We have combined deep photometry in the B, V and I bands from CTIO/MOSAIC of the Sculptor dwarf spheroidal galaxy, going down to the oldest main sequence turn-offs, with spectroscopic metallicity distributions of red giant branch stars. This allows us to obtain the most detailed and complete star formation history to date, as well as an accurate timescale for chemical enrichment. The star formation history shows that Sculptor is dominated by old (>10 Gyr), metal-poor stars, but that younger, more metal-rich populations are also present. Using star formation histories determined at different radii from the centre we show that Sculptor formed stars with an increasing central concentration with time. The old, metal-poor populations are present at all radii, while more metal-rich, younger stars are more centrally concentrated. We find that within an elliptical radius of 1 degree, or 1.5 kpc from the centre, a total mass in stars of 7.8 × 10^6 M