How long is a piece of string?

Armies varied in their relative artillery strengths during the Napoleonic Wars. While the money cost of raising and sustaining an infantry battalion/cavalry squadron/artillery battery was roughly equivalent, the three arms do stress different resources differently. Infantry is very manpower intensive, while cavalry requires greater equine resources; artillery depends most of all on finance. Artillery is an arm for rich powers, especially when their human resources are limited or they can't rely on a national militia.

Sources often discuss less the total strength of artillery, and more the ratio of artillery and infantry, usually expressed in the number of guns per 1,000 men. For example, Napoleon's Grande Armee in 1805 came to include about 200,000 men and 400 guns, so 2 guns per 1,000 men. At the Battle of Austerlitz, the Allies had more than 3 guns per 1,000 men; with a total strength of about 85,000, their artillery park was 278, of which more than half fell into French hands.

Continued losses, declining infantry quality, and the limits of conscription drove Napoleon to increase the ratio of artillery over the course of his campaigns; while manpower became ever more difficult to extract, he still had no shortage of money. In 1809, Napoleon fought the Battle of Wagram with 172,000 men and as many as 600 guns if one includes those sited on the Danube islands, pushing the ratio beyond 3:1,000 . During the course of a campaign, men are usually lost faster than guns; it's very difficult for cannon to desert, after all. As such, Napoleon began his invasion of Russia with roughly two guns per thousand men (nearly 1400 guns for almost 700,000 men), but fought the battle of Borodino with more than four (roughly 600 guns for <150,000 men). By the end of the campaign, the Russian army straggled over the Polish border with ~65,000 men, they were still dragging as many as 439 guns, nearly seven guns per thousand men.

Nevertheless, the typical ratio remained 3-4 per thousand for the later Napoleonic Wars; as armies swelled to hundreds of thousands, several battles featured over a thousand guns roaring. However, in terms of ratios, Napoleonic armies rarely matched those of the later Seven Years War. Similar to Napoleon, Frederick the Great had to compensate for declining infantry strength, thus increasingly relying on his heavy guns for firepower. At the battle of Torgau, for instance, both armies had about five guns for every thousand men, each having roughly 50,000 men.