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Shoelace Length Formulas
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Using the shoelace length factors [P], [H], [V], [W] and [L] from the
Shoelace Lengths page, I created a formula for each
Lacing Method. They have been simplified as much as possible and have been typed both in mathematical notation
using symbols for [√] (square root) and [²] (squared) as well as in more generic notation (coloured
GREEN) compatible with spreadsheet software (like Excel).
These are the underlying formulas of my
Shoelace Length Calculator.
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Army Lacing
(same as Bow Tie Lacing)
Method 1 (Verticals at bottom, Shorter):
(H+V×INT(P÷2)+√(H²+V²)×INT((P−1)÷2)+L)×2
(H+V*INT(P/2)+SQRT(H*H+V*V)*INT((P-1)/2)+L)*2
(H+V×INT((P−1)÷2)+√(H²+V²)×INT(P÷2)+L)×2
(H+V*INT((P-1)/2)+SQRT(H*H+V*V)*INT(P/2)+L)*2
(For odd numbers of eyelet pairs, both formulas work out the same)
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Bi-Colour Lacing
Lace 1 (Bottom, Longer):
H×INT((P+2)÷2)+V×P+L
H*INT((P+2)/2)+V*P+L
H×INT((P+1)÷2)+V×(P−1)+L
H*INT((P+1)/2)+V*(P-1)+L
(These approximate a little extra length to allow for knots)
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Bow-Tie Lacing
(same as Army Lacing)
Method 1 (Verticals at bottom, Shorter):
(H+V×INT(P÷2)+√(H²+V²)×INT((P−1)÷2)+L)×2
(H+V*INT(P/2)+SQRT(H*H+V*V)*INT((P-1)/2)+L)*2
(H+V×INT((P−1)÷2)+√(H²+V²)×INT(P÷2)+L)×2
(H+V*INT((P-1)/2)+SQRT(H*H+V*V)*INT(P/2)+L)*2
(For odd numbers of eyelet pairs, both formulas work out the same)
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Checkerboard Lacing
Lace 1 (Horizontal):
H×P+V×(P−1)+L×2
H*P+V*(P-1)+L*2
(Note that End Lengths can be much shorter than other methods)
V×1.05×(P−1)×(Vertical Passes)+L×2
V*1.05*(P-1)*(Vertical Passes)+L*2
(This approximates 5% longer verticals to allow for weaving)
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Criss Cross Lacing
(H+√(H²+V²)×(P−1)+L)×2
(H+SQRT(H*H+V*V)*(P-1)+L)*2
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Display Shoe Lacing
(same as Criss Cross Lacing)
(H+√(H²+V²)×(P−1)+L)×2
(H+SQRT(H*H+V*V)*(P-1)+L)*2
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Double Lacing
Lace 1 (Bottom, Longer):
(H+√(H²+(V×2)²)×INT((P−1)÷2)+L)×2
(H+SQRT(H*H+V*V*4)*INT((P-1)/2)+L)*2
(H+√(H²+(V×2)²)×INT((P−2)÷2)+L)×2
(H+SQRT(H*H+V*V*4)*INT((P-2)/2)+L)*2
(For even numbers of eyelet pairs, both formulas work out the same)
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Double Back Lacing
Method 1 (Verticals at bottom, Shorter):
(H+V+√(H²+(V×2)²)×(P−2)+L)×2
(H+V+SQRT(H*H+V*V*4)*(P-2)+L)*2
(H+√(H²+V²)+√(H²+(V×2)²)×(P−2)+L)*2
(H+SQRT(H*H+V*V)+SQRT(H*H+V*V*4)*(P-2)+L)*2
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Double Cross Lacing
Method 1 (Even number of eyelet pairs, Skip eyelets near ends, Shorter):
(H+L)×2+√(H²+V²)×(P−4)+√(H²+(V×3)²)×(P−2)
(H+L)*2+SQRT(H*H+V*V)*(P-4)+SQRT(H*H+V*V*9)*(P-2)
(H+L)×2+√(H²+V²)×(P−2)+√(H²+(V×2)²)×4+√(H²+(V×3)²)×(P−4)
(H+L)*2+SQRT(H*H+V*V)*(P-2)+SQRT(H*H+V*V*4)*4+SQRT(H*H+V*V*9)*(P-4)
(H+√(H²+(V×2)²)+L)×2+(√(H²+V²)+√(H²+(V×3)²))×(P−3)
(H+SQRT(H*H+V*V*4)+L)*2+(SQRT(H*H+V*V)+SQRT(H*H+V*V*9))*(P-3)
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Double Helix Lacing
(same as Criss Cross Lacing)
(H+√(H²+V²)×(P−1)+L)×2
(H+SQRT(H*H+V*V)*(P-1)+L)*2
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Footbag Lacing
Method 1 (Basic):
(H+V×5+√(H²+V²)×(P−4)+L)×2
(H+V*5+SQRT(H*H+V*V)*(P-4)+L)*2
(H+V×6+√(H²+V²)×(P−4)+L)×2
(H+V*6+SQRT(H*H+V*V)*(P-4)+L)*2
(Method 2 approximates 50% longer on 2 x verticals wrapped around edges)
(H+V×8+√(H²+V²)×(P−5)+L)×2
(H+V*8+SQRT(H*H+V*V)*(P-5)+L)*2
(H+V×10+√(H²+V²)×(P−5)+L)×2
(H+V*10+SQRT(H*H+V*V)*(P-5)+L)*2
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Hash Lacing
Method 1 (Even number of eyelet pairs, Skip eyelets near ends, Shorter):
(H+L)×2+V×(P−4)+√(H²+(V×3)²)×(P−2)
(H+L)*2+V*(P-4)+SQRT(H*H+V*V*9)*(P-2)
(H+L)×2+V×(P−2)+√(H²+(V×2)²)×4+√(H²+(V×3)²)×(P−4)
(H+L)*2+V*(P-2)+SQRT(H*H+V*V*4)*4+SQRT(H*H+V*V*9)*(P-4)
(H+√(H²+(V×2)²)+L)×2+(V+√(H²+(V×3)²))×(P−3)
(H+SQRT(H*H+V*V*4)+L)*2+(V+SQRT(H*H+V*V*9))*(P-3)
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Hexagram Lacing
(H×(P+4)÷5+L)×2+(V+SQRT(H²+(V×3)²))×(P−1)÷5×4
(H*(P+4)/5+L)*2+(V+SQRT(H*H+V*V*9))*(P-1)/5*4
(Only applicable when number of eyelet pairs P = 6, 11, 16, 21, 26, etc.)
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Hidden Knot Lacing
(same as Straight Bar Lacing)
H×P+(V×(P−1)+L)×2
H*P+(V*(P-1)+L)*2
(Only applicable for even numbers of eyelet pairs)
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Hiking / Biking Lacing
(same as Straight Bar Lacing)
H×P+(V×(P−1)+L)×2
H*P+(V*(P-1)+L)*2
(Only applicable for even numbers of eyelet pairs)
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Knotted Lacing
(H+√(H²+V²)×1.03×(P−1)+L)×2
(H+SQRT(H*H+V*V)*1.03*(P-1)+L)*2
(This approximates 3% longer diagonals to allow for knots)
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Knotted Segment Lacing
(H+√(H²+V²)×(P−0.75)+L)×2
(H+SQRT(H*H+V*V)*(P-0.75)+L)*2
(This approximates 25% longer on two diagonals to allow for knot)
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Ladder Lacing
Method 1 (No lock at top, Shorter):
((H+V)×(P−1)+L)×2
((H+V)*(P-1)+L)*2
((H+V)×P−V+L)×2
((H+V)*P-V+L)*2
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Lattice Lacing
Method 1 (Single verticals, Shorter):
(H+L)×2+(V×4+√(H²+(V×3)²)×6)×(P−1)÷5
(H+L)*2+(V*4+SQRT(H*H+V*V*9)*6)*(P-1)/5
(H+L)×2+(V×8+√(H²+(V×3)²)×6)×(P−1)÷5
(H+L)*2+(V*8+SQRT(H*H+V*V*9)*6)*(P-1)/5
(Only applicable when number of eyelet pairs P = 6, 11, 16, 21, 26, etc.)
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Lock Lacing
Method 1 (High lock, Shorter):
(H+V+√(H²+V²)×(P−2)+√(H²+(V÷2)²)+L)×2
(H+V+SQRT(H*H+V*V)*(P-2)+SQRT(H*H+V*V/4)+L)*2
(H+V+√(H²+V²)×(P−3)+√(H²+(V×2)²)+√(H²+(V÷2)²)+L)×2
(H+V+SQRT(H*H+V*V)*(P-3)+SQRT(H*H+V*V*4)+SQRT(H*H+V*V/4)+L)*2
H×4.1+(√(H²+V²)×(P−1)+L)×2
H*4.1+(SQRT(H*H+V*V)*(P-1)+L)*2
(This approximates 5% longer on two horizontals to allow for loops)
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Loop Back Lacing
(H+√(H²+V²)×1.05×(P−1)+L)×2
(H+SQRT(H*H+V*V)*1.05*(P-1)+L)*2
(This approximates 5% longer diagonals to allow for loop backs)
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One Handed Lacing
H×P+√(H²+V²)×(P−1)+L×1.25
H*P+SQRT(H*H+V*V)*(P-1)+L*1.25
(This approximates the tied off end at 1/4 the length of the loose end)
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Over Under Lacing
(same as Criss Cross Lacing)
(H+√(H²+V²)×(P−1)+L)×2
(H+SQRT(H*H+V*V)*(P-1)+L)*2
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Pentagram Lacing
H×3+V×(P−2)×4+(√(H²+(V×(P−3))²)+√((H÷2)²+(V×(P−2))²)+L)×2
H*3+V*(P-2)*4+(SQRT(H*H+V*(P-3)*V*(P-3))+SQRT(H*H/4+V*(P-2)*V*(P-2))+L)*2
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Riding Boot Lacing
(same as Shoe Shop Lacing)
H×P+√(H²+V²)×(P−1)+√(H²+(V×(P−1))²)+L×2
H*P+SQRT(H*H+V*V)*(P-1)+SQRT(H*H+V*(P-1)*V*(P-1))+L*2
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Roman Lacing
Shoes with 4, 10, 16, 22, etc. sets of eyelets:
Method 1 ("I" at bottom, Short):
(H×(P+2)+V×(P×5−8))÷3+(√(H²+V²)×(P−1)÷3+L)×2
(H*(P+2)+V*(P*5-8))/3+(SQRT(H*H+V*V)*(P-1)/3+L)*2
Method 2 ("X" at bottom, Long):
(H×(P+2)+V×(P×5−2))÷3+(√(H²+V²)×(P−1)÷3+L)×2
(H*(P+2)+V*(P*5-2))/3+(SQRT(H*H+V*V)*(P-1)/3+L)*2
Shoes with 8, 14, 20, 26, etc. sets of eyelets:
Method 1 ("I" at bottom, Short):
(H×(P+4)+V×(P×5−4))÷3+(√(H²+V²)×(P−2)÷3+L)×2
(H*(P+4)+V*(P*5-4))/3+(SQRT(H*H+V*V)*(P-2)/3+L)*2
(H×(P−2)+V×(P×5−4))÷3+(√(H²+V²)×(P+1)÷3+L)×2
(H*(P-2)+V*(P*5-4))/3+(SQRT(H*H+V*V)*(P+1)/3+L)*2
(H×(P+4)+V×(P×5−10))÷3+(√(H²+V²)×(P+1)÷3+L)×2
(H*(P+4)+V*(P*5-10))/3+(SQRT(H*H+V*V)*(P+1)/3+L)*2
All other combinations:
(H×INT((P+5)÷6)+V×INT((P−1)×5÷6)+√(H²+V²)×INT((P+1)÷3)+L)×2
(H*INT((P+5)/6)+V*INT((P-1)*5/6)+SQRT(H*H+V*V)*INT((P+1)/3)+L)*2
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Sawtooth Lacing
H×P+√(H²+(V×2)²)×(P−2)+(V+L)×2
H*P+SQRT(H*H+V*V*4)*(P-2)+(V+L)*2
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Segmented Lacing
Lace 1 (Shorter segment):
(H+√(H²+V²)×INT((P−2)÷2)+L)×2
(H+SQRT(H*H+V*V)*INT((P-2)/2)+L)*2
(H+√(H²+V²)×INT((P−1)÷2)+L)×2
(H+SQRT(H*H+V*V)*INT((P-1)/2)+L)*2
(For even numbers of eyelet pairs, both formulas work out the same)
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Shoe Shop Lacing
Method 1 (Long diagonal, Longer):
(same as Riding Boot Lacing)
H×P+√(H²+V²)×(P−1)+√(H²+(V×(P−1))²)+L×2
H*P+SQRT(H*H+V*V)*(P-1)+SQRT(H*H+V*(P-1)*V*(P-1))+L*2
(H+V)×P+√(H²+V²)×(P−2)+L×2
(H+V)*P+SQRT(H*H+V*V)*(P-2)+L*2
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Spider Web Lacing
(H+(V+√(H²+(V×2)²))×(P−2)+L)×2
(H+(V+SQRT(H*H+V*V*4))*(P-2)+L)*2
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Straight (Bar) Lacing
H×P+(V×(P−1)+L)×2
H*P+(V*(P-1)+L)*2
(Only applicable for even numbers of eyelet pairs)
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Straight (Easy) Lacing
(same as Straight Bar Lacing)
H×P+(V×(P−1)+L)×2
H*P+(V*(P-1)+L)*2
(Only applicable for even numbers of eyelet pairs)
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Straight (European) Lacing
H×P+(√(H²+V²)+L)×2+√(H²+(V×2)²)×(P−2)
H*P+(SQRT(H*H+V*V)+L)*2+SQRT(H*H+V*V*4)*(P-2)
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Train Track Lacing
((H+V)×(P−1)+L)×2
((H+V)*(P-1)+L)*2
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Twistie Lacing
(H+√(H²+V²)×1.07×(P−1)+L)×2
(H+SQRT(H*H+V*V)*1.07*(P-1)+L)*2
(This approximates 7% longer diagonals to allow for twists)
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Zipper Lacing
H×(P+1)+√(H²+(V×2)²)×(P−1)+L×2
H*(P+1)+SQRT(H*H+V*V*4)*(P-1)+L*2
(This approximates diagonals at half the horizontal spacing)
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Lug Bow Tie Lacing
Method 1 (Verticals at bottom, Shorter):
(H+V×INT(P÷2)+W×INT((P+1)÷2)+√(H²+(V−W)²)×INT((P−1)÷2)+L)×2
(H+V*INT(P/2)+W*INT((P+1)/2)+SQRT(H*H+(V-W)*(V-W))*INT((P-1)/2)+L)*2
(H+V×INT((P−1)÷2)+W×INT(P÷2+1)+√(H²+(V−W)²)×INT(P÷2)+L)×2
(H+V*INT((P-1)/2)+W*INT(P/2+1)+SQRT(H*H+(V-W)*(V-W))*INT(P/2)+L)*2
(For odd numbers of lug pairs, both formulas work out the same)
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Lug Criss Cross Lacing
(H+W×P+√(H²+(V−W)²)×(P−1)+L)×2
(H+W*P+SQRT(H*H+(V-W)*(V-W))*(P-1)+L)*2
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Lug Double Lacing
Lace 1 (Bottom, Longer):
(H+W×INT((P+1)÷2)+√(H²+(V×2−W)²)×INT((P−1)÷2)+L)×2
(H+W*INT((P+1)/2)+SQRT(H*H+(V*2-W)*(V*2-W))*INT((P-1)/2)+L)*2
(H+W×INT(P÷2)+√(H²+(V×2−W)²)×INT((P−2)÷2)+L)×2
(H+W*INT(P/2)+SQRT(H*H+(V*2-W)*(V*2-W))*INT((P-2)/2)+L)*2
(For even numbers of lug pairs, both formulas work out the same)
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Lug Double Back Lacing
(H+W×P+√(H²+V²)+√(H²+(V×2−W)²)×(P−2)+L)×2
(H+W*P+SQRT(H*H+V*V)+SQRT(H*H+(V*2-W)*(V*2-W))*(P-2)+L)*2
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Lug Hash Lacing
(H+W×P+√(H²+(V+W)²)×(P−1)+L)×2
(H+W*P+SQRT(H*H+(V+W)*(V+W))*(P-1)+L)*2
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Lug Hexagram Lacing
(H×(P+3)+W×(P×3+1))÷2+√(H²+(V×2)²)×(P−1)+L×2
(H*(P+3)+W*(P*3+1))/2+SQRT(H*H+V*V*4)*(P-1)+L*2
(Only applicable when number of lug pairs P = 5, 9, 13, 17, 21, etc.)
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Lug Hiking / Biking Lacing
(H+V+W×(P−1)+√(H²+(V−W)²)×(P−2)+L)×2
(H+V+W*(P-1)+SQRT(H*H+(V-W)*(V-W))*(P-2)+L)*2
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Lug Infinity Lacing
(H+V×(P−1)+W×(P+1)+√(H²+W²)×P+L)×2
(H+V*(P-1)+W*(P+1)+SQRT(H*H+W*W)*P+L)*2
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Lug Knotted Lacing
(H+W×P+√(H²+(V−W)²)×1.03×(P−1)+L)×2
(H+W*P+SQRT(H*H+(V-W)*(V-W))*1.03*(P-1)+L)*2
(This approximates 3% longer diagonals to allow for knots)
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Lug Knotted Segment Lacing
(H+W×P+√(H²+(V−W)²)×(P−0.75)+L)×2
(H+W*P+SQRT(H*H+(V-W)*(V-W))*(P-0.75)+L)*2
(This approximates 25% longer on two diagonals to allow for knot)
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Lug Ladder Lacing
Method 1 (No lock at top, Shorter):
(H+(V+W)×(P−1)+√(H²+W²)×(P−2)+L)×2
(H+(V+W)*(P-1)+SQRT(H*H+W*W)*(P-2)+L)*2
(H+(V+W+√(H²+W²))×(P−1)+L)×2
(H+(V+W+SQRT(H*H+W*W))*(P-1)+L)*2
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Lug Lattice Lacing
(H+W×P+(√(H²+(V+W)²)+√(H²+(V×2−W)²)×2)×INT((P−1)÷3)+L)×2
(H+W*P+(SQRT(H*H+(V+W)*(V+W))+SQRT(H*H+(V*2-W)*(V*2-W))*2)*INT((P-1)/3)+L)*2
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Lug Loop Back Lacing
(H+W×P+√(H²+(V−W)²)×1.05×(P−1)+L)×2
(H+W*P+SQRT(H*H+(V-W)*(V-W))*1.05*(P-1)+L)*2
(This approximates 5% longer diagonals to allow for loop backs)
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Lug Segmented Lacing
Lace 1 (Shorter segment):
(H+W×INT(P÷2)+√(H²+(V−W)²)×INT(P÷2−1)+L)×2
(H+W*INT(P/2)+SQRT(H*H+(V-W)*(V-W))*INT(P/2-1)+L)*2
(H+W×INT((P+1)÷2)+√(H²+(V−W)²)×INT((P−1)÷2)+L)×2
(H+W*INT((P+1)/2)+SQRT(H*H+(V-W)*(V-W))*INT((P-1)/2)+L)*2
(For even numbers of lug pairs, both formulas work out the same)
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Lug Shoe Shop Lacing
(H+W×P+L)×2+√(H²+(V−W)²)×(P×2−3)+√(H²+(V×(P−1)−W)²)
(H+W*P+L)*2+SQRT(H*H+(V-W)*(V-W))*(P*2-3)+SQRT(H*H+(V*(P-1)-W)*(V*(P-1)-W))
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Lug Spider Web Lacing
(H+(V+√(H×H+(V+V+W)×(V+V+W))×(P−2)+W×(P−1)+L)×2
(H+(V+SQRT(H*H+(V+V+W)*(V+V+W))*(P-2)+W*(P-1)+L)*2
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Lug Twistie Lacing
(H+W×P+√(H²+(V−W)²)×1.07×(P−1)+L)×2
(H+W*P+SQRT(H*H+(V-W)*(V-W))*1.07*(P-1)+L)*2
(This approximates 7% longer diagonals to allow for twists)
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Lug Zipper Lacing
((H+√(H²+(V+W)²)×(P−1))×1.03+W×P+L)×2
((H+SQRT(H*H+(V+W)*(V+W))*(P-1))*1.03+W*P+L)*2
(This approximates 3% longer segments to allow for knots)
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These formulas are theoretically accurate, but in practice they will be out a little depending on the accuracy
of any approximations, the diameter of the eyelets, depth of the eyelets, variations in distances between eyelets,
thickness of the laces, elasticity of the laces, how tightly they are laced, how complex a knot is used, the
curvature of the top of your foot, even the thickness of your socks!
