Generate logarithmic graph paper for semi-log and log-log plots
Logarithmic graph paper uses a logarithmic scale on one or both axes. On a base-10 axis, each cycle spans a factor of ten, so equal distances represent equal ratios rather than equal differences. The default sheet is A4 portrait, Semi-Log Y, with three cycles from 1 to 1,000 on Y. Use it for exponential data, frequency-response plots, and power-law analysis. For an evenly spaced X/Y grid, use the Coordinate Plane Generator or the Cartesian Plane Generator. For rings and angles, use the Polar Graph Paper Generator.
Start with the default sheet
- Scale: Keep Semi-Log Y selected. X stays evenly spaced, and Y runs through three cycles from 1 to 1,000.
- Spacing: Leave Fit decades to page enabled. Decade length is calculated from the printable area and the cycle count, and that field stays disabled.
- Labels: Decade labels stay on, in decimal form: 1, 10, 100, and 1000. The linear axis is not numbered. Its default spacing is 5 mm, so you can write your own values or units on those divisions.
- Paper: The default sheet is A4 portrait with 13 mm margins.
- Printing: Export the PDF and select Actual Size (100%) in the print dialog.
Choose between semi-log and log-log scales
- Semi-Log Y: X is linear and Y is logarithmic. This is the mode the editor opens, for Y values that span several orders of magnitude.
- Semi-Log X: X is logarithmic and Y is linear. Use it when the horizontal variable, such as frequency, spans several orders of magnitude. The sheet does not print a unit.
- Log-Log: Both axes are logarithmic. Fit decades to page stretches each axis to the printable edge, so the X and Y decade lengths can differ and the length field shows a dash. Exact decade length uses one length on both axes. Read a slope as the vertical decade count divided by the horizontal decade count along the line, not from the angle.
- Zero and negative values: Zero and negative values cannot be plotted. The axis starts at a power of ten, such as 0.01, 1, or 10.
Set the number of cycles and the starting power
- Cycles: One cycle is one decade, a factor of ten. An axis holds one to six cycles. Three cycles starting at 10⁰ run from 1 to 1,000. Switching mode keeps the cycles and starting power you already set.
- Starts at: The power of ten at the low end of a logarithmic axis, from 10⁻⁶ to 10⁶. Three cycles starting at 10⁻² cover 0.01 to 10. The control is disabled while decade labels are off, and the power stays until the labels come back.
- Decade labels: Off prints no decade numbers. Decimal prints 1, 10, 100, and 1000, with no thousands separator. Powers of 10 prints the base and the exponent, such as 10⁰, 10¹, and 10².
- Linear spacing: This sets the even divisions on the linear axis. The default is 5 mm. The range is 1–50 mm, or 1/16–2 in. In Log-Log the control is disabled, because neither axis is linear.
Adjust decade length and grid density
- Fit decades to page: The generator divides the printable edge by the cycle count and keeps every cycle you selected. It does not drop a cycle to make a decade longer.
- Exact decade length: Set one length in millimeters or inches. That length is used on every logarithmic axis. The stepper stops at the longest decade that still fits. The shortest length is 20 mm, or 7/8 in. If a later change makes that length too long for the page, the grid is left off and the preview says these decades do not fit. The center controls in Page Margins move that shorter grid; otherwise the unused space stays above it and to the right.
- Additional subdivisions: The .2, .4, .6, and .8 lines split each integer step of a decade when there is room. A line is left out when it would sit closer than 1 mm to its neighbor. Turning them off leaves the lines at 2 through 9. The lines at 2 and 5 use the thick-line color.
- Short decades: When Fit makes a decade shorter than 20 mm, the lines at 6, 7, 8, and 9 are hidden, and the .2, .4, .6, and .8 lines are left out. The lines at 2, 3, 4, and 5 stay. A decade of exactly 20 mm keeps the 6–9 lines.
When should you use logarithmic graph paper?
- Exponential growth and decay: On Semi-Log Y, an exponential relationship can plot as a straight line, so the rate is easier to compare across the page.
- Frequency response: Semi-Log X fits a frequency axis that covers many decades while the vertical scale stays linear, including a level in decibels. Write Hz, dB, or any other unit yourself.
- Power laws: On log-log paper, a power law can plot as a straight line. The slope, counted in decades, is the exponent.
- Wide-range measurements: A logarithmic axis keeps smaller positive values readable when the data cover several orders of magnitude.