Analyze central death rates across selected age intervals. Compare assumptions, hazards, and annualized estimates carefully. Download clean reports for audits, teaching, or actuarial reviews.
| Age | Deaths | Exposure | Central Death Rate | Estimated Force |
|---|---|---|---|---|
| 50 | 12 | 1600 | 0.007500 | 0.007500 |
| 60 | 25 | 1200 | 0.020833 | 0.020833 |
| 70 | 41 | 900 | 0.045556 | 0.045556 |
Central death rate: m(x) = d(x) / E(x)
Constant force relationship: μ(x) = -ln(1 - q(x,n)) / n
Interval survival: p(x,n) = e-μ(x)n
Interval death probability: q(x,n) = 1 - e-μ(x)n
Expected remaining time under constant force: e(x) ≈ 1 / μ(x)
When deaths and exposure are supplied, the calculator starts from the central death rate. Alternative assumptions adjust the link between observed mortality and hazard intensity.
It is the instantaneous rate of death at an exact age. Actuaries interpret it as the hazard intensity governing survival over very small time intervals.
Death probability measures the chance of dying across a stated interval. Force of mortality is an instantaneous rate, which can be transformed into interval probabilities using exponential survival formulas.
Use it when you have observed deaths and person-years exposed to risk. This is common in mortality studies, life tables, cohort summaries, and insurance experience investigations.
It assumes the hazard remains constant throughout the chosen interval. That simplification makes survival calculations easy and is often reasonable for short age ranges.
They offer alternative ways to connect discrete mortality data with continuous-time hazard concepts. Comparing methods helps analysts test sensitivity and understand assumption effects.
Yes. It is useful for actuarial science, demography, survival analysis, and statistics coursework. The example table and formula section make classroom checking easier.
Under a constant hazard interpretation, expected remaining lifetime is approximated by the reciprocal of the force. It is a convenient summary, not a complete life-table replacement.
Yes. The CSV and PDF buttons export the calculated metrics visible in the results panel, making documentation, sharing, and review easier.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.