Log-Log · 1×1 Decade

About Log-Log · 1×1 Decade

Logarithmic ruling on both axes with a 1×1 decade range (1–10 in both directions). Power-law relationships y = a·xⁿ plot as straight lines on log-log paper, which made it the workhorse of allometric biology, fluid dynamics, and statistical physics throughout the 20th century. Further reading: A practitioner reading list covers the standards lineage in more depth.

Standards lineage

Formal definition in ISO 31-11:1992 mathematical signs.

A short history

Log-log paper was developed in the 1900s for engineering pressure-flow relationships in pipes and remained the standard graphical medium for scaling-law work into the 1980s.

Where designers reach for it

• Power-law and allometric plots
• Particle-size distribution charts
• Stress-strain log-log plots in materials science
• Pareto and Zipf-law frequency plots

Printing this grid

Every variant on this page is delivered as a vector SVG with physical millimetre dimensions baked into the file, so a compliant printer driver will reproduce it at exact 1:1 scale by default. Choose the sheet size that matches your printer tray, set scaling to 100 % (never "fit to page"), and verify with the calibration check on our how-to-print guide. Buyer's guide: Comparing the major architectural scale rulers can help you pick the right physical scale rule to use over the printed grid.