Turn a kitchen-scale reading into a practical brewing volume, then scale a recipe without treating the vessel's advertised capacity as your pour size.
Decide which capacity you need
A bowl can hold one amount when filled to its rim and a different amount when prepared for comfortable pouring. A recipe needs the latter. Before measuring, decide where you intend to stop filling: below the rim, with room for the lid and your normal grip. Do this with room-temperature water first. There is no reason to handle hot water while finding a repeatable fill level.
Record both numbers if useful, but name them clearly. 'Rim capacity: 150 ml; working fill: about 130 ml' tells you more than a single unexplained capacity. The numbers here are illustrative; measure your own vessel rather than assuming every advertised 150 ml gaiwan has this working fill.
Use water mass as a kitchen approximation
Set a dry, empty bowl on a level electronic scale and press tare. Add room-temperature water to the chosen line. The reading in grams gives an approximate volume in millilitres: estimated water volume (ml) ≈ water mass (g). Water density is close to 1 g/ml at room temperature, but it is not exactly 1 and changes with temperature. This is a practical brewing estimate, not a calibrated laboratory volume measurement.
If your scale cannot be tared, subtract the empty reading from the filled reading. An empty bowl at 182 g and a filled bowl at 312 g contain approximately 130 ml of water: 312 − 182 = 130 g. Keep the saucer and lid consistently included or excluded between readings.
Check repeatability before adding decimal places
Empty and dry the bowl, then repeat the fill three times. Suppose the readings are 129 g, 131 g and 130 g. Their mean is (129 + 131 + 130) ÷ 3 = 130 g. Calling this 'about 130 ml' is more honest than claiming 130.00 ml. A moving fill line, spilled droplets and a scale displaying only whole grams all limit the result.
Do not put a hot vessel directly onto a scale unless its manufacturer permits it. Use the same room-temperature method for later checks. A different water temperature and a different measuring method can introduce a difference that looks like a change in your vessel.
Scale the leaf, keeping the recipe identifiable
For an example recipe using 5 g of leaf per 100 ml of water, the scaled dose is 5 × 130 ÷ 100 = 6.5 g. The general formula is new leaf mass = original leaf mass × new water volume ÷ original water volume. Write the original ratio beside the calculation so you can reproduce it later.
The linked Dragon Well listing supplies a 5 g / 100 ml gongfu starting point for that particular tea. It is not a universal instruction for all tea. Scaling the ratio alone also does not determine temperature or infusion time; choose those separately from the relevant product directions.
Separate empty-bowl capacity from water added to leaf
Dry and wet leaves occupy space, so filling a bowl containing leaf to the same line will not necessarily add the empty-bowl water volume. For closer comparisons, weigh the actual water added with leaf present, using suitable equipment and a heat-safe setup. Otherwise, keep the fill line and dose consistent and label the volume as an estimate. Leave the measurement in your notebook: it is a useful explanation when the same recipe tastes different in another vessel.