Single photon detectors are important for a wide range of applications each with their own specific requirements, which makes necessary the precise characterization of detectors. Here, we present a simple and accurate methodology of characterizing dark count rate, detection efficiency, and after-pulsing in single photon detectors purely based on their counting statistics. We demonstrate our new method on a custom-made, free-running single photon detector based on an InGaAs based avalanche photo diode (APD), though the methodology presented here is applicable for any type of single photon detector.