Mortality Rate (qx) Calculator

Work out mortality rate (qx) instantly with clear inputs, formula shown and shareable results.

About Mortality Rate (qx) Calculator

qₓ is the probability that a life aged exactly x dies before reaching x+1, measured as deaths divided by lives exposed at the start of the year. The central rate mₓ instead divides by mid-year exposure, which is what population statistics usually publish.

Formula

Mortality rates

qₓ = dₓ / lₓ; mₓ = dₓ / (lₓ - dₓ/2)

dx: Deaths in the year
lx: Lives at start

Worked example

With the default values below, Mortality Rate (qx) Calculator returns Mortality Rate qₓ of 0.85000%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Lives At Start Of Yearaccepts 1–10,000,000: 100,000
Deaths During The Yearaccepts 0–10,000,000: 850

Results

Mortality Rate qₓ: 0.85000%
Survival Rate pₓ: 99.15000%
Deaths Per 1,000 Lives: 8.500 per 1,000
Central Death Rate mₓ: 8.536 per 1,000

Step by step

1Values used
2Mortality rates
3Mortality Rate qₓ= 0.85000
4Survival Rate pₓ= 99.15000
5Deaths Per 1,000 Lives= 8.500 per 1,000
6Central Death Rate mₓ= 8.536 per 1,000

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why are qₓ and mₓ different?

qₓ uses the initial population; mₓ uses average population during the year, so mₓ is slightly the larger of the two.

How is qₓ used?

It drives every life-table quantity — survival curves, annuity factors and life insurance premiums all build up from qₓ.