Demography Tools

Browse all available demography tools.

Available tools

Abridged To Complete Extension Open Calculator Extend an abridged life table into the terminal open interval using L = l / m for person-years lived and e = 1 / m for the remaining expectancy at the open age.
Adult Mortality 45q15 Calculator Convert age-specific death rates for the five-year groups from age 15 into the probability of dying between ages 15 and 60 using q = n m / (1 + (n - a) m), with a default a of n/2 years.
Age Standardized Prevalence Weighted Compute the age-standardized prevalence as the standard-weight weighted average of age-specific prevalences, sum(w_i * p_i) / sum(w_i).
Age-Specific Sex Ratio Checker Compute the sex ratio (males per 100 females) for each age group and flag groups outside a plausibility band; the default band of 90-110 is a stated heuristic and fully adjustable.
Ageing Index Calculator Compute the ageing index, the number of persons aged 65 and over per hundred children under age 15.
AX Average Years Dying Rule Calculator Compute the average person-years lived by those dying in an interval under the midpoint rule (a = n/2) or the Coale-Demeny infant rule (a0 = 0.07 + 1.7 m0), then convert the death rate to the life-table probability of dying q = n m / (1 + (n - a) m).
Bachi Age-Sex Accuracy Index Calculator Compute Bachi's age-sex accuracy index, the sum over both sexes of half the total absolute deviation of terminal-digit shares from ten percent across complete decades of single ages.
Balance Equation Closure Error Close the demographic balancing equation P2 = P1 + births - deaths + immigrants - emigrants and report the absolute and percent discrepancy of the observed end population against the expected value.
Beers Interpolation Lookup Look up the interior Beers oscillatory interpolation multipliers (ordinary or modified fifth-difference form) for one single year of an age group and apply them to the grouped total and its four neighbouring groups.
Bennett Horiuchi Death Distribution Method Estimate death-registration completeness with the Bennett-Horiuchi synthetic extinct generations method: discount reported deaths above a base age back over the interval with the stable-population growth rate and compare their sum to intercensal person-years lived above that age.
Bilateral Stream Matrix Balance Sum an origin-destination migration matrix into out-migration totals per origin, in-migration totals per destination, net inflow per region and the grand total of movers.
Birth Interval Median By Parity Calculator Compute the median length of birth intervals in months for a set of closed intervals observed at a given parity transition.
Bongaarts Proximate Decomposition Calculator Invert the Bongaarts proximate-determinants identity TF = TFR / (Cm x Cc x Ca), recovering total fecundity from the observed TFR and the marriage, contraception and abortion indexes.
Brass Relational Logit Alpha Beta Fit a life table with the Brass relational logit system Y_fit = alpha + beta * Y_standard applied through logit(s) = 0.5 ln((1-s)/s), returning fitted survivorship values for each standard survival probability.
Census Date Midyear Conversion Convert a census count taken on an arbitrary date to a mid-year equivalent by exponential interpolation at an assumed constant annual growth rate over the elapsed days between the two dates.
Census Survival Migration Estimate Estimate intercensal net migration for an age cohort as the observed cohort at the second census minus the survivors implied by applying a national life-table census survival ratio to the first-census cohort.
Child Woman Ratio CWR Calculator Compute the child-woman ratio as children under age five per one thousand women aged 15 to 49.
Children Ever Born CEB Average Calculator Compute mean parity as average children ever born either from a full parity distribution or from aggregate totals of children born and women.
Coale Demeny Region Family Lookup Validate and label a Coale-Demeny regional model life table family (West, North, East or South) at a mortality level from 1 to 25.
Cohort Survival Consistency Checker Project a census cohort forward with the life-table survival ratio L(x+n)/L(x) and report the percent closure error of the observed second census count against it.
Completed Cohort Fertility CFF Calculator Sum age-specific cohort fertility rates over the reproductive years, scaled by the class width, to obtain children ever born per woman at the end of childbearing.
CPR Contraceptive Prevalence Rate Compute the contraceptive prevalence rate as the percent of women in the reference base (usually married women aged 15-49) currently using any contraceptive method.
DALY Calculator Compute disability-adjusted life years as YLL (deaths times standard life expectancy at death) plus YLD (incidence times disability weight times duration), undiscounted and without age weighting per the GBD 2010+ convention.
Demographic Dividend Phase Classifier Classify the demographic dividend phase from age shares using the stated rule: child dependency above old-age dependency with a total dependency ratio over 70 is pre-dividend, otherwise early-dividend; once old-age dependency meets or exceeds child dependency a ratio of 70 or less is late-dividend and above 70 is post-dividend.
Direct Standardized Rate SDR Compute the directly age-standardized rate as the standard-population-weighted average of age-specific rates, SDR = sum(m_i * W_i) / sum(W_i).
Divorce Duration Table Lookup Read a divorce distribution by marriage duration, returning the percentage share of the queried duration year and the modal duration year.
Dual System Chandrasekar Deming Estimator Estimate total population size and undercount from two incomplete enumeration lists using the Chandra Sekar-Deming dual-record estimator N-hat = (a+b+1)(a+c+1)/(a+1) - 1 with the one-per-cell continuity correction.
Ever-Married by Age Interpolation Calculator Linearly interpolate the proportion ever married at a target age from group values placed at five-year-group midpoints, holding the endpoint groups constant outside their midpoints.
First Demographic Transition Phase Lookup Look up the textbook characteristics of a phase of the first demographic transition, with the conventional crude birth-rate and crude death-rate bands stated for each stage.
General Growth Balance Completeness Estimate the completeness of death registration from the aggregate general growth-balance identity B - D/c = r N, solved as c = D / (B - r N) using intercensal births, deaths, person-years and the annual growth rate.
Generation Length T Intrinsic Calculator Compute the intrinsic mean generation length T either as ln(NRR)/r from Lotka's relation or directly as the mean age of mothers at childbirth of the net maternity schedule.
HALE Calculator Compute health-adjusted life expectancy as total life expectancy minus the expected number of years lived in reduced health, per the definitional identity used by summary measures of population health.
Headship Rate Household Projection Project the number of households with the headship-rate method: multiply each age group's adult population by its age-specific headship rate and sum across groups.
IMR Infant Mortality Rate Calculator Compute the infant mortality rate as deaths under age one per one thousand live births.
Indirect Standardized SMR Apply indirect standardization: compute expected deaths from standard age-specific rates and study exposure, divide observed by expected deaths for the SMR, and multiply that ratio by the standard population's crude rate to obtain an indirectly standardized rate.
Intercensal Exponential Estimator Fit the exponential growth model P(t) = P0 exp(r t) with r = ln(P1/P0)/n between two censuses and evaluate the population at any time inside the interval.
Intrinsic Birth Rate B Stable Calculator Compute the stable-population intrinsic birth rate b as the reciprocal of the growth-discounted person-years sum and derive the intrinsic death rate d = b - r.
Intrinsic Death Rate D Stable Calculator Compute the stable-population intrinsic death rate d as the growth-discounted weighted average of age-specific deaths per person-year, accepting deaths directly or death rates times L(x).
Karup King Third Difference Lookup Look up the Karup-King third-difference interpolation factors for one single year of an age group and apply them to the grouped total with its two immediate neighbouring groups.
Keyfitz Momentum Factor Calculator Evaluate the Keyfitz (1971) approximate population-growth momentum factor M = b e0 (1 - exp(-r mu)) / (r mu), the ratio by which a stable growing population would still grow after fertility instantly drops to replacement.
Kitagawa Component Decomposition Split the difference between two crude rates into an age-composition effect and a rate effect using Kitagawa's two-component decomposition with averaged compositions and rates.
Lexis Diagram Cell Classifier Classify a Lexis diagram cell from its two bounded dimensions using the relation cohort = period minus age, naming the class (age-period AP, period-cohort PC or cohort-age LC), the free dimension and the interval the free dimension sweeps.
Life Table Entropy Keyfitz H Calculator Compute Keyfitz' life-table entropy H = e-dagger / e0 from aligned survivor and remaining-life-expectancy columns, including deaths in the terminal age group.
Lifespan Variation Edagger Calculator Compute Keyfitz' lifespan dispersion e-dagger as the death-weighted average of remaining life expectancy, summing d(x) times e(x) over aligned life-table columns with the final interval absorbing all remaining survivors.
Lifetime Vs Recent Migrant Ratio Lookup Compare migration persistence by dividing lifetime migrants (born elsewhere) by recent migrants who moved within a stated interval.
Lotka Intrinsic Growth Rate R Calculator Solve the Euler-Lotka equation for the intrinsic growth rate r from an age-specific female fertility schedule and female life-table person-years, using midpoint ages of equal-width classes.
Marital Status Distribution Calculator Compute the percentage distribution of a population across single, married, widowed and divorced marital statuses.
Median Age Grouped Interpolation Calculator Compute the median age of a grouped age distribution by linear interpolation inside the median class.
Migration Effectiveness Index EM Calculator Compute the migration effectiveness index as the sum of absolute regional net inflows divided by total migration turnover of an origin-destination matrix.
MMR Maternal Mortality Ratio Calculator Compute the maternal mortality ratio as deaths attributed to pregnancy and childbirth per one hundred thousand live births.
Mortality Graduation Chart Smoothing Graduate a schedule of central death rates for charting by applying the symmetric 1-2-1 weighted moving average (weights one, two, one over four) across ages, holding the first and last observed values fixed and repeating for the requested number of passes.
Myers Blended Sex Ratio Index Calculator Compute Myers' blended index of sex ratios, the sum over terminal digits 0-9 of absolute deviations of blended sex ratios from 100, using overlapping age windows to remove digit-weighting bias.
Neonatal Postneonatal Split Lookup Split the infant mortality rate into its neonatal component (deaths under 28 days) and postneonatal component per thousand live births, with the neonatal share of infant deaths.
NLX Person Years Lived Calculator Compute the life-table person-years lived Lx as n times the average of lx and lx-next for an ordinary abridged interval, or as lx divided by nmx when the open terminal interval death rate is supplied.
Old-Age Proportion Calculator Compute the proportion of a population aged 65 years and over, expressed as a percentage.
Omran Epidemiologic Transition Classifier Assign the epidemiologic transition stage from life expectancy at birth under the stated band rule (under 40 pestilence and famine, under 50 receding pandemics, otherwise degenerative and man-made diseases, with 75 or over split into Olshansky-Ault delayed degenerative diseases only in the four-stage framework).
Orphanhood Maternal Before Age Estimate Estimate the proportion of children of a given age whose mother is alive by applying maternal life-table survivorship lM(M + a) / lM(M) at the mean maternal age at birth M, with linear interpolation across five-year groups.
Parity Distribution Percent Calculator Convert counts of women at each parity into a percentage distribution of all women.
Parity Progression Ratio PPR Calculator Compute Brass parity progression ratios a(i), the share of women who have reached parity i and go on to parity i+1 or higher.
Perinatal Rate Definition Lookup Compute the perinatal mortality rate as late fetal plus early neonatal deaths per one thousand total births and state the WHO definitional convention used.
Person Years Exposed Risk Computation Sum exact exposure spells into total person-years lived at risk and convert an event count into the mean exposure per person and the incidence rate per thousand person-years.
Population Pyramid Shape Classifier Classify a pyramid as expansive when the young share exceeds the old share by more than half a point, constrictive when the reverse holds, stationary when they are equal within half a point, and report the age-dependency ratio.
Post Enumeration Error Percent Express post-enumeration survey coverage as the census count relative to a dual-system estimate, reporting the coverage ratio and the net undercount percent where positive values indicate underenumeration.
Postcensal Intercensal Estimator Produce a postcensal estimate by the component method (base plus births minus deaths plus net migration since the census) or an intercensal estimate by linear interpolation between two censuses at a stated fraction of the interval.
Potential Support Ratio Calculator Compute the potential support ratio, the number of persons aged 15-64 per person aged 65 and over.
Primary Infecundity Percent Lookup Compute the percentage of women with primary infecundity and classify it as low below 2.5 percent, moderate from 2.5 to 5 percent, or elevated above 5 percent.
Primate City Rank Size Zipf Apply the Zipf rank-size rule P(n) = P(1) / n^q to predict the population of the n-th largest city from the primate city, optionally reporting how far an observed city deviates from that prediction.
Radix L0 Perinatal A0 Lookup Look up the conventional life-table radix l0 (100000 for the HMD/UN standard or 1 for a unit radix) and the first-interval separation factor a0 under the midpoint rule (n/2) or the Coale-Demeny infant rule (0.07 + 1.7 m0).
Reference Standard Population Lookup Identify a widely used reference standard population by name, origin and typical application so that users can pair it with their own published age weights when direct-standardizing rates.
Remarriage Proportion Calculator Compute the percentage of marriages in a year that involve at least one previously married partner.
Replacement Fertility With Mortality Checker Compute the replacement total fertility rate as the reciprocal of the product of the female birth share and female survival to the reproductive ages, then classify an observed TFR against it within a stated tolerance.
Residual Vital Statistics Net Migration Estimate net migration by the vital-statistics residual method as P2 - P1 - B + D over the intercensal period.
Return Migration Proportion Lookup Compute the proportion of in-migration to a place that consists of former residents moving back, as return migrants per hundred total in-migrants.
Rogers Castro Age Profile Lookup Evaluate the seven-parameter Rogers-Castro migration schedule m(x) = a1 exp(-alpha1 x) + a2 + a3 exp(-alpha2 |x - mu2|), covering the childhood decay, baseline level and labor-force peak, at any requested ages.
Rural Urban Shift Decade Points Measure the rural-to-urban structural shift between two decades as the change in the urban share in percentage points, labelling moves beyond half a point as urbanizing or deurbanizing and anything within half a point as stable.
School Age Population Projection Project a school-age cohort to the next planning date with the census survival ratio method: survivors equal the current cohort times l(x+n)/l(x), plus net school-age migrants.
Second Transition Features Checker Count which of the four classic second-demographic-transition markers are present (below-replacement fertility, postponed parenthood, rising union instability or cohabitation, household diversification) and label the profile full at four markers, partial at two or three, absent otherwise.
SMAM Calculator Compute the singulate mean age at marriage from proportions single in five-year groups starting at 15-19, assuming no marriage below 15 and that those still single in the last group (45-49) never marry.
Spousal Age Gap Calculator Compute the median and mean difference between spouses' ages for paired husband-wife records.
Sprague Multipliers Osculatory Lookup Look up the Sprague fifth-order osculatory interpolation multipliers for one single year of an age group and apply them to the grouped total and its four neighbouring groups.
Stable Age Distribution Proportion Calculator Compute the stable-population age composition c(a) proportional to exp(-r a) times the person-year weight at each age, normalized to sum to one, plus its mean age.
Stable Equivalent Population Size Calculator Compute the stable-equivalent population size as observed annual births divided by the intrinsic birth rate b.
Stationarity Zero Growth Checker Classify zero population growth from an annual growth rate or a two-census count pair, treating |r| within the stated tolerance as stationary, above it as growing and below negative it as shrinking.
Sullivan Method HLE Calculator Apply the Sullivan method to an abridged life table, computing total and disability-free (healthy) life expectancy at the start of each interval where the final interval is open-ended.
Survivorship Ratio Between Census Calculator Compute the intercensal cohort survival ratio as the ratio of life-table survivors at the later age to survivors at the initial age.
Tempo Adjustment Bongaarts Feeney Calculator Apply the Bongaarts-Feeney tempo adjustment, inflating the observed period total fertility rate to TFR / (1 - r) where r is the annual change in the mean age at childbearing.
Terminal Digit Preference Share Measure age-heaping on one terminal digit: the percentage of reported ages ending in the chosen digit relative to a uniform ten percent share across digits.
TX Total Years Lived Above Calculator Sum life-table person-years lived Lx over all intervals from a starting age upward to obtain the total years lived above that age.
U5MR Under Five Rate Calculator Compute the under-five mortality rate as deaths of children under age five per one thousand live births.
UN Joint Age Sex Score Compute the UN Manual IV joint score for age-sex data quality: three times the sum of absolute successive sex-ratio deviations plus the summed male and female age-ratio deviations, classifying below 20 as accurate, 20 to 40 as inaccurate and above 40 as highly inaccurate.
UN Model Life Table Pattern Lookup Validate and label one of the five patterns of the UN Model Life Tables for Developing Countries (1982): General, Latin American, Chilean, South Asian or Far Eastern.
UN WPP Scenario Variant Lookup Identify a World Population Prospects projection or estimation variant by its conventional name and a one-sentence description of how its fertility, mortality and migration assumptions differ from the medium path.
Unmet Need Contraception Percent Compute unmet need for contraception as a percent of married women of reproductive age, plus total demand (prevalence plus unmet need) and the share of demand satisfied by current use.
Voting Age Population Share Compute the share of the total population that has reached voting age (18 and over) as a percentage.
Wanted Versus Actual Fertility Gap Compute the gap between observed total fertility and the wanted total fertility reported in survey style questions, together with the share of observed fertility that exceeds wanted fertility.
Whipple Age Heaping Index Calculator Compute the classic Whipple index of age heaping over ages 23-62, reporting both the five-fold-scaled index and the raw share of reported ages ending in 0 or 5, with UN quality bands. A custom inclusive evaluation window may also be supplied.
Working-Age Share Calculator Compute the share of a population aged 15-64 years, expressed as a percentage.
YLD Calculator Compute years lived with disability as the sum of case counts times disability weights, using either current prevalence or incidence times duration; prevalence is the default per the GBD 2010+ convention.
YLL Calculator Compute total years of life lost as the sum of deaths in each age group times the standard life expectancy remaining at that age, undiscounted and without age weighting per the GBD 2010+ convention.
Youth Bulge Share Checker Check for a youth bulge by testing whether the population aged 15-29 is at least a given share (default thirty percent) of the total adult population aged 15 and over.

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