Logarithmic scale

Semi-log
graph paper

One linear axis and one logarithmic axis. Exponential data plots as a straight line. Ideal for growth curves, decay rates, Bode plots, and any data spanning orders of magnitude.

Generate semi-log PDF →Applications
y = e^0.6x → straighton semi-log paper

About semi-log paper

Linear meets logarithmic

Semi-log graph paper has one axis divided into equal linear intervals and one axis divided into logarithmic intervals. On the logarithmic axis, equal distances represent equal ratios rather than equal differences.

This property makes exponential curves appear as straight lines on semi-log paper. If your data plots as a straight line on semi-log paper, the relationship is exponential.

Key insight: If data plotted on semi-log paper forms a straight line, the underlying relationship is exponential. The slope equals the growth or decay rate.

CyclesData range coveredTypical use
1 cycle×10 (e.g., 1–10)Narrow pH range, tight signal levels
2 cycles×100 (e.g., 1–100)Early bacterial growth phase
3 cycles×1,000Population growth, radioactive decay
4–5 cycles×10,000–100,000Audiometry, wide-range reaction kinetics
6+ cycles×1,000,000+Astronomical distances, geological timescales

Applications

What is semi-log paper used for?

Biology — growth curves

Bacterial growth follows exponential kinetics during the log phase. Semi-log paper linearizes the growth curve, allowing easy calculation of doubling time and generation time.

Bacterial growthDoubling timeDecay

Physics — acoustics and seismology

Sound intensity in decibels and Richter magnitude are both logarithmic scales. Semi-log paper plots these against linear time or distance axes naturally.

DecibelsRichter scaleRadioactive decay

Finance — compound growth

Asset prices growing at a constant percentage rate appear as a straight line on semi-log paper — which is why financial analysts use logarithmic price charts for long-term trend analysis.

Asset pricesCompound growth

Engineering — Bode plots

Bode magnitude and phase plots use a logarithmic frequency axis and a linear dB axis. Semi-log paper allows hand-drawn Bode analysis for filter and amplifier design.

Bode plotsFrequency responseFilter design

Chemistry — reaction kinetics

First-order reaction rates, enzyme kinetics, and pH calculations all involve logarithmic relationships plotted on semi-log paper in physical chemistry courses.

Reaction ratespH curvesHalf-life

Epidemiology — outbreak curves

Disease case counts during epidemic outbreaks grow exponentially in early phases. Public health officials use semi-log graphs to identify when growth is slowing.

Epidemic curvesCase countsInfection rates

PDF Generator

Generate Semi-log paper — download free PDF

Configure below, see a live preview, then click ↓ Download PDF. Runs entirely in your browser.

Settings

Grid color

Live preview — updates as you change settings
Preview is proportional. PDF is full-resolution vector — prints sharply at any size.

FAQ

Frequently asked questions

What is semi-log graph paper?+
Semi-log paper has one linear axis (equally spaced) and one logarithmic axis (spaced by ratio). It linearizes exponential data — any relationship of the form y = a·bˣ appears as a straight line when plotted on semi-log paper.
What is the difference between semi-log and log-log paper?+
Semi-log has one linear and one logarithmic axis — for exponential functions. Log-log has both axes logarithmic — for power-law functions. Use semi-log for exponential data, log-log for power-law data.
How many cycles do I need?+
One cycle represents one order of magnitude (factor of 10). Data ranging from 1 to 100 needs 2 cycles; 1 to 1,000 needs 3 cycles. CustomGraph supports 1 to 6 cycles.
Which axis should be logarithmic?+
By convention, when time (linear) is the x-axis and an exponentially growing quantity is the y-axis, the vertical axis is logarithmic. For Bode plots, the horizontal frequency axis is logarithmic.
Can I download semi-log paper as a PDF?+
Yes. CustomGraph generates all graph paper as vector PDFs — printer-independent, sharp at any resolution, printable on standard paper, transparency film, or laminated stock.

Related types

Other graph paper formats

Log-log paper

Both axes logarithmic — for power-law relationships (y = axⁿ).

Cartesian paper

Standard linear grid — for data with linear relationships.

Engineering paper

Dual-grid for precision data collection on two scale levels.

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