There was no single last day
Ask when the First Crusade ended and you can point to the capture of Jerusalem in 1099. The Fourth Crusade has no equivalent moment. Its stated aim was to recapture Jerusalem by first defeating the Ayyubid sultanate in Egypt; instead the army spent its strength on two Christian cities. It stopped being a crusade in several steps over about three years, and historians pick different steps as "the end" depending on whether they mean the fighting, the political settlement or the legal status of the crusaders' vows.
The timeline below separates those threads so you can see which event answers which version of the question.
Timeline: from the Venice debt to the absolved vows
| Date | Event | Why it matters to the ending |
|---|---|---|
| 1201-1202 | Crusaders contract Venice for transport at 85,000 silver marks; they can initially pay only 35,000 | The debt drives every later diversion |
| November 1202 | Crusaders sack Zara (Zadar), which passes to Venetian control | The first attack on a Catholic city by a Catholic crusader army; Innocent III temporarily excommunicates the army |
| January 1203 | Agreement with Prince Alexios Angelos: 200,000 silver marks and 10,000 troops if his father is restored | Turns the fleet toward Constantinople |
| July 1203 | First siege of Constantinople | Isaac II restored |
| 1 August 1203 | Alexios crowned co-emperor as Alexios IV | His promises prove impossible to pay |
| March 1204 | Crusader and Venetian leaders agree in advance how to divide the empire | Conquest replaces payment as the goal |
| 12-13 April 1204 | Constantinople stormed, then sacked for three days | The military climax; most accounts call this the end |
| 9 May 1204 | Baldwin of Flanders elected Latin emperor; crowned 16 May in Hagia Sophia | Political result: the Latin Empire |
| 1 October 1204 | Partition treaty assigns three-eighths of the empire to Venice | The spoils are formalized |
| 13-14 April 1205 | Battle of Adrianople: Kaloyan of Bulgaria defeats the Latins; Baldwin captured, Louis of Blois killed | Ends the crusaders' offensive power |
| 1204-1205 | Legate Peter Capuano, in Constantinople, absolves crusaders who stayed to defend the city | Legal end: those men no longer owe the journey to the Holy Land |
How the money problem became a conquest
The army's leaders had promised Venice payment for a fleet sized for a much larger force than actually turned up. The contract was set at 85,000 silver marks. The crusaders could at first pay only 35,000, and they raised a further 14,000 only by reducing themselves to extreme poverty. In lieu of the rest, Doge Enrico Dandolo proposed that they help him take Zara on the Adriatic coast.
The next offer came from Alexios Angelos, son of the deposed emperor Isaac II. In January 1203 he promised to pay the entire Venetian debt, give the crusaders 200,000 silver marks, supply 10,000 Byzantine troops, maintain 500 knights in the Holy Land and lend the Byzantine navy to carry the army to Egypt. After the crusaders' first siege of the city, Isaac was restored, and on 1 August 1203 his son was crowned co-emperor as Alexios IV.
Alexios IV could not pay. A court official, Alexios Doukas, nicknamed Mourtzouphlos, led the anti-crusader faction and seized the throne as Alexios V. The crusaders now had a hostile emperor, an unpaid debt and a fleet in the Golden Horn.
The two days that decided it
The record of the final assault is short and specific. On 12 April 1204 a strong northern wind finally let the Venetian ships come close to the sea walls, and after a short fight about seventy crusaders got into the city. Defenders trying to hold them back with a wall of fire burned even more of Constantinople; that fire alone left an estimated 15,000 people homeless. By 13 April the crusaders held the whole city.
What followed is what the crusade is remembered for. The city was sacked for three days, with ancient and medieval works of art stolen or destroyed, civilians killed and churches looted despite the threat of excommunication.
What the sack left behind
The leaders had settled the shares before the final assault. In March 1204, a few weeks before the sack, Doge Enrico Dandolo, Boniface of Montferrat, Baldwin of Flanders and Louis of Blois concluded a preliminary partition agreement, a text that survives in the papal correspondence of Innocent III. A committee of six Venetians and six crusaders would elect the emperor. Whoever won the throne would receive a quarter of the empire and of the capital, plus the Blachernae and Boukoleon palaces; the losing side would get Hagia Sophia and the right to name the Latin Patriarch. The remaining three quarters would be split equally between Venice and the other crusaders. On 9 May they elected Baldwin of Flanders emperor, and he was crowned on 16 May in Hagia Sophia in a ceremony that closely followed Byzantine practice. The partition treaty of 1 October 1204 gave three-eighths of the empire, including Crete and other islands, to Venice. Much of that partition existed only on paper, because Byzantine successor states formed in Nicaea, Trebizond and Epirus. The Latin Empire lasted until 1261, when Constantinople was retaken.
Baldwin's reign was short. At Adrianople in April 1205 the Bulgarian ruler Kaloyan, with Cuman allies, destroyed the Latin field army; Baldwin was taken prisoner and spent his last days in captivity, and Louis of Blois was killed. After that the crusaders were defending a conquest, not waging a crusade.
The pope's verdict
Innocent III had called the crusade and had excommunicated the army over Zara. His anger after Constantinople is preserved in a letter to his legate Peter Capuano, translated in Fordham University's Internet Medieval Sourcebook. Innocent writes that he has learned the legate "absolved from their pilgrimage vows and their crusading obligations all the Crusaders who have remained to defend Constantinople," and tells him that "you neither should nor could give any such absolution." The same letter accuses the army of plundering churches and carrying off crosses and relics.
A collection of contemporary documents published by the University of Leeds identifies Capuano as legate in Constantinople in 1204-1205. In effect, a papal envoy closed the crusade by releasing its remaining men from their vows.
So which answer should you give?
If you need one sentence: the Fourth Crusade ended with the sack of Constantinople in April 1204 and the creation of the Latin Empire, after which its leaders never continued to the Holy Land. If you need precision, add that its fighting strength was broken at Adrianople in 1205 and that a papal legate, not a battle, released the men who stayed.
Earlier crusade history: the Second Crusade's siege of Damascus. The Third Crusade's best-known commander is profiled in Richard the Lionheart.