Example data table
| # | Income ($) | Percentile (%) |
|---|
Formula used
Log-normal model. Let income X follow a log-normal distribution with parameters \(\mu,\sigma\). Then \(\ln X \sim \mathcal{{N}}(\mu,\sigma^2)\) and the percentile is \(100\,\Phi\big((\ln x - \mu)/\sigma\big)\), where \(\Phi\) is the standard normal CDF. We fit \(\mu\) and \(\sigma\) from two anchors: median \(m\) and 90th percentile \(q_{{0.9}}\). Since \(m = e^\mu\), we have \(\mu = \ln m\). Also, \(q_{{0.9}} = e^{{\mu + \sigma z_{{0.9}}}}\) with \(z_{{0.9}} = \Phi^{{-1}}(0.9)\), so \(\sigma = [\ln(q_{{0.9}}) - \mu]/z_{{0.9}}\).
Empirical anchors. When you provide incomes at select percentiles (e.g., P10, P25, P50, P75, P90), the calculator linearly interpolates between these points to estimate any intermediate percentile or the income at a chosen percentile.
How to use this calculator
- Choose a Mode: percentile from income or income from percentile.
- Select a Model: log-normal fit or empirical anchors.
- Enter your value (income or percentile) and adjust model parameters to match your preferred dataset.
- Click Compute. The result appears above the chart; the example table refreshes.
- Use Download CSV or Download PDF for exports.
FAQs
Results reflect whatever you input. If you enter pre-tax income, the percentile corresponds to that basis.
Either. The model is agnostic; use parameters that match the population you care about.
Definitions, survey years, populations, and trimming rules vary. Adjust anchors or parameters to mirror a specific source.
This tool does not adjust for prices. For regional comparisons, deflate or inflate incomes before entering them.
Percentiles are rounded to one decimal place. Real-world data has sampling error and model misspecification risk.