Observed global mean surface temperature (GMST) combines a forced response with internal variability, and quantifying internal variability is important in assessing the reaching of key thresholds, such as the 1.5 °C warming threshold in the Paris Agreement. This paper uses observational data to estimate internal variability. Since the current period of warming began in the 1970s, the 10-year mean of GMST has been very close to the 30-year mean for the period it is centred in and can therefore be considered as a robust indicator of the recent state of the climate. The range between the 5^th and 95^th percentile of annual residuals of observed GMST is 0.319 °C, substantially less than the corresponding range in large model ensembles, implying that the first individual year above 1.5 °C may occur later than indicated by climate models. The largest annual residuals are mostly associated with large-amplitude El Niño-Southern Oscillation (ENSO) events or major volcanic eruptions, with the relationship between cool years and La Niña more consistent than that between warm years and El Niño. The relationship between multi-year GMST means for differing periods indicates that the probability that the 1.5 °C threshold has been crossed (using the IPCC definition of the midpoint of the first 20-year period above the threshold) exceeds 50% once the most recent observed 11-year mean reaches 1.43 °C.