New estimates of the solar cycle length are calculated from an up-to-date monthly sunspot record using a novel but mathematically rigorous method involving multiple regression, Fourier approximation, and analytical expressions for the first derivative based on calculus techniques. The sensitivity of the estimates to smoothing are examined and the analysis is used to identify possible systematic changes in the sun. The solar cycle length analysis indicates a pronounced change in the sun around 1900, before which the estimates fluctuate strongly and after which the estimates show little variability. There have been speculations about an association between the solar cycle length and Earth's climate, however, the solar cycle length analysis does not follow Earth's global mean surface temperature. A further comparison with the monthly sunspot number, cosmic galactic rays and 10.7 cm absolute radio flux since 1950 gives no indication of a systematic trend in the level of solar activity that can explain the most recent global warming.