A geode is a hollow, roughly round rock that holds mineral matter, sometimes crystals. A round stone that is solid all the way through is a nodule, not a geode. That difference is the whole question, and a photo cannot settle it. For a suggestion about a rock or mineral from a photo, there is LithoCanvas, an Android app by Senorit.
How a geode forms
A cavity comes first. It can be a gas bubble in volcanic rock or a rounded hollow in sedimentary rock. After the surrounding rock hardens, groundwater or hot fluids carry dissolved minerals into the hollow and coat its walls. Over a long time crystals can grow inward. When the rock around a geode weathers away, the harder geode is left on the surface, which is why people find them loose.
Signs to look at
The one sign sources agree on is shape: roughly round. Many ordinary stones are round too, so shape only tells you to look closer. We have no sourced guide for tests such as weight or tapping, so we leave them out rather than guess. A rock club, a museum or a dealer can examine a stone in person.
What may be inside
Quartz, which can be clear, white or purple (amethyst), calcite or celestite. Some geodes hold banded agate or chalcedony. Trace elements give the colours, for example iron oxide for reds and yellows and titanium for blues. Very bright blue or pink usually means a geode was dyed.
Where people find them
Many commercial geodes come from Brazil, Uruguay, Namibia and Mexico. In the US, finds are reported in Indiana, Iowa, Missouri, western Illinois, Kentucky and Utah. In the Mendip Hills in England they are called potato stones.
Opening one
We have no sourced guide to opening a geode, so we do not give one. A local rock club or a dealer can show you how, and can tell you what is worth opening.
What it is worth
We do not value stones, and LithoCanvas gives no price either. A museum or a dealer can.
Check what you have
Use the checks in what type of rock is this, and see how a hole forms in a hag stone if your stone has a hole instead of a cavity. LithoCanvas is an Android app by Senorit that suggests what a rock or mineral is from a photo. It shows hardness and crystal system, and the result is a suggestion. The Mohs page on lithocanvas.de explains hardness. Your photo goes to Google Gemini only if you agree.
Questions and answers
How can you tell if a rock is a geode?
A geode is hollow. Shape is only a first hint, and a stone that is solid inside is a nodule.
What is inside a geode?
Often quartz, calcite or celestite, and sometimes banded agate.
Where do you find geodes?
Commercially in Brazil, Uruguay, Namibia and Mexico, and in several US states.