We show a setup for characterising the efficiency of a single-photon-detector absolutely and with a precision better than 1%. Since the setup does not rely on calibrated devices and can be implemented with standard-optic components, it can be realised in any laboratory. Our approach is based on an Erbium-Doped-Fiber-Amplifier (EDFA) radiometer as a primary measurement standard for optical power, and on an ultra-stable source of spontaneous emission. As a proof of principle, we characterise the efficiency of an InGaAs/InP single-photon detector. We verified the correctness of the characterisation with independent measurements. In particular, the measurement of the optical power made with the EDFA radiometer has been compared to that of the Federal Institute of Metrology using a transfer power meter. Our approach is suitable for frequent characterisations of high-efficient single-photon detectors.