How is the state of charge or discharge of a lead-acid battery estimated?

The state of charge or discharge of a lead-acid battery can be estimated by measuring the relative density (or "specific gravity") of the electrolyte with a densimeter (or "hydrometer").
When the relative density has dropped to about 1.05, the battery needs to be recharged.
The electrolyte in a lead-acid battery is a 38% by weight sulfuric acid solution, which has a density of 1.29 g/ml.
When a lead-acid battery is discharged, the sulfuric acid is removed, reducing the density of the electrolyte solution.