A B757-200's right hydraulic system lost fluid enroute. The decision was made to continue to the destination after an emergency was declared.

Narrative

The flight departed and on climbout of about FL310 an EICAS appeared 'HYD FLUID RIGHT' followed by 'RSVR' and 'HYD SYS PRESS RT'; indicating a loss of the right hydraulic system. Checked the status page and found that right hydraulic fluid read 0.03 and decreasing to 0.00. First Officer went into the flight manual and we accomplished the loss of fluid checklist followed by the loss of hydraulic system right checklist. Logged what systems were affected and what would not work for the landing. Checked weather at our destination and it was good; checked landing data and all was good as well. Called Dispatch and tried to get Maintenance on the line but they were busy. Decided that we would continue. Declared an emergency with ATC and also transmitted this with Dispatch; this was done so that if any other unusual things happened on arrival or landing we would have the folks on the ground ready to give us assistance. The A Flight Attendant was called to cockpit and we discussed the nature of our problem and although we were anticipating a normal landing; we set for a cabin advisory. Passengers were briefed as well. Rest of flight was normal and all proceeded normal on approach; landing and taxi to the gate. Spoke with the emergency crews and they found no problems with the aircraft so they were dismissed. The First Officer did a post walk around and also found all ok.