According to an article on GLREA (great lakes renewable energy association) one solar panels measuring one square meter produce about 150 watts of power. So, to produce 2.5kWatts or 2,500watts of power you would need (2,500 watts)(1sq meter panel/150 watts) = 16.67 sq meters of solar panels.
Of course different things will affect the efficiency of solar energy conversion, but in optimal sunlight that it should take about 16 and 2/3 square meters of solar panels, or about 179 square feet.
The answer to this question depends on a lot of factors: the time of year, the latitude of the location of the panels, the weather, how efficient the solar cells are, the size of the panels, the placement of the panels in relation to the sun, etc.
For the sake of argument, we’ll say that in optimum conditions, a solar cell one square inch in area has a power capacity of 50 milliwatts (5 x 10^-2 watts = .05 W). 2.5 kilowatts equals 2.5 x 10^3 watts, or 2500 W. That means that you would need 2500W/.05W to get the number of solar cells required, or
50,000 square-inch solar cells. Approximately 347 square feet of solar panels.
That would be sixteen solar panels, if you could find them at a size of 5 ft x 4.4 ft.
Keep in mind though that the output of a solar array will vary throughout the day, and it is better to measure the KWh (how much power every hour) required by your house before deciding on the number of panels you will need.
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