The Columbus Brothers’ Calculations

The Columbus brothers did not need to convince the king of Portugal that the earth was round. Every European monarch knew that. And, as you shall see, even the Vatican in Rome acknowledged that fact in 1477 when they hired Dominus Nicolaus Germanus to create a globe.

Columbus was a self-taught man. He learned to read and write in Latin. But unfortunately – and at the same time fortunately – he did not, or would not, follow the current teachings of the universities and reigning scholars of his day. Hundreds of portolans, planispheres, and other maps were available to him and his brother. Bartolomé had access to all them through King João’s cartography studio.

One of those documents was Fra Mauro’s Great Mappa Mundi sent to King Afonso V in 1459. We have already shown it to you, but we want to point out some details that would have been important to Christopher and Bartolomé.

Fra Mauno’s Mappa Mundi, Venice, c1450.(1)

The Circumference of the Earth – Among the numerous text boxes containing geographic information, Fra Mauro wrote, “I have found various opinions regarding [the earth’s] circumference, but it is not possible to verify them. It is said to be 22,500 or 24,000 miglia, more or less, according to various considerations and opinions, but they are not of much authenticity, since they have not been tested.”

Miglia was the Italian word for miles. The Romans invented the unit over a thousand years earlier, but it was not standardized. 22,500 Roman miles were equivalent to about 21,400 US miles(2) today. 22,500 Italian miles were equivalent to about 26,750 US miles(3) today. Today’s geographers claim that the meridional circumference of the earth is 24,900 US miles(4). Whether or not Fra Mauro meant Roman miles or Italian miles, his measurement was between 86 and 93 percent accurate. Fra Mauro’s measurement of the earth’s circumference was available to Columbus, but Columbus did not believe it. He thought the world was much smaller.

Many Indias – Even though Fra Mauro drew his planisphere 1300 years after Ptolemy drew his map of the world, Fra Mauro was no more specific about the exact location of India. Ptolemy named today’s Indian peninsula between the Indus and Ganges Rivers, India Intra Gangem Fluvium [India inside the Ganges River]. Ptolemy named today’s southern China, India Extra Gangem Fluvium [India Outside the Ganges River]. Marco Polo had been equally vague, naming several places east of the Indus River, India. The author portraying himself as Sir John Mandeville mentioned three Indias: India the Lesser, India the Greater, and India the Middle. Fra Mauro labeled today’s Indian peninsula, India Prima, and China, India Cin. It is no wonder that Christopher Columbus referred to China as “The Indies.”

Nicolaus Germanus’ Two Globes [1477] and Map of the Ecumene [1482]

The most current maps available to the Columbus brothers were created by Dominus Nicolaus Germanus [Master Nicholas the German] (c1420-c1490)(5). In 1477, the two-year-old Vatican Library(6) paid Nicolaus 200 gold ducats to create two globes depicting the earth and the sky. We do not know if the Columbus brothers saw the globes(7). What is important to us is that in 1477, the Vatican acknowledged that the earth was a sphere.

We do know that Christopher saw the world map Nicolaus created in 1482. That was three years before the Columbus brothers made their presentation to King João II. An inventory of Christopher’s library included the book Cosmographia in which Nicolaus inserted his map.

Nicolas updated Ptolemy’s(8) map from 140 CE. Cartographers still thought Ptolemy’s geography was as infallible as Aristotle’s philosophy. Nicolaus added the latest Portuguese and Genoese discoveries, such as the Atlantic Islands and the Portuguese holdings on the Guinea coast. He also added features of the Far East that Marco Polo described in his Travels, such as the spice islands in the Indian Ocean. But, like Ptolemy, Nicolas did not give Asia an eastern boundary even though Venetian traders, such as Nicholas di Conti, had been traveling around the Far East for several decades.

Dominicus Nicholas Germanus, Interpretation of Ptolemy’s World Map of 150 CE, published in Cosmographia in 148, engraved by Johannes Schnitzer(9).

Before the Columbus brothers could present their case to the king of Portugal, they needed to answer several questions.

  1. What was the circumference of the earth? Eratosthenes and Fra Mauro answered that question with 86 to 93 percent accuracy. The answer defined how many miles were in each degree?
  2. Using the answer from Question Number One, what percentage of that circumference was covered by the Eurasian landmass [the land between Lisbon and Cathay]?
  3. Subtracting Answer Number Two from Answer Number One, how far was it from Lisbon to Cipangu [Japan] sailing westward? The answer to that question revealed how far a ship had to sail in order to reach a known inhabited land so it could restock its supplies.
  4. How far east from Cathay lay Cipangu? Columbus considered Cipangu as one of the Indies and a stepping stone between Lisbon and Cathay. How much farther west from Japan was the mainland?

The Columbus brothers came up with the wrong answers for all four questions.

  1. They underestimated [by 25%] the Earth’s circumference to be about 18,700 miles, when it is actually 24,900 miles [75% accuracy]. That meant they calculated fewer miles per degree around a meridian than there are.
  2. They followed Marinus of Tyre’s calculations and overestimated [by 45%] the width of Eurasia between Lisbon in the west, and Cathay in the east to be 225 degrees, when it is close to 125 degrees.
  3. Believing that the landmass of Eurasia took up more of the earth’s landscape than it does, they underestimated [by 55%] the distance across the ocean from Cathay to Lisbon.
  4. They overestimated the distance between Cipangu [Japan] and Cathay. By thinking that Cipangu lay farther east than it does, they thought the distance their ships had to travel from Lisbon to an island where they could restock was closer than it is.

Put another way, the Columbus brothers thought they only had to sail 3,200 miles to reach inhabited land when the distance between Lisbon to Tokyo [flying over the Americas] is around 11,100 miles. The brothers made other mistakes, too.

  1. They hoped their ships could stop at Antilla, the large island Andrea Bianco drew in the middle of the Ocean Sea, to resupply – even though they did not know who lived on the island, or if its inhabitants could or would provide them with food, water, and wood.
  2. They hoped there were more undiscovered islands sprinkled within the Ocean Sea – like St. Brendons, perhaps – that could and would provide provisions, if not jewels, precious metals, and exotic spices.

The Columbus brothers were following some incorrect information that the landmass of Eurasia took up about six sevenths of the earth’s circumference, leaving only one seventh of the circumference covered in the Ocean Sea. Such a world would look something like this:

On the other hand, if the Columbus brothers had followed the advice of Fra Mauro, Eratosthenes, and or Ptolemy, they would never have attempted their adventure. They would have known that the most advanced carrack or caravel of the day could not carry enough supplies to travel 11,100 miles across the open ocean.

Though we do not know the exact day Christopher Columbus met with King João II, there were witnesses who reported how the meeting went. One witness, João de Barros, said that Christopher referred to Marco Polo’s descriptions of Cipangu, that he mentioned the island’s pearls and other riches, and that the roofs were lined with gold. Columbus referred to the advice Paolo Toscanelli had given to João’s father, King Afonso V, claiming that a route from Lisbon to the Indies – with a pit stop in Cipangu – would be faster and easier than sailing under the as-yet-unreached southern end of Africa.

João de Barros wrote that King João listened to Columbus attentively. Then the king deferred to his “mathematical junta,” the chief scientists of the land. The council of scientists did not take Columbus seriously. They knew the truth. They knew that Columbus had underestimated the distance between Lisbon and Cathay. João de Barros wrote:

“The king, as he observed this Christovão Colon to be a big talker and boastful in setting forth his accomplishments and more puffed up with fancy and imagination about his island Cypango than certain of the things he told about, gave him small credit.”

King João II said “no” to Columbus because Columbus’ calculations were faulty. But João might have said “no” to Columbus anyway.

  1. King João was granting licenses to Portuguese explorers who were offering to pay their own way. Columbus was not making that offer. That same year, 1485, one of the Flemish sea captains living on Terceira named Fernão Dulmo applied to João for a license to search west in the Ocean Sea for Antilla. [Dulmo was also a citizen of Funchal, the main port of Madeira Island, so he might have known Christopher Columbus’ brother-in-law in nearby Pôrto Santo.] Dulmo offered to finance the fitting out of his two ships himself. King João said “yes.” Dulmo did not find anything. He sailed west from Terceira only to be driven back again by the westerlie winds.
  2. João’s focus was eastward, not westward. He was heavily involved with plans for a new expedition under Africa that would result in Bartolomeu Dias’ trip. He was also busy preparing a new land expedition that would travel the Mediterranean route to Abyssinia.
  3. King João was Master the Order of São Tiago, which was determined to find Prester John in the east and beat the Ottoman Turks out of Europe.
  4. The old family squabble between King João’s House of Avis, the House of Bragança [his half-uncle’s family], and the House of Viseu, [his wife’s family] was coming to violent blows. Columbus’ wife belonged to the House of Bragança, whom King João was about to banish from Portugal.


  1. Fra Mauro, Mappa Mundi [World Map], c1450, {{PD-old}} Public Domain.. Image source: commons/9/95/Fra_Mauro_World_Map,_c.1450.jpg
  2. 21,417 US miles = 34,468 km
  3. 26,755 US miles today = 43,059 km
  4. 24,902 US miles = 40,008 km
  5. Theories about his origin include that he was a monk of the Benedictine order, and that he was from the Reichenbach Priory in Baden-Württemberg.
  6. The same Vatican Library refused to stock printed books, and would only stock the traditional hand-written books and manuscripts. In an effort to control the copying of the Bible and other religious material, the Catholic Church pronounced all printed materials as heretical [at odds with accepted theology].
  7. The globes were lost around 1527 when Charles V, King of France and the Holy Roman Emperor, led forces into Rome and sacked the city.
  8. The projection Nicolaus employed, which has since been named after him, the “Donis Projection,” used parallel latitudes, while showing converging longitudes that indicated a sphere.
  9. Dominicus Nicholas Germanus, Le Monde de Ptolémée [The World of Ptolemy], engraved by Johannes Schnitzer, published in Cosmographia in 1482. {{PD-Old}} Public Domain Attribution: By Germanus, Nicholas; Armssheim, Johannes de. via Wikimedia Commons. Image Source:

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