Smoothed particle hydrodynamics (SPH) is a grid-free numerical method that relies on a Lagrangian description of the fluid. It has been used in a variety of multiphysics applications, including applications to free surface flow problems where surface tension plays a pivotal role. Accurate simulations of surface tension are crucial for a realistic description of multiphase flows and small-scale fluid systems, such as drops and bubbles. This article describes a novel approach based on a pair potential force within the SPH framework that simulates surface tension in a physically consistent manner. The Young-Laplace equation is used to calibrate the force term associated with the cohesive action so that there is a close correspondence between the calculated surface tension and the minimization of the surface area. The performance of the model has been assessed against a number of benchmark tests, including the spherization of cubic drops, the spreading of a drop impacting on a solid surface, and the drop oscillation in a gas environment. A comparison of experimentally obtained pendant drop images with the simulation results for distilled water, ethylene glycol and ethanol drops is also provided as a further validation test. The proposed approach has been shown to be accurate enough to simulate surface tension effects in liquid drops under a variety of dynamical conditions irrespective of the length scale, implying that it is particularly suitable for simulating microfluidic systems.