mathematics

The Passport Index

The Passport Index is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand The Passport Index rather than just read about it. In short: The Passport Index is an interactive online tool by Arton Capital that provides its users with insights about passports, including the ability to compare and rank the world's passports. Rankings are based on the freedom of movement and visa-free travel open to holders of particular passports.

Key takeaways

The Passport Index belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect The Passport Index to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of The Passport Index from memory before moving on to harder problems.

Reference excerpt

The Passport Index is an interactive online tool by Arton Capital that provides its users with insights about passports, including the ability to compare and rank the world's passports. Rankings are based on the freedom of movement and visa-free travel open to holders of particular passports. The site allows the display of various territories' passports using a variety of filters such as region and passport cover colour.

World Openness Score The World Openness Score is a measure or index that tracks the ability of the world's population to travel visa-free. It grew from 17,904 to 20,143 between 2015 and August 2018. But due to the COVID-19 pandemic in 2020, the index fell to about 13,000. Despite the COVID-19 pandemic, it rose again. In 2022, the index was nearly 22,000.

Methodology The Passport Index compares passports mainly on their visa-free travel options, but also on how welcoming the countries are to visiting foreigners. In its ranking, The Passport Index looks at 193 United Nations member countries and six territories, which include ROC Taiwan, Macao (SAR China), Hong Kong (SAR China), Kosovo, Palestinian Territory and the Vatican. Territories annexed to other countries such as Norfolk Island (Australia), French Polynesia (France), British Virgin Islands (Britain) are excluded.

Visa-free Score The Passport Index ranks passports based on a "total visa-free score," which assigns passports a point for each country their holders can visit without a visa, with a visa on arrival or by obtaining electronic travel authorization (ETA). The country with the highest visa-free score has the most powerful passport.

Welcoming Score The Passport Index awards one point to each country's passport which allows its bearer to enter visa-free or with visa on arrival. The country with the highest welcoming score is the most welcoming country in the world.

World Openness Score The World Openness Score is a measure that reflects the travel openness between countries. It has grown from 17,904 to 18,680 between 2015 and August 2017. On 21 November 2018 it had reached 20,189.

Global Mobility Score The Global Mobility Score is a benchmark that shows an individual's level of freedom of global mobility reflecting one or more passports in their possession. Higher scores reflect increased freedom of mobility.

Ranking Global Passport Power Rank: World's passports are ranked by their total visa-free score. Countries that share equal visa-free scores, are sorted by the number of visa-free countries portion of that score. Individual Passport Power Rank: Data from the latest UN Human Development Index is used to further break the ties and order the countries in unique ranks. Welcoming Countries Rank: The Passport Index ranks countries by how welcoming they are to other nationalities.

Results Passport Index rankings are in real-time and continue to vary as new changes to visa agreements are made. For the most part, the Top 10 places have been occupied by European countries with the exception of Singapore and the United Arab Emirates. Between 2017 and 2018, at top of the list with a visa-free score of 165 were Singapore and Germany, while the United States of America, South Korea, France, Denmark and Sweden were among the 11 countries that shared the second spot with a score of 164. The UAE passport now takes first place with a visa-free score of 181, in 2026.

Table Passport scores and rankings for the year 2026.

Case studies

United Arab Emirates In 2017, The Passport Index was assigned to monitor the development of the newly launched UAE Passport Force Initiative, with the aim to position the Emirati passport on the list of the five most powerful passports in the world by 2021. By 31 October 2018, the Emirati passport had already reached fourth place. However in 2021, the passport's power trend dropped secondary to the COVID pandemic.

Background The Passport Index was launched by Arton Capital, a financial services firm with a head office in Montreal, Canada, in 2014.

Worked examples

Example 1 — a first encounter with The Passport Index

Start with the simplest possible case. Write down what The Passport Index claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to The Passport Index before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about The Passport Index ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of The Passport Index

In research: The Passport Index appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses The Passport Index in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: The Passport Index is common in secondary-school and first-year university syllabi. It links to neighbouring topics Index numbers, International travel documents, Internet properties established in 2014, so understanding it makes those chapters shorter.
In everyday life: Look for The Passport Index outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study The Passport Index in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what The Passport Index means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain The Passport Index out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is The Passport Index in simple terms?

Why does The Passport Index matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study The Passport Index?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on The Passport Index.