Semi-Log Graph Paper
Logarithmic graph paper for exponential growth, decay, frequency response and power laws. Choose semi-log (one log axis) or log-log (both), and the number of cycles.
Preview with a centimetre and inch rule. The rule is not printed.
Vector PDF, no watermark. Print at Actual size / 100% so squares measure true (why).
Try it: linear vs log scale
On the linear axis, everything under 100 is squashed into the first tenth; your value sits 2% of the way along. On the log axis it sits 43% along, because 1→10, 10→100 and 100→1,000 each get a third. Doubling anything moves the dot the same distance (log 2 ≈ 0.30 of a cycle), which is why steady growth plots as a straight line.
When to use log paper
On a logarithmic axis, equal distances stand for equal ratios instead of equal differences: 1 to 10 takes the same space as 10 to 100. Each of those ×10 bands is one cycle (or decade), and within a cycle the lines bunch up towards the top because log 2 ≈ 0.301 of the way, log 5 ≈ 0.699 of the way.
Semi-log paper turns exponential curves such as bacterial growth, radioactive decay or compound growth into straight lines, so you can read the rate off the slope. Log-log paper straightens power laws like y = a·xk; the slope is the exponent k. Count how many powers of ten your data spans to choose the number of cycles.
Questions
What is a cycle on semi-log paper?
One cycle covers a factor of ten, for example 1–10 or 100–1,000. Data spanning 0.5 to 400 needs four cycles (0.1–1,000).
Where is zero on a log scale?
Nowhere. A logarithmic axis never reaches zero, so you label the bottom line with any power of ten that suits your data.
How do I label the axis?
The printed 1–9 marks repeat every cycle. Multiply them by the power of ten for that cycle, such as 1, 2, 3 … then 10, 20, 30 …