Span Calculator

Section (2x4–2x12) × spacing (400/450/600mm) × species + Korean snow loads → maximum span satisfying both bending and deflection.

Result

Enter member info and click Calculate.

What this tool does

The span calculator uses NDS 2018 (National Design Specification for Wood Construction) allowable stress design to find the maximum safe span for floor joists, ceiling joists, rafters, and headers. It checks both the bending stress limit (M = wL²/8, σ ≤ Fb) and the deflection limit (δ = 5wL⁴/384EI ≤ L/k) simultaneously, reports whichever governs, and applies the repetitive member factor (Cr = 1.15) automatically for closely spaced joists and rafters. Regional snow loads per KDS 41 10 15 are built in for Korean rafter design.

Who uses this

Floor joist design: check how far 2×8 or 2×10 SPF #2 can span for a 2 kN/m² residential live load
Rafter span check: factor in regional snow load to plan roof rafter spacing and size
Ceiling joist planning: size members for attic storage (0.5 kN/m² live load) vs. inaccessible attic
Header sizing: pre-check maximum span for door or window opening headers before framing
Species comparison: see how Douglas Fir or Larch spans compare with SPF for the same member size

How to use (4 steps)

1Select member type: floor joist, ceiling joist, rafter, or header. Default live load, dead load, and deflection limit (L/k) are set automatically based on member type.
2Choose lumber size (2×4 through 2×12) and species/grade. SPF #2 is the most common imported species in Korean light-frame construction. Actual dressed dimensions per KS F 3020 (e.g., 2×8 = 38×184 mm) are applied automatically.
3Enter spacing in mm. Standards are 400, 450, and 600 mm. Narrower spacing reduces the load per member and increases the allowable span. Spacing ≤ 600 mm with 3 or more members triggers the NDS repetitive member factor Cr = 1.15 automatically.
4For rafters, select the snow region. Gangwon Yeongdong (east coast) and Ulleung Island carry 3.0 kN/m² vs. 0.5 kN/m² elsewhere (KDS 41 10 15), which substantially shortens the allowable rafter span.

Formula & basis (NDS Allowable Stress Design)

1. Load assembly Total load (kN/m²) = live load + dead load + snow load (rafters only) Line load w (N/mm) = total load × (spacing mm / 1000) 2. Section properties — KS F 3020 actual dimensions A = b × d I = b × d³ / 12 S = b × d² / 6 (b = 38 mm thickness; d = width — load direction for joists/rafters) 3. Repetitive member factor (NDS Cr) Spacing ≤ 600 mm + floor/ceiling joist or rafter + ≥ 3 members → Fb_eff = Fb × 1.15 4. Bending check: L_b = √(8 × Fb_eff × S / w) (derived from M = wL²/8 ≤ Fb_eff × S) 5. Deflection check: L_d = ∛(384 × E × I / (5 × w × k)) (from δ = 5wL⁴/384EI ≤ L/k) k = 360 (floor) · 240 (ceiling, header) · 180 (rafter) 6. Max span = min(L_b, L_d) Reference values for SPF #2: Fb = 7.6 MPa, E = 9,500 MPa Douglas Fir-Larch #2: Fb = 12.4 MPa, E = 12,400 MPa

Worked examples

Example 1: 2×8 SPF #2 floor joist, 400 mm spacing

Actual section 38×184 mm. Total load 2.5 kN/m² (live 2.0 + dead 0.5). Line load = 2.5×0.4 = 1.0 N/mm. Cr = 1.15, Fb_eff = 8.74 MPa. I = 19,740,672 mm⁴, S = 214,571 mm³. L_b = √(8×8.74×214,571/1.0) = 3,877 mm. L_d = ∛(384×9,500×19,740,672/(5×1.0×360)) = 4,234 mm. Max span 3,877 mm — bending governs.

Example 2: 2×10 SPF #2 rafter, Seoul region, 600 mm spacing

Actual section 38×235 mm. Total load = 0 (live) + 0.5 (dead) + 0.5 (snow Seoul) = 1.0 kN/m². Line load = 1.0×0.6 = 0.6 N/mm. Cr = 1.15, Fb_eff = 8.74 MPa. I = 41,342,729 mm⁴. L_b = 4,985 mm. Deflection k = 180. L_d = ∛(384×9,500×41,342,729/(5×0.6×180)) = 5,801 mm. Max span 4,985 mm — bending governs.

Example 3: 2×6 SPF #2 ceiling joist, 600 mm spacing

Actual section 38×140 mm. Total load 0.8 kN/m² (live 0.5 + dead 0.3). Line load = 0.8×0.6 = 0.48 N/mm. Cr = 1.15, Fb_eff = 8.74 MPa. S = 124,600 mm³, I = 8,722,000 mm⁴. L_b = √(8×8.74×124,600/0.48) = 4,258 mm. Deflection k = 240. L_d = ∛(384×9,500×8,722,000/(5×0.48×240)) = 3,681 mm. Max span 3,681 mm — deflection governs.

Frequently asked questions

What does 'bending governs' vs. 'deflection governs' mean?

Bending governs when the member would reach its stress limit (Fb exceeded) at a shorter span than the deflection limit allows. Deflection governs when the floor or roof would sag beyond L/360 (or L/180 for rafters) before the wood reaches its bending stress limit. The smaller of the two span limits is always the controlling value.

What does the repetitive member factor (Cr = 1.15) do?

When joists or rafters are spaced at 600 mm or less in groups of three or more, adjacent members share load when one is overloaded. NDS recognizes this load-sharing by allowing a 15% increase in the allowable bending stress (Fb). It does not apply to single members such as headers or posts.

This tool uses NDS — does it apply in Korea?

The underlying design approach (allowable stress, Fb, E, deflection limits) closely parallels KDS 41 33 02. Snow loads use Korean regional values from KDS 41 10 15. Allowable stress values are from NDS for Canadian/US imported species (SPF, DF, Hem-Fir); for domestic Korean larch, consult KS F 3019.

Which NDS adjustment factors does this tool NOT apply?

NDS includes CD (load duration), CM (wet service), Ct (temperature), CL (beam stability), CF (size factor), and Ci (incising). Only Cr (repetitive member) is applied here. Actual field conditions — green lumber, high humidity, sustained loads — can reduce the allowable span. A licensed structural engineer must account for these factors in final design.

Why is the Gangwon Yeongdong snow load so much higher?

KDS 41 10 15 Appendix B sets the ground snow load at 3.0 kN/m² for the Gangwon east-coast region (Goseong, Sokcho, Gangneung, Samcheok) and Ulleung Island due to frequent heavy snowfall driven by cold air crossing the East Sea. This is six times the 0.5 kN/m² used for Seoul and most other regions, significantly shortening the allowable rafter span.

Can I use this tool for engineered lumber (LVL, PSL, Glulam)?

No. Engineered wood products have proprietary allowable stress values that differ from sawn lumber and must be taken from the manufacturer's span tables or ICC evaluation reports. This calculator covers dimension lumber (2×4 through 2×12) in sawn species grades only.

Cautions

•Based on NDS 2018. Only the Cr repetitive member factor (1.15) is applied; CD, CM, Ct, CL, CF, and Ci are not. Results may be unconservative if lumber is wet, temperatures are extreme, or loads are sustained.
•Shear and bearing (compression perpendicular to grain) are not checked. Short, heavily loaded headers may be shear-critical — a structural engineer must verify.
•Default live loads (floor 2.0 kN/m², ceiling 0.5 kN/m²) are for standard residential occupancy. Warehouses, offices, and assembly areas require higher values per KDS 41 10 15 — enter them manually using the override fields.
•Spacing outside 400/450/600 mm triggers a warning. The repetitive member factor (Cr = 1.15) is not applied when spacing exceeds 600 mm, which reduces the allowable span.
•Results are for planning and preliminary review only. Final structural design and construction must be reviewed by a licensed structural engineer (Korean PE or equivalent).