Large-area sky surveys show that massive galaxies undergo at least one major merger in a Hubble time .
Ongoing pulsar timing array ( PTA ) experiments are aimed at measuring the gravitational wave ( GW ) emission from binary supermassive black holes ( SMBHs ) at the centres of galaxy merger remnants .
In this paper , using the latest observational estimates for a range of galaxy properties and scaling relations , we predict the amplitude of the GW background generated by the binary SMBH population .
We also predict the numbers of individual binary SMBH GW sources .
We predict the characteristic strain amplitude of the GW background to lie in the range 5.1 \times 10 ^ { -16 } < A _ { yr } < 2.4 \times 10 ^ { -15 } at a frequency of ( 1 { yr } ) ^ { -1 } , with 95 % confidence .
Higher values within this range , which correspond to the more commonly preferred choice of galaxy merger timescale , will fall within the expected sensitivity ranges of existing PTA projects in the next few years .
In contrast , we find that a PTA consisting of at least 100 pulsars observed with next-generation radio telescopes will be required to detect continuous-wave GWs from binary SMBHs .
We further suggest that GW memory bursts from coalescing SMBH pairs are not viable sources for PTAs .
Both the GW background and individual GW source counts are dominated by binaries formed in mergers between early-type galaxies of masses \gtrsim 5 \times 10 ^ { 10 } M _ { \odot } at redshifts \lesssim 1.5 .
Uncertainties in the galaxy merger timescale and the SMBH mass - galaxy bulge mass relation dominate the uncertainty in our predictions .