Power Index

 Yes. I’d treat this as a historical composite index, not an objective scientific measurement. I’ll score each power at its historical peak across six dimensions:

Military power — 25%

Economic power — 20%

Population/resources — 15%

Territorial reach — 15%

Technology/administration — 15%

Global/regional influence — 10%

That prevents sheer land area from automatically making an empire #1. For example, the British Empire was the largest geographically, while the Mongol Empire was the largest contiguous empire. 

🏆 Historical Power Index — Top 20

Rank Empire / nation Peak Power Index /100

🥇 1 🇺🇸 United States 1945–present 98

🥈 2 🇬🇧 British Empire c. 1900–1914 97

🥉 3 🇲🇳 Mongol Empire c. 1270–1290 91

4 🇷🇺 USSR c. 1945–1980 90

5 🇨🇳 Qing Empire c. 1750–1800 88

6 🇷🇴 Roman Empire c. 100–160 CE 87

7 🇨🇳 Han Empire c. 1–100 CE 84

8 🇪🇸 Spanish Empire c. 1580–1650 83

9 🇫🇷 French Empire c. 1805–1812 82

10 🕌 Ottoman Empire c. 1500–1600 81

11 🇮🇷 Achaemenid Persian Empire c. 500 BCE 79

12 🇨🇳 Yuan Empire c. 1300 78

13 🇮🇳 Mughal Empire c. 1650–1700 77

14 🕌 Umayyad Caliphate c. 720 76

15 🕌 Abbasid Caliphate c. 750–800 75

16 🇨🇳 Ming Empire c. 1400–1500 74

17 🇯🇵 Empire of Japan c. 1942 73

18 🇷🇺 Russian Empire c. 1895 72

19 🇵🇹 Portuguese Empire c. 1500–1600 70

20 🇰🇷/🇨🇳 Xiongnu Empire c. 2nd century BCE 68

A fascinating result

The United States vs. British Empire is the closest comparison.

British Empire: enormous territory—about 35.5 million km² at its 1920 territorial peak—and more than 449 million people under its control around that time. 

United States: considerably smaller territorially, but its peak power combines industrial capacity, nuclear weapons, global military projection, advanced technology, financial power, aviation, space capabilities and worldwide alliances. That's why I give it the narrowest #1.

The Mongols are extraordinary

The Mongol Empire gets #3, despite having neither the industrial economy nor technology of the modern superpowers. At its peak it controlled roughly 24 million km² and around 110 million people, making it the largest contiguous empire in history. 

China is particularly interesting

The Qing scores extremely highly because it combined enormous population, territory and economic resources. Historical estimates place the Qing's share of world population around 37% in 1800, one of the highest ever recorded for an empire. 

The Roman Empire, meanwhile, probably reached roughly 60–75 million people at its high point and possessed exceptional military organization, infrastructure, taxation and administrative capacity. 

One important caveat

This ranking changes substantially depending on what you mean by “mightiest.”

If we rank military conquest alone, the Mongols rise dramatically.

If we rank territorial size, the British Empire is #1.

If we rank population controlled, the British Empire also reached the top—Guinness gives about 531 million at its 1938 peak. 

If we rank technological and destructive capability, the modern United States and USSR dominate.

So my overall composite answer is:

> 🥇 United States — 98/100

🥈 British Empire — 97/100

🥉 Mongol Empire — 91/100

These scores are my analytical index, not an established historical ranking.