A systematic programme of calibration observations was carried out to monitor the performance of the Spectral and Photometric Imaging REceiver (SPIRE) Fourier Transform Spectrometer (FTS) instrument on board the Herschel Space Observatory. Observations of planets (including the prime point-source calibrator, Uranus), asteroids, line sources, dark sky and cross-calibration sources were made in order to monitor repeatability and sensitivity, and to improve FTS calibration. We present a complete analysis of the full set of calibration observations and use them to assess the performance of the FTS. Particular care is taken to understand and separate out the effect of pointing uncertainties, including the position of the internal beam steering mirror for sparse observations in the early part of the mission. The repeatability of spectral-line centre positions is <5 km s−1, for lines with signal-to-noise ratios >40, corresponding to <0.5–2.0 per cent of a resolution element. For spectral-line flux, the repeatability is better than 6 per cent, which improves to 1–2 per cent for spectra corrected for pointing offsets. The continuum repeatability is 4.4 per cent for the SPIRE Long Wavelength spectrometer (SLW) band and 13.6 per cent for the SPIRE Short Wavelength spectrometer (SSW) band, which reduces to ∼1 per cent once the data have been corrected for pointing offsets. Observations of dark sky were used to assess the sensitivity and the systematic offset in the continuum, both of which were found to be consistent across the FTS-detector arrays. The average point-source calibrated sensitivity for the centre detectors is 0.20 and 0.21 Jy 1σ; 1 h, for SLW and SSW. The average continuum offset is 0.40 Jy for the SLW band and 0.28 Jy for the SSW band.