Printable Semi-Log Graph Paper

What a log cycle is

On a logarithmic axis every power of ten takes the same distance. One cycle (or decade) runs from 1 to 10, the next from 10 to 100, and so on. The printed labels 1 to 9 repeat in every cycle; you multiply them by the power of ten for that cycle. Count how many powers of ten your data spans: values from 2 to 5,000 cover 1–10, 10–100, 100–1,000 and 1,000–10,000, so you need four cycles.

Why use semi-log paper?

Exponential relationships, y = a·b^x, become straight lines when y is plotted on a log scale. That makes semi-log paper the standard way to:

• check whether data grows or decays exponentially (bacteria growth, radioactive decay, compound interest, capacitor discharge),
• read a growth rate or half-life from the slope of a straight line,
• draw Bode plots, where frequency goes on a log x-axis and gain in decibels on a linear y-axis.

The Bode plot preset puts five cycles across a landscape page, enough for 10 Hz to 1 MHz.

Reading the scale

Between 1 and 10 the lines get closer together: the gap from 1 to 2 is about 30% of the cycle, while the gap from 9 to 10 is under 5%. Half-step lines at 1.5, 2.5, 3.5 and 4.5 help with the wide intervals. Never interpolate linearly between log lines; use the printed sub-lines instead.