As LLMs are increasingly deployed as agents, reliable assessment of their agentic capabilities has become essential. However, reported benchmark scores often jointly reflect model capability and the implementation choices each benchmark is packaged with, making cross-benchmark results difficult to interpret as clean measurements of the underlying model. In this work, we present a unified framework for the fair evaluation of LLM agentic capabilities. Driven by a unified configuration system, the framework integrates diverse benchmarks into a standardized instruction--tool--environment format, executes agents through a fixed ReAct-style architecture within a controllable sandbox, and provides an optional offline setting that replaces volatile live environments with curated snapshots, so that framework effects and environment effects can be analyzed separately. Building on this, we unify the evaluation methodology under each benchmark's original task-success criteria, while introducing unified metrics for resource consumption and a taxonomy for decision- and execution-level failure attribution. Within this framework, we adapt 7 widely used benchmarks spanning 24 domains across single-agent, multi-agent, and safety-critical scenarios, and conduct a large-scale empirical analysis over 400K rollouts and 5B tokens on 15 models. The results show that scaffold choice and environmental volatility materially shift benchmark outcomes in both directions, allowing our framework to disentangle intrinsic LLM capabilities from framework- and environment-induced artifacts. We further demonstrate its extensibility as a secure testbed for safety-critical domains. Codes and benchmarks at are available at https://github.com/whfeLingYu/A-Unified-Framework-for-the-Evaluation-of-LLM-Agentic-Capabilities, https://huggingface.co/AgentFramework/Unified_Farmework.