origami calculator
Calculate origami paper sizes (ISO A-series, squares, rectangles), scaling from diagrams, stripe/pleat spacing, and grid/diagonal lengths. Accessible, mobile-first, and accurate.
Full original guide (expanded)
origami calculator
Plan origami projects with engineering-grade precision: convert ISO A-series sizes to squares, compute required paper for scaling a diagram, lay out stripe/pleat grids with margins and gaps, and get diagonal & grid metrics instantly. Ideal for designers, teachers, and hobbyists.
Origami Calculator Interface
Results
Primary Output
—
Secondary
—
Notes
—
Authoritative Data Source & Methodology
- ISO 216:2007 – Writing paper and certain classes of printed matter — Trimmed sizes — A and B series, and indication of machine direction. Published by ISO (International Organization for Standardization). Official dimensions and √2 aspect rules are used for all A-series computations. Primary standard. Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
- Computational Origami (R. J. Lang). Conceptual background on mathematical modeling in origami design, grids, and scaling relationships. Article.
The Formula Explained
Largest square from rectangle: If rectangle is \(w \times h\) (mm), largest square side \(s\) is:
\[ s=\min(w,h),\quad \text{waste}=\max(w,h)-s \]Scale planner: Original paper side \(P_0\) yields model size \(M_0\). For a target model \(M_t\):
\[ k=\frac{M_t}{M_0},\quad P_t=k\cdot P_0,\quad P_t' = P_t\,(1+m) \] where \(m\) is margin fraction (e.g., 0.03 for 3%).Stripe/Pleat: with usable width \(W\), margins \(L,R\), gap \(g\), stripes \(N\): \[ w=\frac{W-(L+R)-(N-1)\,g}{N} \] Diagonal & grid: for square side \(a\) and grid \(n\): \[ d=a\sqrt{2},\quad \Delta=\frac{a}{n} \]
Glossary of Variables
| Symbol / Field | Meaning | Units |
|---|---|---|
| \(w,h\) | Rectangle width and height | mm |
| \(s\) | Largest square side fitting in the rectangle | mm |
| \(P_0\), \(M_0\) | Original paper side, finished model size from diagram | mm |
| \(M_t\) | Target finished model size | mm |
| \(k\) | Scale factor | — |
| \(P_t\), \(P_t'\) | Required paper side (raw / with margin) | mm |
| \(W\) | Usable sheet width for stripes/pleats | mm |
| \(L,R\) | Left and right margins | mm |
| \(g\) | Gap between stripes | mm |
| \(N\) | Number of stripes/pleats | — |
| \(a\) | Square side | mm |
| \(d\) | Diagonal of square | mm |
| \(\Delta\) | Grid spacing | mm |
How It Works: A Step-by-Step Example
Target a 120 mm crane from a diagram using 150 mm paper → 75 mm model
- From the diagram: \(P_0=150\) mm produces \(M_0=75\) mm. You want \(M_t=120\) mm.
- Scale factor \(k=M_t/M_0=120/75=1.6\).
- Required paper side \(P_t=k\cdot P_0=1.6 \cdot 150=240\) mm.
- Add 3% safety margin: \(P_t' = 240 \times 1.03 = 247.2\) mm → cut a 248 mm square.
Frequently Asked Questions
Is A4 big enough for complex models?
Often not. Use the Scale Planner to compute the required side from the model’s diagram specs. Many complex designs need 250–350 mm squares or larger.
What paper thickness should I assume?
For dry folding, 60–90 gsm works for many models. Wet-folding and complex tessellations often benefit from thinner or specialized papers. Keep a 2–5% size margin.
Why do I get a negative stripe width?
The combination of margins, gaps, and stripe count exceeds the usable width. Reduce margins/gaps or the number of stripes.
How do I convert to inches?
Enter dimensions in millimeters; 25.4 mm = 1 inch. (A4 is ~8.27 × 11.69 in.)
Can I preserve the √2 aspect when trimming?
Yes—halve the long side to keep the A-series ratio. For a square, trim the long side down to the short side.
Formula (LaTeX) + variables + units
s=\min(w,h),\quad \text{waste}=\max(w,h)-s
k=\frac{M_t}{M_0},\quad P_t=k\cdot P_0,\quad P_t' = P_t\,(1+m)
w=\frac{W-(L+R)-(N-1)\,g}{N}
d=a\sqrt{2},\quad \Delta=\frac{a}{n}
Largest square from rectangle: If rectangle is \(w \times h\) (mm), largest square side \(s\) is: \[ s=\min(w,h),\quad \text{waste}=\max(w,h)-s \] Scale planner: Original paper side \(P_0\) yields model size \(M_0\). For a target model \(M_t\): \[ k=\frac{M_t}{M_0},\quad P_t=k\cdot P_0,\quad P_t' = P_t\,(1+m) \] where \(m\) is margin fraction (e.g., 0.03 for 3%). Stripe/Pleat: with usable width \(W\), margins \(L,R\), gap \(g\), stripes \(N\): \[ w=\frac{W-(L+R)-(N-1)\,g}{N} \] Diagonal & grid: for square side \(a\) and grid \(n\): \[ d=a\sqrt{2},\quad \Delta=\frac{a}{n} \]
- No variables provided in audit spec.
- Primary standard — iso.org · Accessed 2026-01-19
https://www.iso.org/standard/36631.html - Home — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/ - Lifestyle Everyday — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/lifestyle-everyday - Hobbies — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/subcategories/hobbies - Article — langorigami.com · Accessed 2026-01-19
https://langorigami.com/article/computational-origami/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.
origami calculator
Plan origami projects with engineering-grade precision: convert ISO A-series sizes to squares, compute required paper for scaling a diagram, lay out stripe/pleat grids with margins and gaps, and get diagonal & grid metrics instantly. Ideal for designers, teachers, and hobbyists.
Origami Calculator Interface
Results
Primary Output
—
Secondary
—
Notes
—
Authoritative Data Source & Methodology
- ISO 216:2007 – Writing paper and certain classes of printed matter — Trimmed sizes — A and B series, and indication of machine direction. Published by ISO (International Organization for Standardization). Official dimensions and √2 aspect rules are used for all A-series computations. Primary standard. Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
- Computational Origami (R. J. Lang). Conceptual background on mathematical modeling in origami design, grids, and scaling relationships. Article.
The Formula Explained
Largest square from rectangle: If rectangle is \(w \times h\) (mm), largest square side \(s\) is:
\[ s=\min(w,h),\quad \text{waste}=\max(w,h)-s \]Scale planner: Original paper side \(P_0\) yields model size \(M_0\). For a target model \(M_t\):
\[ k=\frac{M_t}{M_0},\quad P_t=k\cdot P_0,\quad P_t' = P_t\,(1+m) \] where \(m\) is margin fraction (e.g., 0.03 for 3%).Stripe/Pleat: with usable width \(W\), margins \(L,R\), gap \(g\), stripes \(N\): \[ w=\frac{W-(L+R)-(N-1)\,g}{N} \] Diagonal & grid: for square side \(a\) and grid \(n\): \[ d=a\sqrt{2},\quad \Delta=\frac{a}{n} \]
Glossary of Variables
| Symbol / Field | Meaning | Units |
|---|---|---|
| \(w,h\) | Rectangle width and height | mm |
| \(s\) | Largest square side fitting in the rectangle | mm |
| \(P_0\), \(M_0\) | Original paper side, finished model size from diagram | mm |
| \(M_t\) | Target finished model size | mm |
| \(k\) | Scale factor | — |
| \(P_t\), \(P_t'\) | Required paper side (raw / with margin) | mm |
| \(W\) | Usable sheet width for stripes/pleats | mm |
| \(L,R\) | Left and right margins | mm |
| \(g\) | Gap between stripes | mm |
| \(N\) | Number of stripes/pleats | — |
| \(a\) | Square side | mm |
| \(d\) | Diagonal of square | mm |
| \(\Delta\) | Grid spacing | mm |
How It Works: A Step-by-Step Example
Target a 120 mm crane from a diagram using 150 mm paper → 75 mm model
- From the diagram: \(P_0=150\) mm produces \(M_0=75\) mm. You want \(M_t=120\) mm.
- Scale factor \(k=M_t/M_0=120/75=1.6\).
- Required paper side \(P_t=k\cdot P_0=1.6 \cdot 150=240\) mm.
- Add 3% safety margin: \(P_t' = 240 \times 1.03 = 247.2\) mm → cut a 248 mm square.
Frequently Asked Questions
Is A4 big enough for complex models?
Often not. Use the Scale Planner to compute the required side from the model’s diagram specs. Many complex designs need 250–350 mm squares or larger.
What paper thickness should I assume?
For dry folding, 60–90 gsm works for many models. Wet-folding and complex tessellations often benefit from thinner or specialized papers. Keep a 2–5% size margin.
Why do I get a negative stripe width?
The combination of margins, gaps, and stripe count exceeds the usable width. Reduce margins/gaps or the number of stripes.
How do I convert to inches?
Enter dimensions in millimeters; 25.4 mm = 1 inch. (A4 is ~8.27 × 11.69 in.)
Can I preserve the √2 aspect when trimming?
Yes—halve the long side to keep the A-series ratio. For a square, trim the long side down to the short side.
Formula (LaTeX) + variables + units
s=\min(w,h),\quad \text{waste}=\max(w,h)-s
k=\frac{M_t}{M_0},\quad P_t=k\cdot P_0,\quad P_t' = P_t\,(1+m)
w=\frac{W-(L+R)-(N-1)\,g}{N}
d=a\sqrt{2},\quad \Delta=\frac{a}{n}
Largest square from rectangle: If rectangle is \(w \times h\) (mm), largest square side \(s\) is: \[ s=\min(w,h),\quad \text{waste}=\max(w,h)-s \] Scale planner: Original paper side \(P_0\) yields model size \(M_0\). For a target model \(M_t\): \[ k=\frac{M_t}{M_0},\quad P_t=k\cdot P_0,\quad P_t' = P_t\,(1+m) \] where \(m\) is margin fraction (e.g., 0.03 for 3%). Stripe/Pleat: with usable width \(W\), margins \(L,R\), gap \(g\), stripes \(N\): \[ w=\frac{W-(L+R)-(N-1)\,g}{N} \] Diagonal & grid: for square side \(a\) and grid \(n\): \[ d=a\sqrt{2},\quad \Delta=\frac{a}{n} \]
- No variables provided in audit spec.
- Primary standard — iso.org · Accessed 2026-01-19
https://www.iso.org/standard/36631.html - Home — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/ - Lifestyle Everyday — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/lifestyle-everyday - Hobbies — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/subcategories/hobbies - Article — langorigami.com · Accessed 2026-01-19
https://langorigami.com/article/computational-origami/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.
origami calculator
Plan origami projects with engineering-grade precision: convert ISO A-series sizes to squares, compute required paper for scaling a diagram, lay out stripe/pleat grids with margins and gaps, and get diagonal & grid metrics instantly. Ideal for designers, teachers, and hobbyists.
Origami Calculator Interface
Results
Primary Output
—
Secondary
—
Notes
—
Authoritative Data Source & Methodology
- ISO 216:2007 – Writing paper and certain classes of printed matter — Trimmed sizes — A and B series, and indication of machine direction. Published by ISO (International Organization for Standardization). Official dimensions and √2 aspect rules are used for all A-series computations. Primary standard. Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
- Computational Origami (R. J. Lang). Conceptual background on mathematical modeling in origami design, grids, and scaling relationships. Article.
The Formula Explained
Largest square from rectangle: If rectangle is \(w \times h\) (mm), largest square side \(s\) is:
\[ s=\min(w,h),\quad \text{waste}=\max(w,h)-s \]Scale planner: Original paper side \(P_0\) yields model size \(M_0\). For a target model \(M_t\):
\[ k=\frac{M_t}{M_0},\quad P_t=k\cdot P_0,\quad P_t' = P_t\,(1+m) \] where \(m\) is margin fraction (e.g., 0.03 for 3%).Stripe/Pleat: with usable width \(W\), margins \(L,R\), gap \(g\), stripes \(N\): \[ w=\frac{W-(L+R)-(N-1)\,g}{N} \] Diagonal & grid: for square side \(a\) and grid \(n\): \[ d=a\sqrt{2},\quad \Delta=\frac{a}{n} \]
Glossary of Variables
| Symbol / Field | Meaning | Units |
|---|---|---|
| \(w,h\) | Rectangle width and height | mm |
| \(s\) | Largest square side fitting in the rectangle | mm |
| \(P_0\), \(M_0\) | Original paper side, finished model size from diagram | mm |
| \(M_t\) | Target finished model size | mm |
| \(k\) | Scale factor | — |
| \(P_t\), \(P_t'\) | Required paper side (raw / with margin) | mm |
| \(W\) | Usable sheet width for stripes/pleats | mm |
| \(L,R\) | Left and right margins | mm |
| \(g\) | Gap between stripes | mm |
| \(N\) | Number of stripes/pleats | — |
| \(a\) | Square side | mm |
| \(d\) | Diagonal of square | mm |
| \(\Delta\) | Grid spacing | mm |
How It Works: A Step-by-Step Example
Target a 120 mm crane from a diagram using 150 mm paper → 75 mm model
- From the diagram: \(P_0=150\) mm produces \(M_0=75\) mm. You want \(M_t=120\) mm.
- Scale factor \(k=M_t/M_0=120/75=1.6\).
- Required paper side \(P_t=k\cdot P_0=1.6 \cdot 150=240\) mm.
- Add 3% safety margin: \(P_t' = 240 \times 1.03 = 247.2\) mm → cut a 248 mm square.
Frequently Asked Questions
Is A4 big enough for complex models?
Often not. Use the Scale Planner to compute the required side from the model’s diagram specs. Many complex designs need 250–350 mm squares or larger.
What paper thickness should I assume?
For dry folding, 60–90 gsm works for many models. Wet-folding and complex tessellations often benefit from thinner or specialized papers. Keep a 2–5% size margin.
Why do I get a negative stripe width?
The combination of margins, gaps, and stripe count exceeds the usable width. Reduce margins/gaps or the number of stripes.
How do I convert to inches?
Enter dimensions in millimeters; 25.4 mm = 1 inch. (A4 is ~8.27 × 11.69 in.)
Can I preserve the √2 aspect when trimming?
Yes—halve the long side to keep the A-series ratio. For a square, trim the long side down to the short side.
Formula (LaTeX) + variables + units
s=\min(w,h),\quad \text{waste}=\max(w,h)-s
k=\frac{M_t}{M_0},\quad P_t=k\cdot P_0,\quad P_t' = P_t\,(1+m)
w=\frac{W-(L+R)-(N-1)\,g}{N}
d=a\sqrt{2},\quad \Delta=\frac{a}{n}
Largest square from rectangle: If rectangle is \(w \times h\) (mm), largest square side \(s\) is: \[ s=\min(w,h),\quad \text{waste}=\max(w,h)-s \] Scale planner: Original paper side \(P_0\) yields model size \(M_0\). For a target model \(M_t\): \[ k=\frac{M_t}{M_0},\quad P_t=k\cdot P_0,\quad P_t' = P_t\,(1+m) \] where \(m\) is margin fraction (e.g., 0.03 for 3%). Stripe/Pleat: with usable width \(W\), margins \(L,R\), gap \(g\), stripes \(N\): \[ w=\frac{W-(L+R)-(N-1)\,g}{N} \] Diagonal & grid: for square side \(a\) and grid \(n\): \[ d=a\sqrt{2},\quad \Delta=\frac{a}{n} \]
- No variables provided in audit spec.
- Primary standard — iso.org · Accessed 2026-01-19
https://www.iso.org/standard/36631.html - Home — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/ - Lifestyle Everyday — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/lifestyle-everyday - Hobbies — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/subcategories/hobbies - Article — langorigami.com · Accessed 2026-01-19
https://langorigami.com/article/computational-origami/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.