Income tax
plotIncome tax in most territories in the world is collected based on a progressive tax system with higher tax rates for higher income earners.
This post presents plots for effective (i.e. average) personal income tax rates in selected territories in the world as of assessment year 2020. A plot visualizes the effective tax rates for all income amounts in a specific range for each territory. This is more informative than listing only a few specific income amounts and their corresponding effective tax rates for each territory as seen in a journalistic comparative analysis article found online.
Effective tax rate from tax brackets #
A visual explanation of the shape of the graphs of effective income tax rate against income amount, along with an explicit mathematical formula for effective tax rate is drawn out on a whiteboard, captured, cleaned and vector traced as follows.
My whiteboard explanation of the graphs of effective tax rate presented in vector graphics format
Assumptions and limitations #
Tax laws in different territories are complicated in implementation details. Some assumptions need to be taken for consistency.
 The rates for a resident are taken. Note that the rates for a resident may be higher or lower than or the same as that for a nonresident or expatriate.
 The personal allowance level, if applicable, is assumed to be that for unmarried individuals, which is typically lower than that for married individuals.
 Other deductions, if applicable, are assumed to be zero.
The plots are meant to be for reference only. A direct comparison of a specific metric in different territories with vastly different social security systems and with currencies that have varying purchasing power parity would be oversimplistic.
In practical terms, the values of income tax rates given do not reflect the varying tax situations and law enforcement in different territories. For example, in mainland China, the income of only a small portion of the working population exceeded the allowance level, and a small portion of that actually paid income tax.
The income tax rates for only a limited number of territories are included in this study due to time constraint. For each territory, manual research is conducted to understand its income tax scheme from which a rates table and/or a formula for contributions is derived. There is no aggregated dataset of income tax schemes for different countries in the world that is currently publicly available.
Calculation and expression #
For each territory, the yearly tax bracket graduated rates sourced from the government website are applied on a range of yearly income amounts scaled by the latest exchange rates to compute an effective rate in percentages. The effective rates are plotted against equivalent monthly income amounts (yearly income amounts divided by 12) graphed with a line in a distinct named color.
 Equivalent monthly income amounts are computed following the convention of expressing salaries in monthly terms in Hong Kong and Singapore, as opposed to annual terms in some other countries.
 The yearly income amount includes 13th salaries, bonuses and other taxable income if applicable.
In addition, for each territory, the rates for pension fund and unemployment insurance contributions from the employee, if applicable, are applied on the income amounts to compute an effective contributions rate and then a combined effective rate, which is the sum of (i) effective tax rate and (ii) effective contributions rate, graphed with a dashed line.
The percentage value levels computed are crosschecked with online tools found by searching for "net income calculator" for each territory.
A secondary xaxis scaled for a second currency is added on top border for convenience of reading.
Some territories #
A plot is generated for territories with low but nonzero income tax rates, including:
with the following notes.

For Singapore (SG), It can be interpreted that, the combined effective rate remained roughly at 20% for all income amounts, with a larger proportion going to CPF for individuals with lower income, and a larger proportion going to income tax for individuals with higher income.

For Switzerland (CH), income tax is adopted at the cantonal level in addition to the state level, and one canton with a relatively high cantonal level income tax Zürich (CH_ZH) is chosen for calculation of a sum of taxes at all levels for reference. There are over ten brackets for the two tax schemes, which can be observed in the many inflection points in the curve. The final rate is further complicated by the addition of a municipal tax as a multiple of the cantonal rate, which is chosen to be that for the city of Zürich here.
More territories #
A plot is generated for territories with higher income tax rates, including:
 United States (US) (with FICA and ACA tax)
 Canada (with EI deduction and CPP contribution)
 United Kingdom (UK) (with national insurance)
 Australia (AU) (with super guarantee contribution and Medicare levy)
 New Zealand (NZ) (with ACC levy)
 mainland China (CN)
in addition to the territories mentioned previously.

For the United States (US), income tax is adopted at the state level for most states in addition to the federal level, and a state with a relatively high state level income tax California (US_CA) is chosen for calculation of a sum of taxes at both levels for reference, with tax brackets from 1% to 13.3% for California.

For Canada (CA), income tax is adopted at the provincial level in addition to the federal level, and the province Ontario (ON) is chosen for calculation of a sum of taxes at both levels for reference.

For the United Kingdom (UK), a variable personal allowance level, which transitions from full to zero on a specific range of income amounts, has been applied to compute effective tax rates.

For mainland China, there is no nationally unified pension scheme, and therefore no dashed line is plotted for mainland China (CN).
Higher income earners #
A plot with a larger range of income amounts is generated to show the highest rate levels possible for higher income earners, such as executives and celebrities.

For Hong Kong (HK), the top bracket is 17% but the overall cap is fixed at a standard rate 15%.

For Singapore (SG), the top bracket is 22% but there is no overall cap, and therefore the effective overall cap approaches 22% as income amount approaches infinity.
Plot by others #
While this sort of visualization seems to be uncommon, a similar graphic of effective tax rates found by searching for "tax curve".
Line plot of effective income tax rate against income in Hong Kong in 19981999
(Source: Hong Kong Government 199899 Budget)
Further work #
The income tax rate is a flat zero for some territories in the world, which would give an uninteresting plot. A negative income tax, which would give a more interesting plot, is not implemented in practice.
An interactive presentation of the plots is suggested to reduce clutter due to sometimes intersecting or overlapping lines, and to accommodate lines for rates with a different personal allowance level applied.
Changelog
 Feb 2021 Replaced plots with new versions reexported in SVG format with xaxis major tick labels formatted in thousands.
 Dec 2020 Added more external links regarding plots and images.
 Dec 2020 Renamed labels to include country code to avoid confusion for regions as in
US_CA
andCH_ZH
, and addedCA
andCA_ON
.  Oct 2020 Added more detailed description for images.
 Oct 2020 Updated plots with added dashed lines for combined rates.