A Tandetron accelerator mass spectrometer (AMS) was used to measure natural-level carbon-14 in geological and archaeological samples. The carbon-14/carbon-13 ratio of a modern sample is routinely measured (with a precision of ± 1%) using a carbon-silver target containing only 2-5 milligrams of carbon, in a measurement lasting 5 hours. The error for older samples becomes larger owing to the smaller counts of carbon-14. The accuracy of a single carbon-14/carbon-13 measurement was estimated as ± 1.3%. The carbon-14 background of the Tandetron AMS was estimated by using natural graphite samples, with an age > 1 X 10⁸ year, after treating the sample with 1.2 N HCl, and further heating it in vacuum at 800°. The apparent age of natural graphite was measured at 60, 000 years. Age measurements were performed on small fragments of fossil shells found at 17 different horizons of a 40-meter-long core of Holocene sediment. The sediment was clearly divided into 5 different horizons according to the sedimentation rates calculated using the carbon-14 ages. -- AATA