The Rajaji Formula, proposed in June 1944 by Chakravarti Rajagopalachari (popularly known as Rajaji), represented a significant, albeit ultimately unsuccessful, attempt to find a peaceful resolution to the protracted conflict over Indian independence. Formulated during a crucial juncture in the struggle, it aimed to bridge the widening chasm between the Indian National Congress and the Muslim League, thereby paving the way for a negotiated transfer of power from British rule.

The context of the Rajaji Formula was the escalating tensions between the Congress and the Muslim League. The failure of the Cripps Mission in 1942, which offered dominion status after the war but failed to satisfy the Congress's demand for immediate independence, had deepened the divide. Simultaneously, the Quit India Movement launched by the Congress in August 1942, though eventually suppressed, further complicated the political landscape. Rajaji, a prominent Congress leader known for his pragmatism, believed that a negotiated settlement was still possible.

The core of the Rajaji Formula consisted of three key proposals:

• Formation of an interim government: A temporary government would be formed immediately, comprising representatives from both the Congress and the Muslim League, to handle the administration of India during the transition period. This was intended to promote cooperation and shared governance before the eventual transfer of power.
• Referendum on partition: After the formation of the interim government and a reasonable period of joint administration, a referendum would be held in Muslim-majority provinces to decide whether they desired to remain within an independent India or form a separate state. This addressed the Muslim League's demand for a separate Muslim homeland, Pakistan.
• Acceptance of Congress's claim to form government: The Congress would accept the outcome of the referendum and participate in the formation of the government following the result, indicating a commitment to a negotiated solution.

The Rajaji Formula, while ingenious in its attempt to reconcile conflicting demands, faced numerous obstacles. Firstly, Muhammad Ali Jinnah, the leader of the Muslim League, rejected the proposal outright. He saw the referendum as merely a tactical manoeuvre, believing the Congress wouldn't accept the potential loss of Muslim-majority provinces. He remained steadfast in his demand for a separate Pakistan, based on the “Two Nation Theory” which posited the fundamental difference between Hindu and Muslim cultures.

Secondly, although Gandhi initially endorsed the formula, its rejection by the Muslim League effectively curtailed its implementation. The Congress, torn between its commitment to the formula and the growing support for complete independence, failed to exert enough pressure to compel the League to reconsider its stance. In hindsight, the formula lacked sufficient safeguards to address the deeply rooted suspicions and mistrust between the two major political forces in India.

The failure of the Rajaji Formula is viewed as a critical turning point in the Indian independence struggle. It underscored the inability to resolve the Hindu-Muslim divide through a negotiated settlement, ultimately contributing to the partition of India in 1947, a partition that was marked by immense violence and displacement.

Despite its ultimate failure, the Rajaji Formula remains an important historical document, illuminating the complexities and challenges involved in the struggle for Indian independence. It serves as a reminder of the attempts at peaceful resolutions and the deep divisions that ultimately led to the creation of India and Pakistan.