Large spectroscopic surveys of the Milky Way need to be calibrated against a sample of benchmark stars to ensure the reliable determination of atmospheric parameters. Here we present new fundamental stellar parameters of seven giant and subgiant stars that will serve as benchmark stars for large surveys. The aim is to reach a precision of 1% in the effective temperature. This precision is essential for accurate determinations of the full set of fundamental parameters and abundances of stars observed by the stellar surveys. We observed HD121370 (eta Boo), HD161797 (mu Her), HD175955, HD182736, HD185351, HD188512 (beta Aql), and HD189349 using the high angular resolution optical interferometric instrument PAVO at the CHARA Array. The limb-darkening corrections were determined from 3D model atmospheres based on the STAGGER grid. The Teff were determined directly from the Stefan-Boltzmann relation, with an iterative procedure to interpolate over tables of bolometric corrections. We estimated surface gravities from comparisons to Dartmouth stellar evolution model tracks. The spectroscopic observations were collected from the ELODIE and FIES spectrographs. We estimated metallicities ([Fe/H]) from a 1D non-local thermodynamic equilibrium (NLTE) abundance analysis of unblended lines of neutral and singly ionised iron. For six of the seven stars we measure Teff to better than 1%. For one star, HD189349, the uncertainty in Teff is 2% due to an uncertain bolometric flux. We do not recommend this star as a benchmark until this measurement can be improved. Median uncertainties for all stars in logg and [Fe/H]} are 0.034dex and 0.07dex, respectively. This study presents updated fundamental stellar parameters of seven giant and subgiant stars that can be used as a new set of benchmarks. All the fundamental stellar parameters were based on consistently combining interferometric observations, 3D limb-darkening modelling and spectroscopic analysis. This paper in this series follows our previous papers including dwarf stars and stars in the metal-poor range.