Fit a log-normal distribution using the median and 90th-percentile anchors to estimate your income percentile within a population.
Input Data
Results
At a glance:Using the median and 90th percentile as anchors, the income is mapped onto a log-normal distribution to derive its percentile rank.
Formula
Fit a log-normal by matching median and p90, then compute percentile = Φ((ln(income) − μ) / σ)
$$\mu = \ln(median),\quad \sigma = \dfrac{\ln(p_{90}) - \mu}{1.2816}$$$$Percentile = 100 \times \Phi\!\left(\dfrac{\ln(income) - \mu}{\sigma}\right)$$How to Use
- Enter your income, the population median, and the 90th percentile.
- Read your percentile and the share earning less than you.
FAQ
What does a percentile mean?
The nth percentile means your income is higher than n% of the population and lower than (100 − n)% of it. For example, at the 75th percentile you earn more than about 75% of people and only 25% earn more than you. It turns an abstract income number into a comparable relative position.
Why use the median and the 90th percentile as the two anchors?
Income distributions are usually right-skewed; taking the logarithm makes them close to normal (the log-normal model). With just two points—the median (which sets μ) and the 90th percentile (which sets σ)—you can fit the whole curve and then derive the percentile of any income. You can swap in your own group's actual figures to make the result more accurate.
How accurate is the result—can I use Hong Kong data?
This is a simplified statistical estimate, not an official figure—real income distributions may deviate from the log-normal assumption, especially near the tails. As long as you replace the median and 90th percentile with Hong Kong's (or any group's) actual data, the calculator uses that group as its benchmark; the defaults use Hong Kong individual monthly income as a demonstration.
If income rises a bit, does the percentile jump a lot? What differs between the middle and the tails?
Under a log-normal distribution, income and percentile do NOT rise in proportion—near the median, a small extra amount can lift the percentile sharply; the higher you go, the harder it gets to climb further. Using the defaults (median HK$20,000, 90th percentile HK$50,000): HK$15,000 is about the 34.4th percentile; HK$20,000 is exactly the median at 50th; HK$30,000 already reaches about 71.5th; HK$50,000 is the 90th; and HK$80,000 only reaches about 97.4th. Note the 'marginal effect': from 15k to 30k (a HK$15k rise) the percentile climbs 37 points (34.4% → 71.5%), but from 50k to 80k (a larger HK$30k rise) it rises only 7.4 points (90% → 97.4%). This reflects the 'dense middle, sparse tails' nature of income—most people cluster near the median, so each extra bit in the middle overtakes many; the top is sparse, so overtaking more needs far more income. It also explains why 'climbing from middle-class upward' often feels harder than 'crawling from low income to middle-class'.
What does a high or low percentile represent, and how should I use this result well?
First, emphasise: a percentile is 'neither good nor bad'—it is a snapshot of your relative position on the income ladder, not a judgement of your life's worth. Once understood, the result has several practical uses. First, 'a reference for pay negotiation'—if you find yourself low in your industry and region (e.g. only the 30th percentile), that is an objective basis to review, push for a raise or switch jobs; if already high, focus on other development. Second, 'career and skill planning'—knowing your position, think about what (further study, a career change, a side business) moves you up; but remember the marginal effect—climbing higher needs ever larger income gains, so set realistic goals. Third, 'view it rationally, avoid anxiety or complacency'—social media amplifies a few high earners and makes people feel 'behind'; a percentile computed from real group data corrects that bias. When using it, ensure 'consistent basis': your income, the median and the 90th percentile must all be monthly or all annual, all individual or all household, otherwise the result distorts. Also remember this is a simplified log-normal estimate, rough at the tails. Use it as a self-positioning and planning reference, not a precise official ranking. You can pair it with the Gini coefficient calculator to see overall income inequality.
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.