No, effect size cannot be determined from the p-value. They are different.
There are different effect size statistics for different types of analyses. For example, for a t-test, Cohen's d is often used. For a 2 x 2 chi-square analysis, phi is often used.
The method you are using to calculate the sample size should tell you what effect size statistic it expects.
Assuming a simple situation (e.g., comparing two independent groups), for effect size, p value, and sample sizes, if you know two of the three, you can calculate the third. For example, if you know the sample sizes for two groups and the p-value from the independent t-test comparing the two groups, you can calculate the effect size. See the attached screenshot from Comprehensive Meta-Analysis software. I was too lazy to do it by hand.
While there are ways to estimate the effect size from a p-value, it's easier and more precise to calculate effect size from raw data. If you're reading an article and estimating effect size, try the link below. Effect sizes are generally measured in three broad ways: (1) an odd-ratio is common for very small incidences often in epidemiological studies (which is how Dongshan is thinking), (2) a ratio of the difference between groups to the variation within those groups (Cohen's d that Salvatore mentions is the most common example) and (3) the percent of variance accounted for in one variable by another (Phi is common for chi square, but r-squared is probably the most common example - literally the correlation squared). P-value and effect size are related in the sense that the bigger the effect size the fewer participants you would need to find statistical significance. For your effect size estimate, work backward. For example, with N and a p-value for a correlation you could figure out r, then square it for r-squared. Similarly, with a p value and N, you could work backward for the t-ratio in a comparison between groups (possibly needing to assume the groups were equal size). Then from the t-ratio you can estimate Cohen's d (see link below). Hope this helps some, Heba. ~ Kevin
Will Thalheimer & Samantha Cook "How to Calculate Effect Size from Published Research"
http://www.bwgriffin.com/gsu/courses/edur9131/content/Effect_Sizes_pdf5.pdf
Do you mean calculate the sample size of data from a study, and for one hypothesis you know the p value? If this is all you know, then no, you can't. If you are trying to plan a study and want to know what sample size to have, that is a very different question.
The effect size is measured and expressed using different scales. The most important and sometimes most effective scale of the effect size is the difference mean that is not always effective. But the standardization of the size of the effect, using its expression on the standard deviation unit, is a method introduced by Cohen and seems to be an effective method. This scale, known as d Cohen, tells us how much the average difference depends on the distribution of the scores and proposes a special classification to determine the size of the effect; so that the effect size is 0.2 It has a small amount, 0.5 average and 0.8 has been defined a lot.
The effect size, the size of the sample, the level of the significant crisis (ά), and the ability to assume the statistical test are interrelated and, by determining one of them, the rest are somewhat determined.
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