Life Table Calculator
Calculate survivorship (lx), age-specific mortality (qx), and life expectancy (ex) from cohort or static life table data. Determine net reproductive rate R0 and generation time.
🌿 Ecology📐 lx = Sx/S0, qx = dx/lx🧬 Biology
Starting cohort S0
Age class 1 survivors S1
Age class 2 survivors S2
Age class 3 survivors S3
Age class 4 survivors S4 (or 0 if done)
Please enter valid values.
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Life Table Calculator | — | lx = Sx/S0, qx = dx/lx | probability |
Step-by-Step Examples
Example 1
Human Cohort
1000 born, 800 survive to age 1, 500 to age 2, 200 to age 3.
- l0=1.000, l1=0.800, l2=0.500, l3=0.200
- q0=(1.0-0.8)/1.0=0.200 (20% die in interval 0-1)
- q1=(0.8-0.5)/0.8=0.375 (37.5% die in interval 1-2)
- q2=(0.5-0.2)/0.5=0.600 (60% die in interval 2-3)
✓ Survivorship drops; mortality increasing with age
Example 2
Type I Survivorship
Most deaths at old age: 1000, 990, 970, 800, 200.
- l0=1.0, l1=0.99, l2=0.97, l3=0.80, l4=0.20
- Low mortality early, high mortality at old age
- Characteristic of K-selected species (humans, elephants)
✓ Type I: rectangular survivorship curve
Example 3
Type III
High early mortality: 1000, 100, 90, 85, 80.
- l0=1.0, l1=0.10, l2=0.09, l3=0.085, l4=0.08
- 90% die early, survivors have high subsequent survival
- Characteristic of oysters, sea turtles (many eggs, few survive)
✓ Type III: J-shaped survivorship (high early mortality)
Real-World Applications
Actuarial Science
Life tables are the foundation of insurance pricing and pension fund calculations.
Wildlife Management
Cohort life tables track fates of marked animals to estimate survival rates for population models.
Population Ecology
Net reproductive rate R0 and generation time from life table predict population growth rate.
Demography
Human life tables by age, sex, country: published by CDC, WHO. Used for public health policy.
Common Mistakes to Avoid
⚠️
l0 always equals 1.0
By convention, survivorship starts at 1.0 (100% alive at age 0). l_x = S_x/S_0.
⚠️
qx is probability of dying IN that interval
q_x = probability of dying between age x and x+1, given alive at age x. Not the same as the fraction of original cohort dying.
⚠️
Cohort vs static life table
Cohort: follow actual individuals over time (longitudinal). Static: sample individuals at one time (snapshot). Static assumes stable age distribution.
Frequently Asked Questions
What is a life table? ▾
A table showing age-specific survival and mortality probabilities for a population. Used to calculate life expectancy, net reproductive rate, and stable age distribution.
What are the three types of survivorship curves? ▾
Type I (convex): low early mortality, most die old (humans, elephants). Type II (linear): constant mortality at all ages (birds, some reptiles). Type III (concave): very high early mortality (fish, insects).
What is net reproductive rate R0? ▾
R0 = sum of (l_x * m_x) where m_x is fecundity at age x. R0 > 1: population growing. R0 < 1: declining. R0 = 1: stable. Closely related to lambda (lambda ≈ R0^(1/T) where T is generation time).
What is generation time T? ▾
T = sum(x * l_x * m_x) / R0. The average age at which individuals produce offspring. Combines age structure and reproduction schedule.
What is life expectancy? ▾
e_x = expected remaining years of life for an individual alive at age x. e_0 = life expectancy at birth. Calculated from the survivorship schedule in the life table.