Printable semi-log and log-log graph paper PDF
Logarithmic grids for data that spans many orders of magnitude. Choose semi-log or log-log and the number of decades on each axis.
Ready-to-print semi-log and log-log paper PDFs
One-click downloads with the preset settings and a 10 mm margin. They print at actual size.
Popular semi-log and log-log paper downloads
About semi-log and log-log paper
On logarithmic paper the spacing of the lines is proportional to the logarithm of the number rather than the number itself. Each repeating block is called a cycle or decade and covers a factor of ten, for example from 1 to 10 or from 10 to 100. Within a cycle the lines bunch up toward the top, just as the logarithms of 2, 3, 4 ... 9 do.
Semi-log paper has a logarithmic vertical axis and a linear horizontal axis. Exponential growth and decay plot as straight lines on it, so it is used for population growth, radioactive decay and charging curves. Log-log paper has logarithmic scales on both axes, where power laws plot as straight lines.
The generator draws the lines at 1 through 9 of every decade with the 1 line of each cycle drawn heavy and the 5 line drawn a little stronger, and labels each cycle as a power of ten. You can start the first cycle at any exponent, so a graph can run from 0.01 to 100 or from 1000 to 1000000.
What you can use it for
- Exponential growth and decay in biology, physics and finance
- Frequency response and Bode plots in electronics
- Power-law relationships such as scaling laws
- Earthquake, sound and pH data across many magnitudes
- Lab reports that require log paper
The options explained
- Paper type. Semi-log (linear x, logarithmic y) or log-log (both logarithmic).
- Vertical and horizontal cycles. Between 1 and 7 decades per axis. The presets use 2, 3 and 4.
- Horizontal divisions. For semi-log paper, how many linear divisions appear across the page.
- Number the cycles. Prints 1, 10, 100 and so on along the log axes.
- First cycle exponent. Start the scale at 10 to any power from minus 6 to 6.
Printing tips
- Choose the number of cycles from your data. If values run from 3 to 8000, you need four cycles.
- A straight line on semi-log paper means exponential behaviour. A straight line on log-log paper means a power law.
- Print in portrait on Letter or A4 for the best use of the page.
For more detail, read the guide to printing grid paper at true size.
Frequently asked questions
What is a cycle on log paper?
A cycle, or decade, is one repeat of the pattern covering a factor of ten, such as 1 to 10.
When do I use semi-log instead of log-log?
Use semi-log when only the y values cover a wide range, as in exponential growth. Use log-log when both axes do, as in power laws.
Can the scale start at something other than 1?
Yes. Set the first cycle exponent. Zero starts at 1, minus 2 starts at 0.01.
Why is there no zero on log paper?
The logarithm of zero is undefined, so the scale never reaches zero.
