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To extract maximum output power from a solar cell, it is essential to know the solar cell parameters such as the photo-current (Iph), the series resistance (Rse), the shunt resistance (Rsh), the reverse saturation current (I0), and the diode ideality factor (n). This paper presents new and simple methods for estimating the cell parameters. First, Rse and Rsh are estimated from the intercepts of the linear slope equations dV/dI and dI/dV at the open circuit voltage (Voc) and the short circuit current (Isc) regions, respectively. The slopes of these equations also give I0 and n, known as method-1. In method-2, using Rse and Rsh obtained by method-1, I0 and n are estimated using Newton-Raphson technique. The methods presented here are applied to the illuminated I-V characteristics of silicon solar cells, an organic solar cell, and a dye sensitized solar cell previously reported in the literatures. The studies show that method-1 is more suitable for the solar cells with 70% or above fill factor whereas method-2 is suitable for all kinds of solar cells irrespective of fill factor.