Formula to calculate the isotropic range of a signal
The FCC calculates the field strength from an AM station as follows:
E (dBu) = 107 + ERP (dBk) - 20*log10(d/km)
wherein

E is the field strength at distance d from the transmitter. Recall that E has unit unit V/m, (not Watt) and &quot;dBu&quot; means db-micro-volt-per-meter
ERP is the radiated power in dB relative to 1 kW
d is the distance in km

A field strength of 60dBu is considered easily received by consumer grade AM receivers. This includes the quality of the electronics (noise etc..) and the gain of the built-in antenna. If you have higher or lower expectations you can scale the numbers accordingly.
Here are some worked-out examples for a few transmitters, based on the above equation:

The minimum ERP for FCC allowance (in general) is 250W, which yields a field strength of 10mV/m at 10km.
There's a line for 10W, and (about) 60dBu is attained at maximum 32km. AM waves don't just travel in free-space but interact with the earth's soil and -at night- with the ionosphere. During the day, AM propagates in greatest part by ground waves that depend on the soil/earth conductivity.

Image from: https://flexbooks.ck12.org/cbook/ck-12-middle-school-physical-science-flexbook-2.0/section/18.5/primary/lesson/radio-waves-ms-ps
Dry land performs much worse than the ocean's salt water, and propagation data under these circumstance is available from the FCC.

(Original available from https://www.fcc.gov/media/radio/am-groundwave-field-strength-graphs )
And here's a zoom into the region of interest:

The straight but slanted line is for ideal propagation in free space, reporting the field strength for 250W ERP. The curve closest to it, marked &quot;5000&quot; refers to propagation over salt water. The other curves represent ever decreasing earth conductivity.
In the table above I cited a few of these charted conductivity cases for the 250W ERP case: a 250W ERP delivers 40.9dBu at 1000km in free space. Over salt water the range is reduced to 650km (65%), and over dry land it's 45km (4.5%).
For 10W transmission at 580kHz expect the same discount. As a baseline take 56.8dBu (60dBu rounded), and 32km, and after applying the discount you get somewhere between 20km and 1.4km during day time.
Once the locale of the transmitter is known, the actual receive strength can be measured by &quot;driving the signal&quot; (drive &amp; measure) or modelling it. The Longley-Rice model considers the terrain along the propagation path and considers atmospheric properties, free-space, localized ground cover and receive antenna characteristics.
Here's an example for an FM station (so much less reach), with a contour at 60dBu: