The formula for the compound formed by calcium ions and chloride ions is \(CaCl_2\). This compound is known as calcium chloride, and it is an ionic compound consisting of positively charged calcium ions \(Ca^{2+}\) and negatively charged chloride ions \(Cl^-\). The formula \(CaCl_2\) indicates that for every calcium ion, there are two chloride ions in the compound, resulting in a neutral overall charge.