Unidimensional measurements for estimating bill size, like length and width, are commonly used in ecology and evolution, but can be criticised due to issues with repeatability and accuracy. Furthermore, formula‐based estimates of bill surface area tend to assume uniform bill shapes across species, which is rarely the case. 3D surface scanning can potentially help overcome some such issues by collecting detailed external morphology and direct measurements of surface area, rather than composite estimates of size. Here, we evaluate the use of 3D surface scanners on avian museum specimens to test the repeatability of 3D‐based measurements and compare these to traditional formula‐based methods of estimating bill size from unidimensional measurements. Using 28 Australian bird species, we investigate inter‐observer repeatability of surface area measurements from 3D surface scans. We then compare 3D‐based size estimates to formula‐based size estimates to infer the accuracy and precision of formula‐based measurements of bill surface area. We find that morphometric measurements from 3D surface scans are highly repeatable between observers, without the need for extensive training, demonstrating an advantage over unidimensional measuring methods, like callipers. When comparing 3D‐based measurements to formula‐based estimates of bill surface area, most formulae for estimating size consistently underestimate surface area, and with considerable variation between species. Where 3D scanning is not possible, we find that a commonly used cone formula for estimating bill size is most precise across diverse bill shapes, therefore supporting its use in interspecific contexts. However, we find that incorporating an additional unidimensional measure of bill curvature into formulae improves the accuracy of the calculated area. Our results reveal the high potential for 3D surface scanners in avian morphometric research, especially for studies necessitating large sample sizes collected by multiple observers, and gives suggestions for formula‐based approaches to estimate bill size.