All of the underlying mathematical formulas from the Shoelace Length Calculator are shown here both in mathematical notation and in generic notation (colored GREEN) compatible with spreadsheet software (like Microsoft Excel).

See the Accurate Shoelace Lengths page for more details.

P = Pairs of eyelets; H = Horizontal spacing; V = Vertical spacing; W = Width of lugs; L = Length of ends.

NOTE: These length formulas are based on five measurements:

Formulas for Total Shoelace Length

=H+(V×4+√(H²+(V×3)²)×6)×INT((P−1)÷5)+(√(H²+V²)×((P−1) MODULO 5)+L)×2

=H+(V*4+SQRT(H*H+V*V*9)*6)*INT((P-1)/5)+(SQRT(H*H+V*V)*MOD((P-1),5)+L)*2

Army Lacing (same formula 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

Method 2 (Diagonals at bottom, Longer): =(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)

=(H×INT(P÷6+1)+√(H²+(V×2)²)×P÷3+L)×2+V×(P×4÷3−2)

=(H*INT(P/6+1)+SQRT(H*H+V*V*4)*P/3+L)*2+V*(P*4/3-2)

(Only applicable for multiples of three eyelet pairs: P = 3, 6, 9, 12, etc.)

Bow Tie Lacing (same formula 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

Method 2 (Diagonals at bottom, Longer): =(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)

CAF Combat Boot Lacing (same formula as Criss Cross Lacing)

=(H+√(H²+V²)×(P−1)+L)×2

=(H+SQRT(H*H+V*V)*(P-1)+L)*2

=H+V×((P−1)×2−(P MODULO 2))+√(H²+V²)×((P MODULO 2)+(P−2)×1.03)+√(H²+(V×(P−2))²)×1.03+L×2

=H+V*((P-1)*2-MOD(P,2))+SQRT(H*H+V*V)*(MOD(P,2)+(P-2)*1.03)+SQRT(H*H+(V*(P-2))*(V*(P-2)))*1.03+L*2

(This approximates 3% longer diagonals to allow for loop unders)

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)

Lace 2 (Vertical): =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)

Chevron Lacing (same formula as Gap Lacing)

=(H+V+√(H²+V²)×(P−2)+L)×2

=(H+V+SQRT(H*H+V*V)*(P-2)+L)*2

Method 1, 2 or 3 (Low, Mid or High X): =H×(P−2)+√(H²+V²)×6+√(H²+(V×2)²)×(P−4)+L×2 =H*(P-2)+SQRT(H*H+V*V)*6+SQRT(H*H+V*V*4)*(P-4)+L*2

Method 4 or 5 (Two Xs): =H×(P−3)+√(H²+V²)×8+√(H²+(V×2)²)×(P−5)+L×2 =H*(P-3)+SQRT(H*H+V*V)*8+SQRT(H*H+V*V*4)*(P-5)+L*2

Method 6 (Three or more Xs): =(H+√(H²+V²)×(P−1)+L)×2 =(H+SQRT(H*H+V*V)*(P-1)+L)*2

Method 7 (Bottom X): =H×(P−1)+√(H²+V²)×4+√(H²+(V×2)²)×(P−3)+L×2 =H*(P-1)+SQRT(H*H+V*V)*4+SQRT(H*H+V*V*4)*(P-3)+L*2

=H×P+V×(P−1)+L+75 mm

=H*P+V*(P-1)+L+75

(This allows 75 mm = 3 inches for the anchoring knot)

=H×3+√(H²+V²)×(P−1)×2+L×4

=H*3+SQRT(H*H+V*V)*(P-1)*2+L*4

=(H+√(H²+V²)×(P−1)+L)×2

=(H+SQRT(H*H+V*V)*(P-1)+L)*2

=H+V×((P−1)×2−(P MODULO 2))+√(H²+V²)×(2.06−(P MODULO 2)×0.03)+√(H²+(V×2)²)×1.06×(P−3)+L×2

=H+V*((P-1)*2-MOD(P,2))+SQRT(H*H+V*V)*(2.06-MOD(P,2)*0.03)+SQRT(H*H+V*V*4)*1.06*(P-3)+L*2

(This approximates 3% longer diagonals to allow for loop unders)

Lace 1 (Horizontal): =(H×(P−1)+L)×2+V×((P×2)−3) =(H*(P-1)+L)*2+V*((P*2)-3) (Note that End Lengths can be much shorter than other methods)

Lace 2 (Vertical) (same formula as Lace 2 of Checkerboard Lacing): =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)

Display Shoe Lacing (same formula as Criss Cross Lacing)

=(H+√(H²+V²)×(P−1)+L)×2

=(H+SQRT(H*H+V*V)*(P-1)+L)*2

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

Lace 2 (Second, Shorter): =(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)

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

Method 2 (Diagonals at bottom, Longer): =(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

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)

Method 2 (Even number of eyelet pairs, Use all eyelets, Longer): =(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)

Method 3 (Odd number of eyelet pairs, Skip eyelets near one end): =(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)

Double Helix Lacing (same formula as Criss Cross Lacing)

=(H+√(H²+V²)×(P−1)+L)×2

=(H+SQRT(H*H+V*V)*(P-1)+L)*2

Double Sided Lacing (each lace, same as Criss Cross Lacing)

=(H+√(H²+V²)×(P−1)+L)×2

=(H+SQRT(H*H+V*V)*(P-1)+L)*2

=H×(P+(P MODULO 2))+V×((P−(P MODULO 2))²÷2+(P MODULO 2)×2)+L×2

=H*(P+MOD(P,2))+V*((P-MOD(P,2))*(P-MOD(P,2))/2+MOD(P,2)*2)+L*2

=(H+V×INT((P−1)÷2)+√(H²+(V×2)²)+L)×2+√(H²+V²)×INT(P÷2)+√(H²+(V×3)²)×INT((P−4)÷2)

=(H+V*INT((P-1)/2)+SQRT(H*H+V*V*4)+L)*2+SQRT(H*H+V*V)*INT(P/2)+SQRT(H*H+V*V*9)*INT((P-4)/2)

Method 1 (Basic): =(H+V×5+√(H²+V²)×(P−4)+L)×2 =(H+V*5+SQRT(H*H+V*V)*(P-4)+L)*2

Method 2 (Corkscrew): =(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)

Method 3 (Extended): =(H+V×8+√(H²+V²)×(P−5)+L)×2 =(H+V*8+SQRT(H*H+V*V)*(P-5)+L)*2

Method 4 (Double extended): =(H+V×10+√(H²+V²)×(P−5)+L)×2 =(H+V*10+SQRT(H*H+V*V)*(P-5)+L)*2

Method 1 (Single vertical) (same formula as Chevron Lacing) =(H+V+√(H²+V²)×(P−2)+L)×2 =(H+V+SQRT(H*H+V*V)*(P-2)+L)*2

Method 2 (Double vertical): =(H+V×2+√(H²+V²)×(P−3)+L)×2 =(H+V*2+SQRT(H*H+V*V)*(P-3)+L)*2

=H×(P−2)+V×2+√(H²+V²)×(P−4)+√(H²+(V×2)²)+√(H²+(V×INT((P+1)÷2))²)×2+√(H²+(V×(P−2))²)+L×4

=H*(P-2)+V*2+SQRT(H*H+V*V)*(P-4)+SQRT(H*H+V*V*4)+SQRT(H*H+V*INT((P+1)/2)*V*INT((P+1)/2))*2+SQRT(H*H+V*(P-2)*V*(P-2))+L*4

Method 1 (Bi-color shoelace) (same formula as Criss Cross Lacing): =(H+√(H²+V²)×(P−1)+L)×2 =(H+SQRT(H*H+V*V)*(P-1)+L)*2

Method 2 (Knotted halves, each half-shoelace): =H+√(H²+V²)×(P−1)+L+50 mm =H+SQRT(H*H+V*V)*(P-1)+L+50 (This allows 50 mm = 2 inches for the joining knot)

Method 3 (Separate halves, each half-shoelace): =H÷2+√(H²+V²)×(P−1)+L+75 mm =H/2+SQRT(H*H+V*V)*(P-1)+L+75 (This allows 75 mm = 3 inches for the anchoring knot)

Method 1 (Bi-color shoelace) (same formula as Straight Bar Lacing): =(H×INT((P+1)÷2)+V×(P−1)+L)×2 =(H*INT((P+1)/2)+V*(P-1)+L)*2

Method 2 (Knotted halves), Half-shoelace 1 (Bottom): =H×(INT(P÷2)+0.5)+V×(P−0.5)+L+50 mm =H*(INT(P/2)+0.5)+V*(P-0.5)+L+50 (This allows 50 mm = 2 inches for the joining knot)

Method 2 (Knotted halves), Half-shoelace 2 (Second): =H×((P−1)÷2+(P MODULO 2)×1.5)+V×(P−1.5)+L+50 mm =H*((P-1)/2+MOD(P,2)*1.5)+V*(P-1.5)+L+50 (This allows 50 mm = 2 inches for the joining knot)

Method 3 (Separate halves), Half-shoelace 1 (Bottom, Longer): =H×(INT(P÷2)+0.5)+V×(P−1)+L+75 mm =H*(INT(P/2)+0.5)+V*(P-1)+L+75 (This allows 75 mm = 3 inches for the anchoring knot)

Method 3 (Separate halves), Half-shoelace 2 (Second, Shorter): =H×(INT((P−1)÷2)+0.5)+V×(P−2)+L+75 mm =H*(INT((P-1)/2)+0.5)+V*(P-2)+L+75 (This allows 75 mm = 3 inches for the anchoring knot)

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)

Method 2 (Even number of eyelet pairs, Use all eyelets, Longer): =(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)

Method 3 (Odd number of eyelet pairs, Skip eyelets near one end): =(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)

=(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.)

Hidden Knot Lacing (same formula as Straight Bar Lacing)

=(H×INT((P+1)÷2)+V×(P−1)+L)×2

=(H*INT((P+1)/2)+V*(P-1)+L)*2

Hiking / Biking Lacing (same formula as Straight Bar Lacing)

=(H×INT((P+1)÷2)+V×(P−1)+L)×2

=(H*INT((P+1)/2)+V*(P-1)+L)*2

=(H+V)×(2−(P MODULO 2))+SQRT(H×H+V×V)×((P MODULO 2)+INT((P−1)/2)×2.06)+L×2

=(H+V)*(2-MOD(P,2))+SQRT(H*H+V*V)*(MOD(P,2)+INT((P-1)/2)*2.06)+L*2

(This approximates 3% longer diagonals to allow for loop unders)

=(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)

=(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)

Method 1 (No lock at top, Shorter): =((H+V)×(P−1)+L)×2 =((H+V)*(P-1)+L)*2

Method 2 (With lock at top, Longer): =((H+V)×P−V+L)×2 =((H+V)*P-V+L)*2

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

Method 2 (Double verticals, Longer): =(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.)

Left Right Lacing (same formula as Criss Cross Lacing)

=(H+√(H²+V²)×(P−1)+L)×2

=(H+SQRT(H*H+V*V)*(P-1)+L)*2

=H×(2−(P MODULO 2))+√(H²+V²)×(P−1)+√(H²+(V×(P−1))²)+(V×INT((P−1)÷2)+L)×2

=H*(2-MOD(P,2))+SQRT(H*H+V*V)*(P-1)+SQRT(H*H+(V*(P-1))*(V*(P-1)))+(V*INT((P-1)/2)+L)*2

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

Method 2 (Low lock, Medium): =(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

Method 3 (Looped lock, Longer): =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)

Locked Double Helix Lacing (same formula as Criss Cross Lacing)

=(H+√(H²+V²)×(P−1)+L)×2

=(H+SQRT(H*H+V*V)*(P-1)+L)*2

NASA Space Boot Lacing (same formula as Train Track Lacing)

=((H+V)×(P−1)+L)×2

=((H+V)*(P-1)+L)*2

=(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)

=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)

Over Under Lacing (same formula as Criss Cross Lacing)

=(H+√(H²+V²)×(P−1)+L)×2

=(H+SQRT(H*H+V*V)*(P-1)+L)*2

Method 1 or 2 (Upright pentagrams, Longer): =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

Method 3 (Inverted pentagram, Shorter): =H×3+(V×(P−1)+√(H²+(V×(P−3))²)+√((H÷2)²+(V×(P−2))²)+L)×2 =H*3+(V*(P-1)+SQRT(H*H+V*(P-3)*V*(P-3))+SQRT(H*H/4+V*(P-2)*V*(P-2))+L)*2

Shoes with 4 Pairs of eyelets: =(H+√(H²+V²)+√(H²+(V×2)²)+L)×2+V×2 =(H+SQRT(H*H+V*V)+SQRT(H*H+V*V*4)+L)*2+V*2

Shoes with 5 Pairs of eyelets: =(H+√(H²+V²)+√(H²+(V×2)²)+L)×2+V×4 =(H+SQRT(H*H+V*V)+SQRT(H*H+V*V*4)+L)*2+V*4

Shoes with 6 Pairs of eyelets: =(H+√(H²+V²)+√(H²+(V×2)²)+√(H²+(V×3)²)+L)×2+V×6 =(H+SQRT(H*H+V*V)+SQRT(H*H+V*V*4)+SQRT(H*H+V*V*9)+L)*2+V*6

Shoes with 7 Pairs of eyelets: =(H+√(H²+V²)+√(H²+(V×2)²)+√(H²+(V×3)²)+L)×2+V×8 =(H+SQRT(H*H+V*V)+SQRT(H*H+V*V*4)+SQRT(H*H+V*V*9)+L)*2+V*8

Shoes with 8 Pairs of eyelets: =(H+√(H²+V²)+√(H²+(V×2)²)+√(H²+(V×3)²)+√(H²+(V×4)²)+L)×2+V×6 =(H+SQRT(H*H+V*V)+SQRT(H*H+V*V*4)+SQRT(H*H+V*V*9)+SQRT(H*H+V*V*16)+L)*2+V*6

Shoes with 4 Pairs of eyelets: =(H+√(H²+V²)+√(H²+(V×2)²)+L)×2 =(H+SQRT(H*H+V*V)+SQRT(H*H+V*V*4)+L)*2

Shoes with 5 Pairs of eyelets: =(H+√(H²+V²)×2+√(H²+(V×2)²)+L)×2 =(H+SQRT(H*H+V*V)*2+SQRT(H*H+V*V*4)+L)*2

Shoes with 6 Pairs of eyelets: =(H+V+√(H²+V²)+√(H²+(V×2)²)+√(H²+(V×3)²)+L)×2 =(H+V+SQRT(H*H+V*V)+SQRT(H*H+V*V*4)+SQRT(H*H+V*V*9)+L)*2

Shoes with 7 Pairs of eyelets: =(H+V+√(H²+V²)×2+√(H²+(V×2)²)+√(H²+(V×3)²)+L)×2 =(H+V+SQRT(H*H+V*V)*2+SQRT(H*H+V*V*4)+SQRT(H*H+V*V*9)+L)*2

Shoes with 8 Pairs of eyelets:

Method 1 (High horizontal section, Shorter): =(H+V×2+√(H²+V²)+√(H²+(V×2)²)+√(H²+(V×3)²)+√(H²+(V×4)²)+L)×2 =(H+V*2+SQRT(H*H+V*V)+SQRT(H*H+V*V*4)+SQRT(H*H+V*V*9)+SQRT(H*H+V*V*16)+L)*2

Shoes with 8 Pairs of eyelets:

Method 2 (Low horizontal section, Longer): =(H+V×5+√(H²+V²)+√(H²+(V×2)²)+√(H²+(V×3)²)+√(H²+(V×4)²)+L)×2 =(H+V*5+SQRT(H*H+V*V)+SQRT(H*H+V*V*4)+SQRT(H*H+V*V*9)+SQRT(H*H+V*V*16)+L)*2

=H×(P−2+(P MODULO 2))+V×((P−2)×2+(P MODULO 2))×2+L×2

=H*(P-2+MOD(P,2))+V*((P-2)*2+MOD(P,2))*2+L*2

=H×P+√(H²+V²)×(P−2)+√(H²+(V×INT((P+1)÷2))²)+√(H²+(V×INT(P÷2))²)+L×2

=H*P+SQRT(H*H+V*V)*(P-2)+SQRT(H*H+V*INT((P+1)/2)*V*INT((P+1)/2))+SQRT(H*H+V*INT(P/2)*V*INT(P/2))+L*2

Riding Boot Lacing (same formula 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

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

Shoes with 4, 10, 16, 22, etc. sets of eyelets:

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

Shoes with 8, 14, 20, 26, etc. sets of eyelets:

Method 2 ("X" at bottom, Ends tied at side, Medium): =(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

Shoes with 8, 14, 20, 26, etc. sets of eyelets:

Method 3 ("X" at bottom, Ends tied across top, Long): =(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

=H×P+√(H²+(V×2)²)×(P−2)+(V+L)×2

=H*P+SQRT(H*H+V*V*4)*(P-2)+(V+L)*2

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

Lace 2 (Longer segment): =(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)

Method 1 (Long diagonal, Longer) (same formula 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

Method 2 (Long straight, Shorter): =(H+V)×P+√(H²+V²)×(P−2)+L×2 =(H+V)*P+SQRT(H*H+V*V)*(P-2)+L*2

=(H+(V+√(H²+(V×2)²))×(P−2)+L)×2

=(H+(V+SQRT(H*H+V*V*4))*(P-2)+L)*2

=(H+V×INT(P÷2)+L)×2 ...

... +√(H²+(V×2)²)×2 (for 3 or more eyelet pairs) ...

... +√(H²+(V×4)²)×2 (for 5 or more eyelet pairs) ...

... +√(H²+(V×6)²)×2 (for 7 or more eyelet pairs) ...

... +√(H²+(V×8)²)×2 (for 9 or more eyelet pairs) ... (etc.)

=(H+V*INT(P/2)+L)*2 ...

... +SQRT(H*H+V*V*2*2)*2 (for 3 or more eyelet pairs) ...

... +SQRT(H*H+V*V*4*4)*2 (for 5 or more eyelet pairs) ...

... +SQRT(H*H+V*V*6*6)*2 (for 7 or more eyelet pairs) ...

... +SQRT(H*H+V*V*8*8)*2 (for 9 or more eyelet pairs) ... (etc.)

=(H×INT((P+1)÷2)+V×(P−1)+L)×2

=(H*INT((P+1)/2)+V*(P-1)+L)*2

Straight Easy Lacing (same formula as Straight Bar Lacing)

=(H×INT((P+1)÷2)+V×(P−1)+L)×2

=(H*INT((P+1)/2)+V*(P-1)+L)*2

=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)

=(H+L)×2 ...

... +√(H²+(V×1)²)×2 (for 2 or more eyelet pairs) ...

... +√(H²+(V×2)²)×2 (for 3 or more eyelet pairs) ...

... +√(H²+(V×3)²)×2 (for 4 or more eyelet pairs) ...

... +√(H²+(V×4)²)×2 (for 5 or more eyelet pairs) ... (etc.)

=(H+L)*2 ...

... +SQRT(H*H+V*V*1*1)*2 (for 2 or more eyelet pairs) ...

... +SQRT(H*H+V*V*2*2)*2 (for 3 or more eyelet pairs) ...

... +SQRT(H*H+V*V*3*3)*2 (for 4 or more eyelet pairs) ...

... +SQRT(H*H+V*V*4*4)*2 (for 5 or more eyelet pairs) ... (etc.)

Train Track Lacing (same formula as NASA Space Boot Lacing)

=((H+V)×(P−1)+L)×2

=((H+V)*(P-1)+L)*2

=(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)

=(H+√(H²+V²)×(P−3)+√(H²+(V×2)²)×2+L)×2

=(H+SQRT(H*H+V*V)*(P-3)+SQRT(H*H+V*V*4)*2+L)*2

Method 1 (Ends stop-knotted): =H+(√(H²+V²)×(P−2)+L)×2 =H+(SQRT(H*H+V*V)*(P-2)+L)*2

Method 2 (Ends tied together): =(H+√(H²+V²)×(P−2)+L)×2 =(H+SQRT(H*H+V*V)*(P-2)+L)*2

=(H+V×(P−3)+√(H²+(V×2)²)×(P−2)+L)×2

=(H+V*(P-3)+SQRT(H*H+V*V*4)*(P-2)+L)*2

=(H+V×(P−1)+L)×2

=(H+V*(P-1)+L)*2

=(H+√((H×3)²+(V×3)²)×1.05×(P−1)+L)×2

=(H+SQRT(H*H*9+V*V*9)*1.05*(P-1)+L)*2

(This approximates 5% longer diagonals to allow for weaving)

=(H+L)×2+(V+√((H×2)²+V²))×(P−1)

=(H+L)*2+(V+SQRT(H*H*4+V*V))*(P-1)

=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)

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

Method 2 (Diagonals at bottom, Longer): =(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)

=(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

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

Lace 2 (Second, Shorter): =(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)

=(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

=(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

=(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.)

=(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

=(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

=(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)

=(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)

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

Method 2 (With lock at top, Longer): =(H+(V+W+√(H²+W²))×(P−1)+L)×2 =(H+(V+W+SQRT(H*H+W*W))*(P-1)+L)*2

=(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

=(H+V+W×(P−1)+√(H²+(V−W)²)×(P−2)+√(H²+((V+W)÷2)²)+L)×2

=(H+V+W*(P-1)+SQRT(H*H+(V-W)*(V-W))*(P-2)+SQRT(H*H+(V+W)/2*(V+W)/2)+L)*2

=(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)

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

Lace 2 (Longer segment): =(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)

=(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))

=(H+(V+√(H²+(V+V+W)²)×(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

Method 1 (Single pass at top/bottom, Shorter): =((H+V+W)×(P−1)+L)×2 =((H+V+W)*(P-1)+L)*2

Method 2 (Single pass at top/bottom, Longer): =((H+W)×(P+1)+V×(P−1)+L)×2 =((H+W)*(P+1)+V*(P-1)+L)*2

=(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)

=((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)