Semi-Log Graph Paper

Semi-logarithmic paper has a linear x-axis and a logarithmic y-axis. Exponential relationships, which curve dramatically on linear paper, become straight lines on semi-log paper. That single property is why every physics, chemistry, biology and engineering lab still keeps a stack of it.

Print Open

Download generates a crisp vector PDF directly, no print dialog needed.

Choose a different paper size:

Choose a different line color:

Great for

Plotting exponential growth or decay (bacterial cultures, radioactive isotopes, capacitor discharge)
Reading half-life and time-constants directly from the slope
Dose-response curves in pharmacology and toxicology
Frequency response magnitudes (gain vs frequency in dB-style work)

About semi-log graph paper

Semi-log paper is the workhorse of any field where quantities span several orders of magnitude or where the underlying process is multiplicative rather than additive. On linear paper, y = A·e^(kx) plots as a curve that's flat-then-explosive; on semi-log paper the same equation becomes log y = log A + (k/ln 10)·x, a straight line whose slope is proportional to the rate constant k. That property turns curve fitting into ruler work: line up a straightedge, read the slope, recover the time-constant or growth rate. The format is old enough that it predates calculators by decades, but it survived the calculator era because the visual intuition it gives is hard to replicate on a screen. A scientist who has plotted a hundred cultures on semi-log paper can spot the moment a curve stops being exponential at a glance, which is exactly the moment the data starts telling you something interesting.

What's on the page

A linear horizontal grid at 5 mm spacing (with heavier lines every 5 cells, matching the regular grid paper templates) crossed with a logarithmic vertical grid covering four decades. Each decade contains nine minor lines (the 1, 2, 3, … 9 values within the decade) and one heavier line at the start (1, 10, 100, 1000). Decade labels run down the left margin so you can choose what 1 represents. 1 mm, 1 µg/mL, 1 Hz, whatever your data needs. The four-decade range covers most lab-scale work; if you need more range, stack two sheets or use log-log paper.

How to use it well

Pick the bottom decade to match your smallest value

If your data starts at 0.03, label the bottom decade '0.01' so the value lands in the third subdivision up. If it starts at 30, label it '10'. The decades themselves are unitless; you anchor them when you label.

Read the slope as a multiplicative rate

A straight line covering one full decade in 5 cm tells you the quantity multiplies by 10 every 5 cm of x. Convert by dividing: k = ln(10) / (x-span per decade). For exponential decay, this is also how you read off the half-life from the line.

Curves on semi-log mean it's not exponential

If the data doesn't form a straight line, the process isn't a pure exponential. Concavity tells you whether it's slowing down (saturation) or speeding up (autocatalysis). That diagnostic is the main reason to plot data on semi-log even before you fit a model.

Never plot zero or negative values

log(0) is undefined and log(-1) is imaginary. Either drop those points or shift the data by a known offset before plotting. Don't pretend a 0 is a 0.01; that's a tell that hides real noise.

Common mistakes to avoid

Treating the minor lines as evenly spaced. They aren't, log(2) ≈ 0.301, log(5) ≈ 0.699, so the '5' line sits roughly seven-tenths of the way up each decade. Reading the y-value requires looking up the line label, not counting cells.
Mixing up which axis is logarithmic. On semi-log, only one axis is log (here, the y-axis). For data where both variables span orders of magnitude, you need log-log paper, not semi-log. Plotting the wrong format will produce a wildly misleading slope.
Forgetting to label what the bottom decade is. Without an anchor, '1' could mean 1, 0.001, or 1000. Always write the units and the value of the lowest line before plotting.

FAQ, Semi-Log Graph Paper

How is semi-log different from log-log paper?＋

Semi-log has a linear x-axis and a logarithmic y-axis: it's for data where one variable is exponential and the other is linear (time, dose). Log-log has both axes logarithmic, used when both variables span orders of magnitude (power laws, allometry, frequency response on Bode plots).

Why four decades and not two or six?＋

Four covers most common lab data without crowding. Two-decade paper is too narrow for genuinely exponential data; six-decade paper compresses each decade so much that fine reading gets harder. Four is the sweet spot, and it matches what most published lab notebook templates use.

Can I plot negative values on semi-log paper?＋

No. The logarithm of a negative number isn't defined on the real line. If your data swings through zero, semi-log paper is the wrong tool. Either split the positive and negative branches onto separate plots, or use a linear y-axis with a different transformation.

Does the line slope give me the half-life directly?＋

Indirectly. For decay y = y₀·e^(-t/τ), a straight line on semi-log has slope -1/(τ·ln 10) per unit x. The half-life is τ·ln 2. So if the line drops one full decade per (say) 10 minutes, the time-constant is 10/ln 10 ≈ 4.34 minutes and the half-life is about 3 minutes. The graphical shortcut: half-life ≈ (decade span) × 0.301.

What scale should I use on the x-axis?＋

Whatever makes the line take up most of the page. The linear axis is at 5 mm per cell. You assign units. Time data might use 1 cell = 1 minute or 1 cell = 1 hour; concentration data might use 1 cell = 0.5 mg. Set the scale before plotting so the line spans the page without crowding either margin.

Printing tips for best results＋

1. Click Print above. A new tab opens the template at exact size.
2. The print dialog appears automatically. Set Scale to 100%. Never "Fit to page", which silently shrinks every cell.
3. Set Margins to None or Minimum so the grid reaches the page edge.
4. For a PDF, click Download instead. It generates a vector PDF directly without going through the printer driver.