We introduce methods and software for estimating total seawater alkalinity from salinity and any combination of up to four other parameters (potential temperature, apparent oxygen utilization, total dissolved nitrate, and total silicate). The methods return estimates anywhere in the global ocean with comparable accuracy to other published alkalinity estimation techniques. The software interpolates between a predetermined grid of coefficients for linear regressions onto arbitrary latitude, longitude, and depth coordinates, and thereby avoids the estimate discontinuities many similar methods return when transitioning from one regression constant set to another. The software can also return uncertainty estimates scaled by user-provided input parameter uncertainties. The methods have been optimized for the open ocean, for which we estimate globally averaged errors of 5.8-10.4 mol kg(-1) depending on which combination of regression parameters is used. We expect these methods to be especially useful for better constraining the carbonate system from measurement platformssuch as biogeochemical Argo floatsthat are only capable of measuring one carbonate system parameter (e.g., pH). It may also provide a useful way of simulating alkalinity for Earth system models that do not resolve the tracer prognostically.