There are a lot of variables involved. I typically see direct-buried feeds, table 310-16 with 75 degree connections for up to 100 feet, which would be #3AWG. What is the voltage reading at the source? What is the power for? Do you need the voltage drop equation E(vd) = R(ohms) x I(amps)? NEC does not require that we limit voltage drop on conductors, but the Code does suggest that we consider its effects.
NEC 310.15(B)(6) will tell you that you need a certain minimum size of wire for a 100A service: 4ga copper or 2ga aluminium.
But the NEC won't tell you what to do in order to prevent voltage drop. Voltage drop is a design issue; you need to figure out what sort of voltage drop you can tolerate, what loads will be causing voltage drop, and what other system elements will be causing voltage drop.
1) What are your voltage drop constraints; do you have extremely sensitive loads that cannot tolerate much change in supply voltage, eg. esoteric electronics, normal loads that can tolerate some drop (eg. normal incandescent lamps), or do you have extremely tolerant loads (heaters, electronically regulated lamps, etc) A common rule of thumb is to have no more than a 5% voltage drop from supply to final load, including both the service conductors, any feeders, and the branch circuit conductors.
2) What are the loads; are they steady or highly variable. Are there any 'inrush' or 'starting surges'? If there are any large motors, eg for heat pumps, then they can draw quite a bit of current during starting, which will cause an extreme voltage drop for the few moments that the motor is starting. This sort of load might cause unacceptable lamp flicker on a long service.
3) The service conductors are not the only issue; you can have 'voltage drop' (actually impedance) at the transformer, such that the supply voltage changes considerably with load current.
Chapter 9 table 8 will help you with conductor properties, which you can use to calculate voltage drop. There are also voltage drop calculators around the web.
I think that you need to revisit your assumptions and your calculation methods.
1) It is very common to simply assume that the current involved is the 'rating' of the circuit. eg. for a service protected by a 100A main breaker, it is very common to calculate the voltage drop at 100A. However this assumption could easily be wrong in either direction. A 100A residential service is rarely used at even close to the full 100A capacity, yet transient loads (say an AC starting) can easily exceed 100A for short periods of time. You really need to spend time figuring out what sort of loads will be running, and how they will be perceived.
2) Even assuming 100A, I believe that your math is in error.
The supply voltage is 240 feet. Presume 3% allowed drop (which may or may not be appropriate; the NEC 'suggests' a 3% drop for branch circuits, and a 2% drop for feeders, but does not give any explicit rules.) giving an allowed loss in the wires of 7.2V.
Apply Ohm's law (E/I = R) to get an allowed resistance of 7.2/100 = 0.072 ohms.
You have a 250 foot run, thus 500 feet of conductor. 0.072 ohms/500 feet = 0.144 ohms/1000 feet
#1 conductors will do to meet these assumptions.
(As a side note: the table gives 0.160 ohms/1000 feet for 'coated' copper wire, or 0.154 ohms/1000 feet for bare wire. But the resistance is tabulated at 75C; when you oversize wires to accommodate voltage drop, the temperature goes down, and you can use the note at the bottom of the page to figure the reduced resistance.)
Thanks Jon; that look much more adequate (and cheap, by the way). I made the calculation with 120 volts, in which case the maximum voltage drop is 3.6 volts instead of 7.2; that accounts for the different result in wire size.
But you are right, the initial load will be one third or less of the 100 amps mentioned. I'm just covering for future growth.
A good book to own is the American Electricians' Handbook by Croft & Summers. This book is a great tool and every electrician should have one. In this book this topic is covered and has all the info needed to compute voltage drop.