Serverless computing is a cloud computing paradigm that allows developers to focus exclusively on business logic as cloud service providers manage resource management tasks. Serverless applications follow this model, where the application is decomposed into a set of fine-grained Function-as-a-Service (FaaS) functions. However, the obscurities of the underlying system infrastructure and dependencies between FaaS functions within the application pose a challenge for estimating the performance of FaaS functions. To characterize the performance of a FaaS function that is relevant for the user, we define Function Capacity (FC) as the maximal number of concurrent invocations the function can serve in a time without violating the Service-Level Objective (SLO). The paper addresses the challenge of quantifying the FC individually for each FaaS function within a serverless application. This challenge is addressed by sandboxing a FaaS function and building its performance model. To this end, we develop FnCapacitor - an end-to-end automated Function Capacity estimation tool. We demonstrate the functioning of our tool on Google Cloud Functions (GCF) and AWS Lambda. FnCapacitor estimates the FCs on different deployment configurations (allocated memory & maximum function instances) by conducting time-framed load tests and building various models using statistical: linear, ridge, and polynomial regression, and Deep Neural Network (DNN) methods on the acquired performance data. Our evaluation of different FaaS functions shows relatively accurate predictions, with an accuracy greater than 75% using DNN for both cloud providers.