In calculating the total solar energy input into a salt gradient solar pond, the current method is insufficient mainly caused by two problems. Firstly, the existing equations of solar pond energy analysis can be only used for momentary calculations but it is very time-consuming for long time periods. Secondly, the shading effect inside the pond affects significantly the energy storage performance of the pond, especially in small ones. To solve the first problem, the mean values of variable parameters during the concerned time period is proposed in this work and the 'first mean value theorem for definite integrals' is used to derive the average values. For the second problem, a rectangular pond with vertical walls is investigated as an example, and the exact sunny areas in different depths of the pond are calculated at different time conditions. The experimental data of a published study is used for the validation. The energy efficiency of the low convective zone of the experimental pond is calculated theoretically, which shows a good agreement with the experimental value. The experimental data and theoretical results for the energy efficiency are 9.68% and 11.38% for January, 17.54% and 18.92% for May, and 28.11% and 30.94% for August, respectively. The modified equations can be used to predict a pond performance before its construction. (C) 2017 Elsevier Ltd. All rights reserved.