Density is the weight of an object divided by the volume it occupies. Water has a density of one kilogram (kg) per liter (L) at 4 °C. In other words, if you had exactly 1 L of water at 4 °C and placed it on a (properly calibrated) scale, it would weigh exactly 1 kg. Expressed in English units, the density of water is roughly 8 lbs. 5.5 oz. per gallon. (In this column, I’ll mostly be using metric units and will only give conversions to English units if that knowledge is useful.)

At 4 °C, water is at its maximum density. If you heat it above this temperature, it expands slightly. Oddly enough, when you cool it below this temperature, it also expands.

When we use our hydrometers, we are measuring the density of extract in our wort or beer. (“Extract” here means dissolved solids, not malt extract — although malt extract may account for some of the total of your extract.) Homebrewers tend to express this in terms of specific gravity, which is the density of a liquid relative to pure water. Liquids that are equally as dense as water have a specific gravity of 1.

Homebrewers usually express specific gravity to three decimal places. Using that convention, the specific gravity of a liquid that was as dense as water would be 1.000. Because specific gravity is the density of a liquid relative to that of water, specific gravity has no units. In other words, the specific gravity of pure water is 1.000, not 1.000 followed by a weight and volume (such as kg/L or lbs./gallon).

Since homebrewers almost always express specific gravity to three decimal places, many simply express their gravity in “gravity points” — the value of the last three decimals. For example, ale with an original specific gravity of 1.060 can be described as having 60 “gravity points.”

### A single-point calibration

If your hydrometer is properly calibrated, it should read 1.000 when floating in pure water. Because the density of water changes with temperature, hydrometers are meant to be used at a specific temperature (either 60 °F/16 °C or 68 °F/20 °C). This temperature is almost always printed on the slip of paper inside the hydrometer. Tables that take temperature into account can be found in most beginning homebrew books.

So, to check if your hydrometer accurately measures the specific gravity of water, simply float it in pure water (distilled or reverse osmosis water) at the correct temperature. Spin the hydrometer to dislodge any bubbles that may be clinging to it and bring the test jar up to eye level.

You will see that, in the middle of the test jar, the water will be level. However, it will climb up the sides of the test jar, making the liquid surface look like a “U” or smiley face. The curved surface of a liquid in a container is called a meniscus. When reading your hydrometer, take your reading from the lowest point of the meniscus — the point where the liquid level intersects with the hydrometer scale gives you your reading.

If you’re lucky, your hydrometer reads 1.000 at the specified temperature. If it reads either higher (1.001 or more) or lower (0.9999 or less), simply add or subtract the amount of error from your readings in wort or beer. For example, let’s say your hydrometer reads 0.998 in pure water at 60 °C (its calibration temperature). This means that it’s reading two “points” low and you should add two “points” from any reading you take in wort or beer. In other words, if your wort reads 1.050, your corrected reading would be 1.052.

### A two-point calibration

Checking the reading of your hydrometer in pure water is a single point calibration, and this is all most homebrewers will ever do for their hydrometers. However, what if the hydrometer read correctly at 1 but the scale printed on the paper sleeve inside the hydrometer was compressed or elongated compared to what it should be?

To check to see if your hydrometer reads correctly in the range you use it in, you need to do a two-point calibration. And, in order to do a two-point conversion, you need to be introduced to Plato — not the Greek philosopher, but a measure of extract weight frequently used by professional brewers.

Degrees Plato (°Plato) is the percentage of sucrose (table sugar), by weight, dissolved in a water solution. For example, if you had 10 g of sucrose dissolved in 90 g of water, you would have a 10 °Plato solution — i.e. 10 g of sugar in a solution that weighs 100 g overall is 10% sugar (w/w).

There is a quick and dirty way to convert between degrees Plato and specific gravity — just multiply the value in degrees Plato by four to get the value in “gravity points.” Conversely, you can divide the number of “gravity points” by four to yield the value in degrees Plato. For example, the 10 °Plato solution mentioned before would have a specific gravity of 40 “gravity points — 1.040.

This “times 4” rule is only an approximation however, as specific gravity and degrees Plato do not have a linear relationship. A 10 °Plato wort really does have a specific gravity of 1.040. However, as you get farther away from 10 °Plato, this approximation gets less accurate. Most brewing texts have a table that converts between degrees Plato and specific gravity. In his book, “New Brewing Lager Beer” (1996, Brewers Publications), Greg Noonan gives a regression equation that allows us to calculate extract weight in Plato from specific gravity readings. The equation is:

*P(°Plato) = 135.997(SG)3 – 630.272(SG)2
+ 1111.14(SG) – 616.868*

where P is extract weight in °Plato and SG is specific gravity.

### The second point

If you have a (calibrated) scale, you can make a sugar solution with a density equivalent to the average density of your wort. You can use this to check if your hydrometer reads correctly in that range.

For example, let’s say you brew mostly pale ales and porters and your target original gravity is SG 1.048. A specific gravity of 1.048 is equivalent to 12 ° Plato. (Actually 12 °Plato is 1.04838, but the difference here is only 0.38 “gravity points.”)

If you dissolve 12 g of sucrose in 88 g of water, you will have a 12 °Plato or SG 1.048 solution. (Actually, to have enough liquid to be able to float a standard-sized homebrew hydrometer, you will need to use 24 g of sucrose and 176 g of water.)

When you make this sugar solution, you must use sucrose (table sugar), not corn sugar. Why? Because most corn sugar has water associated with it. The most common kind of corn sugar sold at homebrewing stores is dextrose (D-glucose) monohydrate. What this means is that water is complexed with the sugar and makes up part of its weight. In contrast, sucrose is just plain sucrose.

You can probably guess the next step — float your hydrometer in your test solution. Remember to apply your correction from your pure water reading. In our previous example, our hydrometer read two points low at 1.000, so we will have to correct for this by subtracting 2 from our specific gravity reading.

If your hydrometer’s scale is correct, your (corrected) specific gravity reading should be 1.048 (or 12 °Plato). If your second reading is correct, you only need to apply your initial correction for how far off your hydrometer was in pure water, if at all. If your hydrometer is off at this second point, you will have to apply a point-slope correction to all your hydrometer readings. The easiest way to do this is to make a graph. For our example, let’s say our hydrometer read 1.047 in the 12 °Plato (SG 1.048) solution. Corrected, this means it read SG 1.045 (11.2 °Plato) when it should have read 1.048 (12.0 °Plato).

### Graphic gravity adjustment

Begin by labeling the x axis (the horizontal one) from 1.000 to some specific gravity value at the high end of your normal range. For example, if the biggest beer you plan to brew is an SG 1.080 Scottish wee heavy, make the scale on the x axis go from 1.000 to, say, 1.090. On the y axis (the vertical one), label your scale from the reading of your hydrometer in pure water to the same upper value as before. Following our previous example, we would label the y axis starting at 0.998 and extend it to 1.090. Now, with a ruler, draw a straight line between the two points indicated by your pure water test and the sucrose solution test. This line is called the calibration curve.

In our example, our first point is (1.000, 0.998) — in pure water, in which the value should have yielded a reading of 1.000, our hydrometer read 0.998. Our second point is (1.048, 1.045) because in a solution with a specific gravity of 1.048, our (corrected) reading was 1.045.

To get corrected readings from your hydrometer, take a hydrometer reading and do not add or subtract anything. Find the value from your hydrometer on the y axis and trace a horizontal line over to the calibration curve. Now, drop a vertical line down to the x axis — the value at which the line intersects the x axis is your corrected specific gravity.

So there, wasn’t that easy? The correct answer here is, “No, that was a huge pain in the gluteal region. Why would you go through all that every time you use your hydrometer?” The answer to that is, I don’t. Personally, I wouldn’t go to these lengths unless my hydrometer was way off. And if it was that far off, I’d just buy a new hydrometer. However, performing the second point check on your hydrometer is a useful way to ensure the accuraccy of your readings.

### Volume

One reason homebrewers measure specific gravity is so they can estimate their extract efficiency — how much extract they get from their grains and adjuncts. Homebrewers often express this in points per pounds per gallon. In other words, how many gravity points they yielded from weight of their ingredients divided by the volume of wort they obtained. (For more on calculating this, see the November 2000 issue of BYO.) In order to accurately estimate this, however, you need to be able to accurately measure the volume of your wort. Likewise, it pays to calibrate all of your brewing vessels so you can read the volume of liquid in them anytime during the brew day.

The basic idea for calibrating brewing vessels is simple — add a known volume of water to the vessel and make a mark at that level. For example, you could pour a gallon of water into your carboy and place a piece of tape on the outside that corresponds to that level. Repeat this process four more times to mark the 2-, 3-, 4- and 5-gallon marks. The only catch to the above plan is — how do we measure exactly one gallon?

Standard kitchen measuring cups are not very accurate. (Neither are the hash marks printed on the outside of your brewing bucket.) What you need is something that measures volume accurately. Scientists use volumetric glassware for this. Unfortunately, good volumetric glassware is very expensive. For homebrewing, we need something that is reasonable accurate, but much cheaper. Fortunately, just such a thing is sold at many homebrewing shops — a graduated cylinder. Chemists use graduated cylinders when they need a measure of volume more accurate than that stamped on the sides of beakers and flasks, but not so accurate that they need to drag out their expensive (and fragile) volumetric flasks.

For homebrewers, a 250-mL graduated cylinder will work well (and can double as a hydrometer test jar). A decent graduated cylinder will say how accurate it is. Mine says 250 mL +/- 2 mL at 20 °C. So, it’s accurate to about 1% — which should be good enough for most homebrewing applications.

Calibrating a 5-gallon (19-L) carboy by pouring in 250 mL at a time would be very tedious. You’d need to do this almost 75 times to get to the 18,927-mL (18.9-L/5-gallon) mark. To help in calibrating larger vessels, I like to make an intermediate calibrated vessel. A one gallon

(3.8 L) milk or water jug works well for this. Pour 250 mL in it almost 16 times, and you can measure out 3.79 L or 3,790 mL (1.00 gallon). Mark the 1-gallon mark on the jug and then use it to calibrate your larger vessels.

To calibrate brewing buckets, you can use a permanent marker to write on the outside of the bucket. For carboys, labeled pieces of tape can be placed at every gallon (or half-gallon) mark. For water tanks or other vessels with sight glasses, volume marks can be painted on the sight glass. For any vessel that is not see-through, you can make a dip stick.

### Scales and balances

With a reasonably accurate 250 mL graduated cylinder, you can easily make 1 L of water — 4 X 250 mL = 1 L. Recall that 1 L of water at 4 °C (refrigerator temperature) weighs exactly 1 kg. With this information, you should be able to calibrate any scales or balances in your brewery.

Once you’ve calibrated the equipment in your brewery, you will know that your readings of temperature, specific gravity, volume and weight are accurate. This knowledge can help you to consistently brew high-quality beers.