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One square foot is 144 square inches, so if you cover that with an inch of water you'll need 144 cubic inches. One gallon is 231 cubic inches. Dividing 231 by 144 = 0.62 gallons. So a plant growing in about 1 square foot of soil needs a bit more than half a gallon of water a week to equal 1 inch. A 4 ft x 8 ft bed = 32 sq. ft. so at 0.62 gal/sq.ft. you'd want to give it about 20 gallons of water a week.

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Q: If a plant needs 1 inch of water per week how many gallons is needed?
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