This paper introduces the Domain-specific Continual Pre-Training (D-CPT) Law, a scaling law designed to determine the optimal mixture ratio between general-corpus and domain-corpus for Large Language Models (LLMs) in domain-specific continual pre-training. The D-CPT Law is derived from the Scaling Law, which is used to predict performance based on model size, dataset size, and training costs. The D-CPT Law allows for the prediction of general and domain-specific performance for various mixture ratios, model sizes, and dataset sizes with limited training costs. Additionally, the paper proposes the Cross-Domain D-CPT Law, which extends the D-CPT Law to cross-domain settings, enabling the prediction of D-CPT laws for new domains with minimal training costs. The D-CPT Law is validated through extensive experiments on six downstream domains, demonstrating its effectiveness and generalizability. The paper also discusses three practical applications of the D-CPT Law: optimizing the trade-off between general and domain-specific abilities, optimizing mixture ratios for limited domain-specific data, and resource allocation. The results show that the D-CPT Law significantly reduces the need for costly grid-searching efforts and provides a more efficient way to determine optimal mixture ratios for domain-specific continual pre-training. The Cross-Domain D-CPT Law further enhances the applicability of the D-CPT Law by enabling predictions for new domains with minimal training costs. The paper concludes that the D-CPT Law is an important step forward in the optimization of training LLMs for specific downstream domains and provides a foundation for further research in this area.This paper introduces the Domain-specific Continual Pre-Training (D-CPT) Law, a scaling law designed to determine the optimal mixture ratio between general-corpus and domain-corpus for Large Language Models (LLMs) in domain-specific continual pre-training. The D-CPT Law is derived from the Scaling Law, which is used to predict performance based on model size, dataset size, and training costs. The D-CPT Law allows for the prediction of general and domain-specific performance for various mixture ratios, model sizes, and dataset sizes with limited training costs. Additionally, the paper proposes the Cross-Domain D-CPT Law, which extends the D-CPT Law to cross-domain settings, enabling the prediction of D-CPT laws for new domains with minimal training costs. The D-CPT Law is validated through extensive experiments on six downstream domains, demonstrating its effectiveness and generalizability. The paper also discusses three practical applications of the D-CPT Law: optimizing the trade-off between general and domain-specific abilities, optimizing mixture ratios for limited domain-specific data, and resource allocation. The results show that the D-CPT Law significantly reduces the need for costly grid-searching efforts and provides a more efficient way to determine optimal mixture ratios for domain-specific continual pre-training. The Cross-Domain D-CPT Law further enhances the applicability of the D-CPT Law by enabling predictions for new domains with minimal training costs. The paper concludes that the D-CPT Law is an important step forward in the optimization of training LLMs for specific downstream domains and provides a foundation for further research in this area.