The world's fragile hopes and calculations for the Middle East were placed in jeopardy yesterday by the death of Anwar Sadat of Egypt.

More than any other single figure in that volatile region plagued by ancient hatreds, Sadat sought to be a personal bridge to a different future. Without him as Egypt's president, the assumptions that guided Arab, Israeli or superpower strategies are no longer secure.

"The world is different now than it was a day ago," an American expert on the Middle East said.

Beyond the other intrinsic consequences of Sadat's demise, there was particular concern about commando clashes or even open warfare between Egypt and Libya, due to the likelihood that Libyan leaders will be blamed in Cairo for the assassination. U.S. policies toward Libya, which have hardened dramatically in the Reagan administration, were also reported to be under reconsideration.

In Washington, Moscow and other key capitals, national leaders and their diplomatic experts had their eyes trained first on Cairo for clues to the unfolding political drama. For it will be in Egypt, in the first instance, that the future is decided.

The assumption in official Washington last night was that the new leader, whoever he is, will not possess Sadat's imaginative flair, nor will he have Sadat's unchallenged authority, at least initially. Vice President Hosni Mubarak, who appeared to have the best chance of taking over, was rated as an able political operator with his hands on the levers of power, but in this sense "not a Sadat."

Mubarak and the other members of the present Egyptian leadership are considered here to be loyal followers of Sadat's policies, including the policy of peace with Israel. But several Middle East experts who have had extensive contact with Mubarak in the past said that, at the same time, they expect him to seek a rapprochement with Saudi Arabia and the other mainstream Arab states.

Mubarak may be in a better position than Sadat was to achieve this, they added, because he does not bear the burden of as much personal hostility. According to former U.S. ambassador to Egypt Hermann F. Eilts, now of Boston University, it was Mubarak who took the initiative in winning Sadat's approval to seek improved relations with the other Arabs in a so far unsuccessful cause.

Former assistant secretary of state Harold H. Saunders, a key diplomatic aide in the negotiation of the Camp David accords and all that flowed from them, said that because Sadat's peace initiative was so highly personalized, the new leaders may move away from that approach somewhat, "not throwing it over but gradually turning toward Sadat's original purposes." Saunders said Sadat never intended "a separate peace" with Israel that did not deal with the Palestinian problem.

It remains to be seen whether Egypt under new leadership can move more forcefully on behalf of the Palestinians and restore the Arab consensus without destroying the still-delicate relationship with Israel. The immediate questions on the Israeli front were the future of the negotiations on Palestinian autonomy and the scheduled return to Egypt next April of the major part of its Sinai territory lost in the 1967 war.

Sadat's death caught the still-evolving foreign policy of the Reagan administration at midpassage on the tactics if not the grand strategy of Egyptian-Israeli issues. After Sadat's trip here in August and that of Israeli Prime Minister Menachem Begin last month, Washington policy makers still had not come to grips with the next steps in the Palestinian autonomy negotiations. Washington was still in the process of creating an international force to police the Sinai after the scheduled Israeli withdrawal. And Sadat, at least, went to his death believing that there had been no final decision on the proposal he carried to Washington that the Palestinian Liberation Organization be brought into the peace process.

In a variety of world capitals, including this one, particular scrutiny is trained on the immediate course of conflict between Egypt and Libya. Only late last week, Sadat dispatched Mubarak to Washington on what was described as an "urgent" appeal for American action to reassure states in the area which felt threatened by the Libyan-Ethiopian-South Yemen pact sponsored by Libyan leader Muammar Qaddafi in mid-August.

Mubarak, on this mission, saw President Reagan, Vice President Bush, Secretary of State Alexander M. Haig Jr., Defense Secretary Caspar W. Weinberger and other top officials last Friday, Saturday and Sunday. Officials said last night that additional aid for Egypt and Sudan, already under consideration before the assassination, has new urgency now. And in the hours after Sadat's death, the president of another state that feels threatened by Libya, Col. Seyni Kountche of the Republic of Niger, conferred with Bush.

Sadat, who considered Qaddafi "a lunatic" and perhaps his bitterest enemy, was greatly concerned about the new tripartite pact involving Libya. According to State Department officials, Washington was studying "an abundance of evidence" of joint military planning by the three pact countries, all of which are friendly to Moscow.

Lending further credence to Sadat's worries were reports of Libyan bombing attacks on Sudan, Egypt's neighbor to the south, and of assassination plots against Sudanese President Jaafar Nimeri.

In the immediate aftermath of Sadat's assassination, Egypt placed its forces in the western desert near Libya on special alert. Among officials familiar with U.S. intelligence, Egyptian commando raids or more powerful military action was considered a distinct possibility.

[The Pentagon announced that elements of the U.S. Rapid Deployment Force and U.S. warships in the Mediterranean "have been placed on increased readiness," The Associated Press reported.]

[The Rapid Deployment Force was formed in the Carter administration to enable quick response to events in the Persian Gulf. The airborne divisions and support elements total 56,000 Army troops, while the Marine brigade numbers about 12,000 men. The administration statement was purposely vague as to units affected.]

William B. Quandt of the Brookings Institution, who was a senior aide at the National Security Council specializing in Middle East matters for most of the Carter administration, said "there is a significant chance of an Egyptian-Libyan war" in the wake of the Sadat assassination. If Egypt seems to be winning, the Soviet Union and Cuban forces might intervene, he said.

It was Anwar Sadat who moved hard against the Soviet Union with important consequences, changing partners for his nation from Moscow to Washington. There was no indication last night that the Russians will be able to reverse Sadat's direction, if Egyptian leadership is able to achieve internal security and national stability. But the very fact that the question must be asked is the source of apprehension in government circles.

Due to his powerful personal leadership and his mastery of modern mass communications, Sadat's impact on world events was far beyond the norm for an Egyptian leader and beyond that of leaders of far more powerful nations. His sudden absence, for the same reason, is a major international development and more difficult to assess than would be the demise of another leader.

As seen from Washington amid the initial shock, the probable consequences include:

* An Egypt that is less sure of itself and thus less able to provide steady leadership in the cause of Arab-Israeli peace.

* An Israel that consequently is more apprehensive about Egypt and less inclined to bet its future on diplomacy and international accord.

* An Arab consensus that is more willing to seek renewed accommodation with Egypt on terms that do not require a total change in Cairo's alignments and policies.

Greater danger of an Egyptian-Libyan military clash, which could spread to the regional forces of the nuclear superpowers.

* New problems and questions for the Reagan administration's search for an anti-Soviet strategic consensus in the Middle East and for the culmination of an Arab-Israeli peace. Egypt, most populous of the Arab nations, was and is the cornerstone of these efforts.