Measure your futon. Measure from side seam to side seam to get the width, and from the top seam to the bottom seam to get the length. If using an envelop opening, add 12 inches to the front of the futon cover, and subtract 4 inches from the back measurement.
One sheet may be large enough to cover the futon; if not, use two and seam them together. Launder the sheets before cutting in case they shrink.
Add seam allowances to the measurements of the futon. Seam allowances should be 1 inch on all sides.
Cut the sheet to the desired size, and pin with right sides together. Fold the top section over to meet the back to fashion an envelop opening. Leave the top and the bottom hems on the sheet for the hoop and loop opening. Sew on three sides. Turn right sides out and turn the cover. Slip it on the futon to make sure it doesn't need to be tighter.
Turn the cover with right sides together to miter the corners. Sew a 3-inch seam perpendicular to the side and bottom seams.
Turn and sew the hoop and loop to the opening to close the envelop opening.
Slip the futon mattress into the cover. Close the hook and loop tape, and replace the futon mattress on the frame.