How to Make an A4 Rectangle from a Square (Origami Guide)

Overview

This origami construction shows how to transform any square sheet of paper into a perfect A4 rectangle, following the ISO 216 standard proportion (1 : √2).

Unlike traditional origami models, this is a geometric construction that is extremely useful for paper resizing, printing alignment, and mathematical exploration using paper folding techniques.

What is the A4 Proportion?

The A4 format follows a unique aspect ratio defined by the ISO 216 standard:

• Ratio: 1 : √2 (approximately 1 : 1.414)
• This ratio allows a sheet to be folded in half while preserving proportions

This is why all A-series paper sizes (A0, A1, A2, A3, A4, etc.) maintain the same shape when scaled.

Difficulty

Beginner to Intermediate

While the folds themselves are simple, precision is important to achieve the exact mathematical proportion.

Tips for Accuracy

• Use thin paper for better precision
• Align edges carefully before creasing
• Repeat folds lightly before committing
• Small errors can affect the final proportion

Applications

This construction is useful for:

• Creating A4 sheets from square paper
• Understanding geometric constructions
• Teaching mathematical concepts visually
• Origami design and paper engineering

Mathematical Insight

This model is a great demonstration of how origami can be used as a tool for geometric construction.

By using folds instead of measurements, it is possible to accurately recreate irrational ratios like √2 with surprising precision.