It is possible for a kidney stone to cause right abdominal pain, but right abdominal pain does not necessarily have a kidney stone.
In patients with kidney stones, there is mostly pain in the right side of the lower back, which the patient may think of as the right abdomen. The pain is usually caused by the stone moving around in the kidney. The pain mostly comes on late at night to early in the morning and the patient may toss and turn, may wake up from a deep sleep and usually lasts for several minutes or hours.
In addition to kidney stones, right abdominal pain can also be due to conditions such as appendicitis and cholecystitis and should be distinguished.