A life table is a grid of numbers that tracks what happens to a population as it ages, row by row, from birth to the oldest possible age. Each row represents an age (or age group), and the columns tell you how many people survive to that age, how many die, the probability of dying, and how many years of life remain on average. Once you understand what each column means, the entire table clicks into place.
The Starting Point: Age and the Radix
The first column, labeled x, is simply the age. In a complete life table, every single year of age gets its own row, from 0 all the way up. In an abridged life table, ages are grouped into intervals of five or ten years, which is common when data is limited or when a quick summary is the goal.
The second column you’ll encounter is lx, the number of survivors at exact age x. This is where the “radix” comes in. Life tables don’t use actual population counts. Instead, they start with a hypothetical group of 100,000 newborns at age 0. Every row after that shows how many of those original 100,000 are still alive. If l(65) is 82,437, that means 82,437 out of the starting 100,000 would survive to their 65th birthday under the mortality rates in that table. The radix of 100,000 is a universal convention used by the Social Security Administration, the CDC, and statistical agencies worldwide, making it easy to compare tables across countries or time periods.
The Core Columns and What They Tell You
Six columns do most of the work in a standard life table. Here’s what each one means:
- qx (probability of dying): The chance that a person who has reached exact age x will die before their next birthday. If q(70) is 0.02, a 70-year-old has a 2% chance of dying within the year.
- lx (survivors): The number of people from the original 100,000 still alive at the start of age x.
- dx (deaths): The number of deaths occurring between age x and x+1. It’s calculated by multiplying the survivors by the probability of dying: dx = lx × qx. If 90,000 people reach age 60 and q(60) is 0.01, then 900 die during that year.
- Lx (person-years lived): The total years lived by the group between age x and x+1. People who survive the whole year each contribute one full year. People who die during the year contribute a partial year, typically estimated as half a year. The formula for most ages is Lx = lx − 0.5 × dx.
- Tx (total person-years remaining): The total number of years the group will collectively live from age x onward. It’s the sum of all Lx values from age x to the end of the table.
- ex (life expectancy): The average number of years remaining for someone at age x. This is the column most people care about. It’s calculated by dividing the total years remaining by the number of survivors: ex = Tx / lx.
You might also see a column labeled mx, the central death rate. This is the actual observed death rate for a given age, calculated from real population and death data. It’s the raw input used to derive qx. For ages above 1, the conversion formula is qx = 2 × mx / (2 + mx). You don’t need to memorize that, but it explains why some tables include both columns.
How the Columns Connect
The beauty of a life table is that every column flows from the one before it. Start with qx, the observed probability of dying at each age. From there, the survivors column builds itself: l(x) = l(x−1) × (1 − q(x−1)). If 95,000 people reach age 50 and q(50) is 0.005, then l(51) = 95,000 × 0.995 = 94,525. Deaths are just the difference: dx = lx × qx. Person-years lived (Lx) adjusts for partial years. Total years remaining (Tx) sums everything from that age forward. And life expectancy (ex) divides that total by the number of people still alive.
This chain means you can reconstruct any column if you have the others. In practice, the probability of dying (qx) is the foundation. Everything else is built on top of it.
Calculating Survival Between Two Ages
One of the most useful things you can do with a life table is calculate the probability of surviving from one age to another. The formula is straightforward: divide the number of survivors at the later age by the number at the earlier age. If you want to know the chance of a 40-year-old reaching 70, take l(70) / l(40). If l(40) is 96,123 and l(70) is 78,542, the probability is 78,542 / 96,123 = 0.817, or about 82%.
This works for any age gap. A 55-year-old wondering about reaching 90 would use l(90) / l(55). The lx column is all you need.
Period Tables vs. Cohort Tables
Most life tables you’ll find online, including those published by the Social Security Administration and national statistics agencies, are period life tables. A period table takes the death rates from a single year (or a few years) and applies them to the hypothetical 100,000 people as if those rates never changed. It’s a snapshot of mortality conditions right now.
A cohort life table does something different. It follows an actual birth cohort, people born in the same year, and uses observed death rates for past years combined with projected improvements in mortality for future years. Because medical advances and public health improvements tend to reduce death rates over time, cohort life expectancy is almost always higher than period life expectancy. A period table for 2024 might say a newborn male can expect to live 76.4 years, but a cohort table for the same year would project a longer life because it factors in the likelihood that mortality rates will keep falling.
Period tables are more common because they’re objective and easy to compare across countries and time periods. Cohort tables are considered more realistic for predicting how long people will actually live, but they depend on assumptions about the future.
Reading Life Expectancy Correctly
The most common misreading of a life table is treating life expectancy at birth as a hard prediction. It isn’t. According to the SSA’s 2024 projections, a male born today has a period life expectancy of about 76.4 years and a female about 81.3 years. But a 65-year-old male already has 18.2 more years of expected life (to about 83), and a 65-year-old female has 20.8 more years (to nearly 86). That’s not a contradiction. Life expectancy recalculates at every age because you’ve already survived the risks of all previous years.
Life expectancy at birth is heavily influenced by infant and childhood mortality. In populations with high infant death rates, life expectancy at birth can be dramatically low even though adults who survive childhood live to old age. This is why looking at ex at multiple ages gives you a fuller picture than the single number at birth.
Because age-specific mortality rates change over time, period life expectancy does not accurately predict the actual number of years any individual will live. It reflects the mortality pattern at a moment in time, not a forecast.
Survivorship Curves: Visualizing the Table
If you plot the lx column on a graph, with age on the horizontal axis and survivors on the vertical axis, you get a survivorship curve. For humans in developed countries, this curve stays flat and high for most of the lifespan, then drops steeply in old age. This is called a Type I curve: most individuals die of old age rather than in youth.
Biologists and demographers recognize two other patterns. A Type II curve is a straight diagonal line on a logarithmic scale, meaning the same proportion of the population dies in each time period regardless of age. Some bird species follow this pattern. A Type III curve drops almost vertically at the start, reflecting massive early mortality, then flattens out for the few survivors. Many fish and invertebrates that produce thousands of offspring follow this pattern. Plotting life table data as a survivorship curve makes it immediately clear which pattern a population follows and where the greatest mortality risk falls.
Complete vs. Abridged Tables
A complete life table has one row for every single year of age. This gives you precise values for any age-to-age comparison and is the standard format published by agencies like the CDC and SSA. An abridged life table groups ages into intervals, typically five-year bands (0, 1-4, 5-9, 10-14, and so on). Abridged tables are used when detailed year-by-year mortality data isn’t available, or when a broad summary is sufficient. The columns work the same way in both formats, but in abridged tables, the values cover multi-year intervals rather than single years, so lx represents survivors at the start of an age group rather than at a single birthday.