On a radiograph you need the right film and enough time upright; on CT you need a lung window, and that is where small volumes live.

Free gas rises. On an ERECT film it collects under the diaphragm; on a LEFT LATERAL DECUBITUS it collects over the liver, away from the gastric bubble.
The patient must be upright or decubitus for AT LEAST 5–10 minutes for gas to migrate. A film taken immediately after sitting up can be falsely negative — this is the commonest technical cause of a missed perforation.
A supine film is the worst study for free gas, and most ward films are supine. Know the supine signs, because that may be all you get.
On CT, free gas is obvious on a LUNG WINDOW and easy to miss on a soft-tissue window. Always re-window.

RADIOGRAPH: erect chest (not abdomen) is the most sensitive film — it includes both hemidiaphragms with the patient upright. If the patient cannot sit, do a LEFT lateral decubitus, left side down, after 10 minutes.
CT: any phase will show gas. Review the whole abdomen on a LUNG WINDOW deliberately as a separate pass.
On CT, look at the non-dependent surfaces with the patient supine: anterior to the liver, and in the anterior abdominal wall recesses.

On an erect film, look for a lucent crescent beneath either hemidiaphragm, with a visible thin diaphragm above it.
Distinguish it from Chilaiditi interposition of colon — look for haustra inside the lucency.
On a supine film, know the indirect signs: Rigler sign (both sides of the bowel wall visible), the football sign, the falciform ligament sign, triangular gas in the recesses, the doubled-wall appearance.
On CT, do a dedicated LUNG-WINDOW pass over the whole abdomen.
Locate the gas and use its distribution to suggest the source: perigastric or perihepatic gas with wall thickening suggests a peptic perforation; pericolic gas with diverticula suggests a colonic one.
Look for the wall defect itself, focal wall thickening, adjacent fat stranding and any collection.
Note whether gas is intraperitoneal, retroperitoneal or in the bowel wall — they mean different things.

Gas outside the bowel lumen, in a non-dependent position, on either an erect/decubitus radiograph or a lung-window CT.

⚠️ A supine film does not exclude free gas, and a hurriedly taken erect film may not either. State the technique and the time upright, or say the study is not adequate to exclude it.
A properly-windowed CT is a genuine exclusion.
Remember that post-operative free gas is expected and can persist for days — correlate with the date of surgery before calling a perforation.

Free intraperitoneal gas

See it on real cases