Based on a numerical method to analyse the full-range behaviour of prestressed concrete beams with unbonded tendons, parametric studies are carried out to investigate the influence of 11 parameters on the curvature ductility of unbonded prestressed concrete (UPC) beams. It is found that, among various parameters studied, the depth to prestressing tendons, depth to non-prestressed tension steel, partial prestressing ratio, yield strength of non-prestressed tension steel and concrete compressive strength have substantial effects on the curvature ductility. Although the curvature ductility of UPC beams is affected by a large number of factors, rather simple equations can be formulated for reasonably accurate estimation of curvature ductility. Conversion factors are introduced to cope with the difference in partial safety factors, shapes of equivalent stress blocks and the equations to predict the ultimate tendon stress in BS8110, EC2 and ACI318. The same equations can also be used to provide conservative estimates of ductility of UPC beams with compression steel.