Sounds like it, that is way too low for a Radeon 7870.
You should check the CPU usage during gaming, HWINFO64 is a great tool to do so. If it's at a constant 100% while gaming, then you got yourself a bottleneck.
You could also by using a rivatuner server show usage, clocks, memory used - Everything in your PC - On screen screen while gaming.
This guide will help you through:http://www.overclock.net/t/1229915/how-to-cpu-and-gpu-usage-along-with-fps-in-game