Explained
| Input | Meaning |
|---|---|
| Span | Clear distance between supports |
| Joist size | Actual dimensions (a 2×10 is 1½ × 9¼ in) |
| Live load | Design live load for the floor |
| E | Modulus of elasticity for your species and grade |
| Limit | L/360, L/480 or L/720 |
Example Calculation
Given: 14 ft span, 2×10 at 16 in o.c., 40 psf live load, E = 1,600,000 psi
Load per joist: 40 × 1.333 ≈ 53.3 lb/ft
Deflection: Δ ≈ 0.291 in
Result: L/Δ ≈ 577 — meets L/360 (limit 0.467 in)
Engineering Assumptions
- Simply supported joist with a uniform live load; dead load, point loads and composite action with the subfloor are not included.
- Deflection limits help control bounce and finish cracking; stiffer limits are often recommended for tile and stone — check the finish manufacturer’s or industry guidance.
- Passing a deflection check doesn’t confirm strength; check bending with the Floor Joist Span Calculator.
Formula Variations
A center point load uses Δ = PL³ ÷ (48EI). Engineered joists publish their own stiffness (EI) values.
Units and Dimensions
Keep span in feet (or m) and joist size in inches (or mm); the calculator converts internally and shows deflection in inches.
Frequently Asked Questions
How do you calculate floor joist deflection?
Δ = 5wL⁴ ÷ (384EI) with w = load × spacing.
What does L/360 mean?
Deflection must not exceed the span divided by 360 — about 0.47 in on a 14 ft span.
What deflection limit is needed for tile?
Tile and stone often call for stiffer floors than L/360; follow the tile or stone manufacturer’s requirements.
How can I reduce floor bounce?
Deeper joists, closer spacing, shorter spans (a mid-span beam) or sistering joists all increase stiffness.
Why is L/Δ higher than the limit a pass?
A higher ratio means less sag relative to the span.