Vibration from equipment mounted on the telescope and in summit support buildings has been a source of performance degradation at existing astronomical observatories, particularly for adaptive optics performance. Rather than relying only on best practices to minimize vibration, we present here a vibration budget that specifies allowable force levels from each source of vibration in the observatory (e.g., pumps, chillers, cryocoolers, etc.). This design tool helps ensure that the total optical performance degradation due to vibration is less than the corresponding error budget allocation and is also useful in design trade-offs, specifying isolation requirements for equipment, and tightening or widening individual equipment vibration specifications as necessary. The vibration budget relies on model-based analysis of the optical consequences that result from forces applied at different locations and frequencies, including both image jitter and primary mirror segment motion. We develop this tool here for the Thirty Meter Telescope but hope that this approach will be broadly useful to other observatories, not only in the design phase, but for verification and operations as well.