Custom Envelope Calculator (Metric) – Precision Fit Using √2 Geometry

Description

Create perfectly fitted envelopes for any paper size using a mathematically consistent model.

This calculator is based on a 45° diagonal projection method, allowing you to generate a square envelope blank from any rectangular insert. Unlike standard Vaessen Creative scoring boards, this approach is not limited to predefined sizes and gives you full control over fit and clearance.

The algorithm:

L=x+y2+2z,S1=x2+z,S2=y2+zL = \frac{x + y}{\sqrt{2}} + 2z,\quad S_1 = \frac{x}{\sqrt{2}} + z,\quad S_2 = \frac{y}{\sqrt{2}} + z

You define:

  • Insert width (x)
  • Insert length (y)
  • Padding (z)

The system calculates:

  • Required square paper size
  • Two scoring distances

Padding (z) controls how tight or loose the envelope fits.
Recommended defaults:

  • 10 mm → tight fit
  • 15 mm → standard (default)
  • 20 mm → loose / bulky inserts

This method is ideal for:

  • Non-standard paper sizes (JIS, custom cuts)
  • Folded sheets
  • Precision crafting

Calculator

Envelope Calculator (Metric)

Enter the finished folded insert size in millimetres.

Use the folded size of the insert, not the original flat sheet size.



Padding (z)

Precalculated Values For Folded Sheets

A series

Paper / FoldWidth (x) in mmLength (y) in mmPadding (z)Square paper sizeScore 1Score 2Rounded cut sizeRounded score marks
A4 half-fold (A5)210148.510 mm273.5 mm × 273.5 mm158.5 mm115.0 mm273 mm × 273 mm158 mm and 115 mm
A4 half-fold (A5)210148.515 mm283.5 mm × 283.5 mm163.5 mm120.0 mm283 mm × 283 mm163 mm and 120 mm
A4 half-fold (A5)210148.520 mm293.5 mm × 293.5 mm168.5 mm125.0 mm293 mm × 293 mm168 mm and 125 mm
A4 tri-fold2109910 mm238.5 mm × 238.5 mm158.5 mm80.0 mm238 mm × 238 mm158 mm and 80 mm
A4 tri-fold2109915 mm248.5 mm × 248.5 mm163.5 mm85.0 mm248 mm × 248 mm163 mm and 85 mm
A4 tri-fold2109920 mm258.5 mm × 258.5 mm168.5 mm90.0 mm258 mm × 258 mm168 mm and 90 mm
A5 half-fold (A6)14810510 mm198.9 mm × 198.9 mm114.7 mm84.2 mm199 mm × 199 mm115 mm and 84 mm
A5 half-fold (A6)14810515 mm208.9 mm × 208.9 mm119.7 mm89.2 mm209 mm × 209 mm120 mm and 89 mm
A5 half-fold (A6)14810520 mm218.9 mm × 218.9 mm124.7 mm94.2 mm219 mm × 219 mm125 mm and 94 mm
A6 half-fold (A7)1057410 mm146.6 mm × 146.6 mm84.2 mm62.3 mm147 mm × 147 mm84 mm and 62 mm
A6 half-fold (A7)1057415 mm156.6 mm × 156.6 mm89.2 mm67.3 mm157 mm × 157 mm89 mm and 67 mm
A6 half-fold (A7)1057420 mm166.6 mm × 166.6 mm94.2 mm72.3 mm167 mm × 167 mm94 mm and 72 mm

B series — ISO

Paper / FoldWidth (x) in mmLength (y) in mmPadding (z)Square paper sizeScore 1Score 2Rounded cut sizeRounded score marks
B5 ISO half-fold (B6)17612510 mm232.8 mm × 232.8 mm134.5 mm98.4 mm233 mm × 233 mm134 mm and 98 mm
B5 ISO half-fold (B6)17612515 mm242.8 mm × 242.8 mm139.5 mm103.4 mm243 mm × 243 mm139 mm and 103 mm
B5 ISO half-fold (B6)17612520 mm252.8 mm × 252.8 mm144.5 mm108.4 mm253 mm × 253 mm144 mm and 108 mm
B6 ISO half-fold (B7)1258810 mm170.6 mm × 170.6 mm98.4 mm72.2 mm171 mm × 171 mm98 mm and 72 mm
B6 ISO half-fold (B7)1258815 mm180.6 mm × 180.6 mm103.4 mm77.2 mm181 mm × 181 mm103 mm and 77 mm
B6 ISO half-fold (B7)1258820 mm190.6 mm × 190.6 mm108.4 mm82.2 mm191 mm × 191 mm108 mm and 82 mm

B series — JIS

Paper / FoldWidth (x) in mmLength (y) in mmPadding (z)Square paper sizeScore 1Score 2Rounded cut sizeRounded score marks
B5 JIS half-fold (B6)182128.510 mm239.6 mm × 239.6 mm138.7 mm100.9 mm240 mm × 240 mm139 mm and 101 mm
B5 JIS half-fold (B6)182128.515 mm249.6 mm × 249.6 mm143.7 mm105.9 mm250 mm × 250 mm144 mm and 106 mm
B5 JIS half-fold (B6)182128.520 mm259.6 mm × 259.6 mm148.7 mm110.9 mm260 mm × 260 mm149 mm and 111 mm
B6 JIS half-fold (B7)1289110 mm174.9 mm × 174.9 mm100.5 mm74.3 mm175 mm × 175 mm101 mm and 74 mm
B6 JIS half-fold (B7)1289115 mm184.9 mm × 184.9 mm105.5 mm79.3 mm185 mm × 185 mm106 mm and 79 mm
B6 JIS half-fold (B7)1289120 mm194.9 mm × 194.9 mm110.5 mm84.3 mm195 mm × 195 mm111 mm and 84 mm

How to Make a Custom Envelope for JIS B5 Folded in Half

Finished insert size

A JIS B5 sheet is 182 mm × 257 mm. Folded in half, the insert becomes:

182 mm × 128.5 mm

Using 15 mm padding, the calculator gives:

MeasurementExactPractical (Rounded)
Square paper size249.6 mm × 249.6 mm250 mm × 250 mm
Score 1143.7 mm144 mm
Score 2105.9 mm106 mm

Tools and materials

You will need:

Practical reference

For a JIS B5 sheet folded in half with 15 mm padding, use:

Cut size: 250 mm × 250 mm
Score marks: 144 mm and 106 mm
Score pattern: 144 → 106 → 144 → 106

Step 1: Prepare the workspace

Set out the paper cutter, scoring board, diagonal guide, folding tool, punch, glue and paper.

Step 2: Cut the donor sheet

Start with a JIS B4 donor sheet.

Cut it to:

250 mm × 250 mm

The calculated size is 249.6 mm, so 250 mm is the practical cut size.

Step 3: Set up the scoring board

Place the diagonal scoring guide into the Vaessen Creative Score Easy board.

Step 4: Make the first score

Place the square sheet on the scoring board with one corner aligned to the diagonal guide.

Score at:

144 mm

Step 5: Rotate and make the second score

Rotate the paper 90 degrees.

Score at:

106 mm

Step 6: Complete all four score lines

Continue rotating the paper and alternate the score marks:

144 mm → 106 mm → 144 mm → 106 mm

When finished, the sheet should have four score lines.

Step 7: Check the score pattern

The score lines should form an X-style structure where the folds meet.

Step 8: Punch out the corners

Use the corner punch to remove the small corner sections where the folds meet. This reduces bulk and helps the envelope fold cleanly.

Step 9: Test the insert fit

Place the folded JIS B5 sheet into the future envelope before gluing. Confirm that it fits comfortably.

Step 10: Optional: round the flap corner

Use a 10 mm Corner Punch if you want a cleaner finished flap.

Step 11: Fold the envelope

Fold along all score lines. Bring the side flaps inward first, then fold the bottom flap up.

Step 12: Apply glue

Apply a small amount of glue to the smaller side flap or overlap area. Avoid using too much glue.

Step 13: Press the glued flap

Fold the glued flap into place and press firmly. Let the glue set.

Step 14: Insert the folded sheet

Place the folded JIS B5 sheet into the finished envelope.

Step 15: Close the final flap

Fold the top flap down to close the envelope.

Step 16: Finished envelope

The finished envelope should fit the folded JIS B5 insert neatly with 15 mm padding.

Step 17: Store the tools

Store the diagonal guide and folding knife in the back of the Score Easy board.

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