Origami Paper Size Calculator

What the inputs mean

• Original paper size (P): the side length of the square paper you used for the test fold (e.g., 15 cm).
• Model size from original paper (M): one consistent measurement of the finished model from that test fold (e.g., height, wingspan, or box width).
• Desired model size (M_f): the finished measurement you want the model to be after scaling, using the same measurement method as M.

Tip: If the model has several notable dimensions (height and wingspan, for example), pick the one that matters for your use case and use it consistently for both M and M_f.

Formula (uniform scaling)

Let:

• P = original square paper side length
• M = model size produced from that original paper
• M_f = desired model size
• P_f = required new square paper side length

The proportional scaling relationship is:

P_f = P × (M_f / M)

This assumes the model’s proportions scale uniformly with paper size (i.e., doubling the finished size requires doubling the starting paper side). For many traditional and modular designs this is a good approximation.

Interpreting the result

The output is the side length of a square sheet to start with. If you only have rectangular paper, you can still use the result as a target for the largest square you can cut from that sheet.

If the computed paper size is inconvenient (for example 23.7 cm), round to a size you can actually obtain, then expect the finished model size to shift by the same factor. If you increase paper by 2%, the finished dimension you measured will also increase by about 2%.

Worked example

Suppose you folded a model from a 15 cm square and measured the finished model height as 5 cm. You want the height to be 10 cm.

• P = 15
• M = 5
• M_f = 10

Compute:

P_f = 15 × (10 / 5) = 15 × 2 = 30

So you should start with a 30 cm square to get approximately a 10 cm model (using that same height measurement).

Common ratios (example table)

The table below assumes a model that is 5 cm tall when folded from a 15 cm square (so P/M = 3). It shows how different targets scale the required paper size.

Assumptions & limitations

• Uniform scaling: The calculation assumes the model scales linearly with paper side length. This can be less accurate for designs with many locked layers or strong 3D shaping.
• Measurement choice matters: If you measure height for M, use height again for M_f. Mixing dimensions (e.g., wingspan vs height) breaks the proportional relationship.
• Paper thickness and stiffness: Very thick paper can “consume” more material in layers, making the final dimension slightly smaller than predicted (especially for small folds). Very large models may sag unless you use sturdier paper.
• Precision limits: Rounding the paper size and real-world folding tolerances (creasing accuracy, humidity) introduce small deviations.
• Non-square starts: This calculator is for square origami. If a diagram starts from a rectangle (e.g., A4), you’ll need a different approach.
• M must be > 0: If the measured original model size is zero or extremely small, the ratio becomes undefined or unstable.