Turbine performance at extreme off-design conditions is growing in importance for properly computing turbocharged reciprocating internal combustion engines behaviour during urban driving conditions at current and future homologation cycles. In these cases, the turbine operates at very low flow rates and power outputs and at very high blade to jet speed ratios during transitory periods due to turbocharger wheel inertia and the high pulsation level of engine exhaust flow. This paper presents a physically based method that is able to extrapolate radial turbines reduced mass flow and adiabatic efficiency in blade speed ratio, turbine rotational speed and stator vanes position. The model uses a very narrow range of experimental data from turbine maps to fit the necessary coefficients. By using a special experimental turbocharger gas stand, experimental data have been obtained for extremely low turbine power outputs for the sake of model validation. Even if the data used for fitting only covers the turbine normal operation zone, the extrapolation model provides very good agreement with the experiments at very high blade speed ratio points; producing also good results when extrapolating in rotational speed and stator vanes position. (C) 2016 Elsevier Ltd. All rights reserved.