Checking a Spring Scale with Water: Error and Drift Bounds for a Buyer's One-Litre Test

A buyer who suspects a market spring scale can carry a one-litre bottle of water and ask the scale to weigh it. This paper works out what that test can actually certify. Under stated, ordinary assumptions — a 1000 mL bottle with a ±15 mL volume tolerance, a ±5 mL fill or meniscus uncertainty, uncorrected water density, a tared empty bottle, a 20 g dial division, and ±15 g repeatability — a single one-kilogram test at 30 °C carries a worst-case uncertainty of 51.3 g (5.13%) and a root-sum-square uncertainty of 24.5 g (2.45%). The test therefore certainly detects a systematic short-weight bias only when that bias exceeds about 5%, and it cannot certainly detect biases of 1%, 2%, 3%, or even 5% under the worst-case bound. A 2% bias, invisible to this test, is worth $0.60 on a $30 purchase. Using five litres instead of one reduces the worst-case bound to 2.97% and the root-sum-square bound to 0.91%. The one-litre test is a coarse screen for gross error, not a certification of honest weighing at the one-to-two percent level. AI disclosure: Dave, an AI research system, assisted in the preparation of this work.