Lexis Diagram
A demographic chart that maps events across both age and calendar time — with diagonal life lines that reveal cohort patterns invisible to standard charts.
// 01 — The chart
What it looks like
A Lexis diagram with one life line (diagonal) from birth to death. The grid cells can be shaded to show mortality rates by age and period.
// 02 — Definition
What is a Lexis diagram?
A Lexis diagram is a two-dimensional coordinate system where the x-axis is calendar time and the y-axis is age. Individual people are represented as diagonal life lines that move upward and to the right (ageing one year per calendar year).
The grid that forms can be shaded to show rates or counts — mortality, fertility, disease incidence — within each age × period cell. Diagonal bands across the grid represent birth cohorts — people born in the same year.
This unique structure lets demographers disentangle three effects: age effects (vertical), period effects (horizontal), and cohort effects (diagonal).
Origin: Named after Wilhelm Lexis (1837–1914), a German statistician who introduced this framework for demographic analysis.
// 03 — Anatomy
Parts of a Lexis diagram
// 04 — Usage
When to use it — and when not to
- Analysing demographic data across age and calendar time simultaneously
- You need to disentangle age, period, and cohort effects
- Studying mortality, fertility, or migration patterns over decades
- Visualising individual life trajectories alongside population trends
- Comparing how different birth cohorts experienced the same age range
- Your data lacks an age dimension — a standard line chart will suffice
- The audience has no demographic background — the concept is unintuitive
- You have only cross-sectional data (one time point)
- You want to show magnitudes precisely — Lexis diagrams prioritise patterns over values
- Your data isn't about people or living organisms
// 05 — Reading guide
How to read a Lexis diagram
Orient the axes
X-axis is calendar time (years); y-axis is age. Each cell covers one age group × one time period.
Read the diagonals
Diagonal lines or bands represent birth cohorts. People born in the same year age along parallel diagonals.
Look for horizontal patterns
Consistent shading in a horizontal band means an age effect — something that affects all cohorts at the same age.
Look for vertical patterns
A vertical stripe means a period effect — something that hit all age groups at the same calendar time (e.g. a war, pandemic).
Look for diagonal patterns
A diagonal stripe is a cohort effect — something unique to people born in a specific year (e.g. baby boomers).
// 06 — Data format
What data you need
A matrix with age groups as rows and calendar periods as columns. Each cell contains a demographic measure (rate, count, or percentage). Optionally, individual-level data with birth year, event year, and event type.
// 07 — Construction
How to build one
Step 1: Set up a grid with calendar years on the x-axis and age on the y-axis (equal intervals).
Step 2: Draw diagonal grid lines to demarcate birth cohorts.
Step 3: Shade each age × period cell using a sequential colour scale mapped to the demographic variable.
Step 4: Optionally overlay individual life lines as thin diagonals to show specific trajectories.
// 08 — Common mistakes
Mistakes to avoid
Confusing age and cohort effects
A horizontal pattern (same age, different years) is an age effect. A diagonal pattern is a cohort effect. Mixing them up is the most common error.
Unequal age or period intervals
When age groups and time periods are different widths, the diagonal cohort bands don't align properly.
Omitting the diagonal structure
Without diagonal cohort lines, a Lexis diagram is just a heatmap. The diagonals are what make it a Lexis diagram.
Using it for non-demographic data
Lexis diagrams are specifically designed for age × time analysis. Using them for unrelated data creates confusion.
// 09 — Real-world examples
Where you’ll see them
Human Mortality Database
The HMD provides Lexis-surface visualisations of mortality rates across age and time for 40+ countries.
Fertility analysis
Demographers use Lexis diagrams to track fertility rates by age and birth cohort, revealing shifts in childbearing timing.
Data journalism
The New York Times and The Economist have published Lexis-style visualisations for COVID-19 mortality by age and time.
// 10 — Quick reference
Key facts
// 11 — Accessibility
Making it accessible
Lexis diagrams rely heavily on colour encoding and spatial reasoning. Provide a companion data table with age-group rows and year columns. Add tooltips showing exact rates. Use ARIA labels to describe the main patterns (age, period, or cohort effects). Consider a simpler line-chart alternative for non-specialist audiences.
// 12 — Variations
Common variations
Lexis surface (filled)
All cells shaded with a colour scale — the most common modern form.
Lexis with life lines
Individual diagonal trajectories overlaid on the grid, showing specific people's paths.
Contour Lexis
Iso-rate contour lines replace cell shading for a smoother visual.
Interactive Lexis
Hover for exact rates; click to filter by cohort or period.
// 13 — FAQs
Frequently asked questions
What is a lexis diagram?+
A Lexis diagram is a two-dimensional coordinate system where the x-axis is calendar time and the y-axis is age. Individual people are represented as diagonal life lines that move upward and to the right (ageing one year per calendar year).
When should you use a lexis diagram?+
Use a Lexis diagram when analysing demographic data across age and calendar time simultaneously. It also works well when you need to disentangle age, period, and cohort effects, and when studying mortality, fertility, or migration patterns over decades.
When should you avoid a lexis diagram?+
Avoid a Lexis diagram when your data lacks an age dimension — a standard line chart will suffice. It is also a poor fit when the audience has no demographic background — the concept is unintuitive, or when you have only cross-sectional data (one time point).
What data do you need to make a lexis diagram?+
A matrix with age groups as rows and calendar periods as columns. Each cell contains a demographic measure (rate, count, or percentage). Optionally, individual-level data with birth year, event year, and event type.
How is a lexis diagram different from a heatmap?+
Both a Lexis diagram and a heatmap can look similar at first glance, but they answer different questions. Reach for a Lexis diagram when the comparisons and patterns it was designed to reveal match what you need to communicate, and choose a heatmap when its particular strengths better fit your data and audience.
What is another name for a lexis diagram?+
Lexis Diagram is also known as Lexis surface, age-period-cohort diagram. The name varies between fields, but the visualisation technique is the same.
What size of dataset works best for a lexis diagram?+
Lexis Diagram works best for Demographic data with age and time dimensions. Outside that range the chart either looks empty or becomes too cluttered to read clearly.
Are lexis diagrams accessible to screen readers?+
Lexis diagrams rely heavily on colour encoding and spatial reasoning. Provide a companion data table with age-group rows and year columns. Add tooltips showing exact rates. Use ARIA labels to describe the main patterns (age, period, or cohort effects). Consider a simpler line-chart alternative for non-specialist audiences.