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42 Formulas

Joinery & Furniture Formulas

Joint geometry, proportion and deflection equations.

Sag & Deflection

Open the Sag & Deflection →
Simply Supported UDL
δ = (5 × w × L⁴) / (384 × E × I)
Used in Sag & Deflection
Simply Supported Point
δ = (P × L³) / (48 × E × I)
Used in Sag & Deflection
Cantilever Point
δ = (P × L³) / (3 × E × I)
Used in Sag & Deflection
Moment of Inertia
I = (b × h³) / 12
Used in Sag & Deflection

Compound Miter

Open the Compound Miter →
Compound Miter
Miter = arctan( sin(S) x tan(C/2) ) [S = spring, C = corner angle]
Used in Compound Miter
Compound Miter
Bevel = arcsin( cos(S) x sin(C/2) )
Used in Compound Miter
Compound Miter
Dihedral = arccos( cos2(S) x cos(C) + sin2(S) )
Used in Compound Miter
Compound Miter
Polygon corner = 180 - (360 / N_sides)
Used in Compound Miter

Golden Ratio

Open the Golden Ratio →
Golden Ratio
φ = (1 + √5) / 2 = 1.6180339887…
Used in Golden Ratio
Golden Ratio
Given width a → height b = a × φ
Used in Golden Ratio
Golden Ratio
Given height b → width a = b / φ
Used in Golden Ratio
Golden Ratio
Diagonal d = a × √(1 + φ²) = a × 1.9021…
Used in Golden Ratio

Ring Segment

Open the Ring Segment →
Miter angle
theta = 90 - (180 / N) where N = number of segments
Used in Ring Segment
Outer chord
L = 2 x R_outer x sin(PI / N)
Used in Ring Segment
Kerf correction
dL = kerf / sin(theta) [material lost per cut end]
Used in Ring Segment
Cut length
L_cut = outer_chord - kerf_correction
Used in Ring Segment
Volume/seg
V = PI x (Rout2 - Rin2) x H / N
Used in Ring Segment

Drawer Reveal

Open the Drawer Reveal →
Face height (N equal)
FH = (OH - bot_reveal - reveal x (N+1)) / N
Used in Drawer Reveal
Face width (frameless)
FW = OW - 2 x reveal
Used in Drawer Reveal
Box width (undermount)
BW = OW - 3mm
Used in Drawer Reveal
Box width (side-mount)
BW = OW - 2 x slide_clearance
Used in Drawer Reveal
Y position (drawer n)
Yn = bot_reveal + (n-1) x (FH + reveal) + reveal
Used in Drawer Reveal

Box Joint

Open the Box Joint →
Box Joint
N (odd) = nearest odd to (W / finger_width)
Used in Box Joint
Box Joint
Actual fw = W / N
Used in Box Joint
Box Joint
Glue area = 2 × N × fw × thickness
Used in Box Joint
Box Joint
Strength ratio = glue_area / (W × thickness) [typically 3–6×]
Used in Box Joint

Mortise & Tenon

Open the Mortise & Tenon →
Mortise & Tenon
Tenon thickness = Rail thickness / 3
Used in Mortise & Tenon
Mortise & Tenon
Tenon width = Rail width − 2 × shoulder_allowance
Used in Mortise & Tenon
Mortise & Tenon
Tenon length = 4.5 × tenon_thickness (max = 80% of stile thickness)
Used in Mortise & Tenon
Mortise & Tenon
Mortise depth = Tenon length + 2mm clearance
Used in Mortise & Tenon
Mortise & Tenon
Cheek = (Rail thickness − Tenon thickness) / 2
Used in Mortise & Tenon

Dovetail

Open the Dovetail →
Angle
theta = arctan(1 / ratio)
Used in Dovetail
Tail wide end
TW = T_narrow + 2 × thickness × tan(theta)
Used in Dovetail
N tails
round((W − min_pin) / (TW + min_pin))
Used in Dovetail
Spacing
S = (W − pin_width) / N_tails
Used in Dovetail

Expansion Gap

Open the Expansion Gap →
Expansion Gap
Movement = W × S × ΔMC (W=width, S=coeff/MC%, ΔMC=change %)
Used in Expansion Gap
Expansion Gap
Radial coeff ≈ Tangential × 0.55
Used in Expansion Gap
Expansion Gap
Gap per board = max(shrink, swell) × 1.15 (15% safety factor)
Used in Expansion Gap

Screw Strength

Open the Screw Strength →
IS 883
2016 — W = k × d × L (k = 12/10/7/5 by density group)
Used in Screw Strength
Screw Strength
NDS 2018 — W = 124.9 × G^1.5 × D^0.75 (lbs/in penetration)
Used in Screw Strength
Screw Strength
Eurocode 5 — f_ax,k = 0.52 × d^-0.5 × L^-0.1 × ρ^0.8
Used in Screw Strength
Screw Strength
Group factor — Cg = max(0.4, 1 − 0.05×(n−1))
Used in Screw Strength

Common questions

Where do these formulas come from?

Every formula on this page comes from a published source — standards, handbooks or long-established trade rules for joinery and furniture making. The source is named next to each formula. Nothing here is invented by us.

Can I use these formulas in my own spreadsheets or software?

Yes. The formulas themselves are public knowledge and free to use anywhere. If our page helped you, a link back is appreciated but not required.

Are the calculators on this site using these exact formulas?

Yes. Each calculator runs the formula shown here, and automated tests check the results against worked examples from the original sources before anything goes live.