what age is elementary school

In the USA, children start school when they are five or six years old. Depending on the state, schooling is compulsory until the age of 16 or 18. Children younger than five can go to a nursery school or preschool.
At the age of five or six, the children attend elementary school (also known as grade school or grammar school), which last six years. The fist year at elementary school is called kindergarten.

Children must stay in full-time education until they reach school leaving age.
For example, if your child reaches compulsory school age on 31 March, they must start full-time education at the beginning of the next term (summer term that year).

The effects of children’s ages at entrance to first grade upon success in elementary school was examined in a cohort of urban children who entered first grade in 1983. A set of demographic, social, and early experience variables was used as covariates in the analysis. Older children did slightly, but significantly better academically in first grade, primarily because of better performance in mathematics. There was no relationship between age of entrance and a measure of conduct in the first grade. Four years later, no effect of age at entrance to first grade upon academic performance or upon placement inside or outside the mainstream of regular education was found. Age at entrance was a far less powerful predictor than the socioeconomic variables in our covariate set.
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References:

http://www.gov.uk/schools-admissions/school-starting-age
http://www.sciencedirect.com/science/article/pii/0885200691900012
http://www.goodschoolsguide.co.uk/