There is enough power in Earth’s winds to be a primary source of near-zero-emission electric power as the global economy continues to grow through the twenty-first century. Historically, wind turbines are placed on Earth’s surface, but high-altitude winds are usually steadier and faster than near-surface winds, resulting in higher average power densities1. Here, we use a climate model to estimate the amount of power that can be extracted from both surface and high-altitude winds, considering only geophysical limits. We find wind turbines placed on Earth’s surface could extract kinetic energy at a rate of at least 400 TW, whereas high-altitude wind power could extract more than 1,800 TW. At these high rates of extraction, there are pronounced climatic consequences. However, we find that at the level of present global primary power demand (~ 18 TW; ref. 2), uniformly distributed wind turbines are unlikely to substantially affect the Earth’s climate. It is likely that wind power growth will be limited by economic or environmental factors, not global geophysical limits.