We have applied the relation for the mean of the expected values of the maximum excursion in a bounded random walk to estimate the random walk length from time series of eight independent global mean quantities (temperature maximum, summer lag, temperature minimum and winter lag in land and over the ocean) derived from the NOAA-CIRES twentieth century reanalysis (V2) for 1871–2008 and the ECHAM5 IPCC AR4 twentieth century run for 1860–2100, and also the Millenium 3100 yr control run mil01, which was segmented into records of specified period. The results for NOAA-CIRES, ECHAM5, and mil01 (mean of thirty 100 yr segments) are very similar and indicate a random walk length on land of 24 yr and over the ocean of 20 yr. Using three 1000 yr segments from mil01, the random walk lengths increased to 37 yr on land and 33 yr over the ocean. This result indicates that the shorter records may not totally capture the random variability of climate relevant on the time scale of civilizations, for which the random walk length is likely to be about 30 years. For this random walk length, the observed standard deviations of maximum temperature and minimum temperature yield respective expected maximum excursions on land of 1.4 and 2.3°C and over the ocean of 0.5 and 0.7°C, which are substantial fractions of the global warming signal.