Information about glacier volume and ice thickness distribution is essential for many glaciological applications, but direct measurements of ice thickness can be difficult and costly. We present a new method that calculates ice thickness via an estimate of ice flux. We solve the familiar continuity equation between adjacent flowlines, which decreases the computational time required compared to a solution on the whole grid. We test the method on Columbia Glacier, a large tidewater glacier in Alaska, USA, and compare calculated and measured ice thicknesses, with favorable results. This shows the potential of this method for estimating ice thickness distribution of glaciers for which only surface data are available. We find that both the mean thickness and volume of Columbia Glacier were approximately halved over the period 1957–2007, from 281m to 143 m, and from 294 km3 to 134 km3, respectively. Using bedrock slope and considering how waves of thickness change propagate through the glacier, we conduct a brief analysis of the instability of Columbia Glacier, which leads us to conclude that the rapid portion of the retreat may be nearing an end.