A gold dealer in Antwerp hands you a small bar and claims it is pure. How do you check without melting it down? You weigh it. You measure its volume by water displacement. Then you compare its density to water. That ratio is specific gravity. Specific gravity (SG) is the ratio of a substance's density to a reference density, usually water at 4 degrees Celsius. It is dimensionless. If SG is greater than 1, the object sinks in water. If SG is less than 1, it floats. This is the practical link to Archimedes' principle, which says a submerged object feels an upward force equal to the weight of fluid it displaces. Hydrometers exploit this idea. Brewers use them to track sugar in fermenting beer. Gemologists use them to tell real gems from glass. Petroleum labs use them to grade crude oil.
What This Calculator Does
This tool solves the specific gravity formula for any one of its three variables. Pick what you want to find: specific gravity, substance density, or reference density. Enter the two known values. The calculator returns the missing third value. It handles unit conversions for you, so you can enter density in g/cm3 or lb/ft3 without converting first.
For related tools, see our Density Calculator, the Mass Calculator, or the Weight Calculator. Density and mass sit at the core of every SG calculation.
Inputs Required
- Substance density: a numeric value with a unit (kg/m3, g/cm3, g/mL, lb/ft3, lb/gal, or lb/in3)
- Reference fluid: a preset (Water at 4C, Water at 20C, Seawater, Mercury, Air at 20C) or a custom reference density
- Specific gravity: required only when solving for substance or reference density
Outputs Provided
- Primary result: the solved value (SG, substance density, or reference density) in a highlighted box
- Calculation breakdown: the exact arithmetic with units shown
- Reference table: common specific gravities for water, ice, aluminum, iron, gold, mercury, gasoline, olive oil, and air
How the Calculation Works
SG = density_substance / density_reference
density_substance = SG x density_reference
density_reference = density_substance / SG
SG is dimensionless because it is a ratio of two densities. The units cancel. A substance with a density of 2700 kg/m3 measured against water at 1000 kg/m3 has an SG of 2.7. The same substance measured as 2.7 g/cm3 against 1 g/cm3 water also gives 2.7. The number does not change when you switch unit systems, as long as both densities use the same units.
The reference fluid matters. Water at 4C is the default because it has a density of 1000 kg/m3, which makes the math clean. Other references shift the result. Mercury as a reference gives very different SG values than water. For gases, the reference is usually air at 20C (1.204 kg/m3) rather than water. This calculator stores reference presets in kg/m3 and converts your substance density to kg/m3 before dividing, so the ratio is always correct.
How to Use the Calculator
- Choose what to solve for: Specific Gravity, Substance Density, or Reference Density
- Enter the substance density and pick its unit
- Select a reference fluid preset, or choose Custom and enter your own reference density
- If solving for substance or reference density, enter the known SG value
- Read the result in the highlighted box on the right
- Use the Copy button to save the result, and check the reference table for comparison
Example Calculations
Testing Gold Purity in Antwerp
A jeweler in Antwerp receives a bar stamped 24-karat gold. She measures its density at 18,900 kg/m3 and uses water at 4C as the reference (1000 kg/m3). SG = 18900 / 1000 = 18.9. Pure gold has an SG of 19.32. Her bar falls short, which suggests it is alloyed with a lighter metal. She orders a further assay. The quick SG check saved her from paying pure-gold prices for a diluted bar.
Measuring Beer Wort in Portland
A brewer in Portland checks his beer wort with a hydrometer. The wort has a density of 1050 kg/m3 against water at 4C. SG = 1050 / 1000 = 1.050. Brewers call this the original gravity. A higher original gravity means more fermentable sugar and a stronger final beer. He records 1.050 in his batch log. After fermentation he will measure again. The drop in SG tells him how much sugar the yeast consumed and lets him estimate alcohol content.
Real-World Scenarios
Identifying a Gemstone in New York
A gemologist in New York receives a clear blue stone and must confirm whether it is aquamarine, topaz, or glass. She weighs it at 8.20 g and measures its volume at 2.45 cm3 by water displacement. Density = 8.20 / 2.45 = 3.35 g/cm3, or 3350 kg/m3. Against water at 4C, SG = 3350 / 1000 = 3.35. Aquamarine has an SG near 2.7. Topaz sits around 3.5. Glass usually falls between 2.4 and 2.8. The 3.35 reading points to topaz, and she books a refractive index test to confirm.
Testing Crude Oil in Houston
A petroleum engineer in Houston tests a crude oil sample. The oil has a density of 875 kg/m3. Using water at 4C as the reference, SG = 875 / 1000 = 0.875. He converts this to API gravity with the formula API = (141.5 / SG) - 131.5 = (141.5 / 0.875) - 131.5 = 30.3. An API of 30.3 marks the oil as medium-light crude, which refiners pay a premium for because it yields more gasoline and diesel per barrel. The SG value feeds straight into pricing and refinery scheduling.
Measuring Seawater Salinity in Monterey Bay
A marine biologist in Monterey Bay tracks estuary salinity after a winter storm. She samples surface water and finds its density at 1021 kg/m3. Against pure water at 4C, SG = 1021 / 1000 = 1.021. Standard seawater has an SG near 1.025. The lower reading shows fresh runoff diluting the bay. She logs the value alongside temperature and depth. Over several weeks the SG climbs back toward 1.025 as the estuary mixes with ocean water again.
Common Mistakes to Avoid
- Wrong reference temperature: Water at 4C has a density of 1000 kg/m3, but water at 20C is 998.2 kg/m3. Using the wrong reference shifts your SG by a small but real amount. Always confirm which temperature a published value assumes.
- Confusing SG and density: Density has units. SG does not. A density of 2700 kg/m3 and an SG of 2.7 describe the same material, but they are not interchangeable numbers. Mixing them up leads to errors of 1000x.
- Forgetting the dimensionless nature: SG has no units, so you cannot add or subtract SG values the way you would densities. A blend of two liquids does not have an SG equal to the sum of their SG values. Compute the mixture density first, then divide by the reference.
- Ignoring temperature effects on density: Both the substance and the reference change density with temperature. A hot liquid measured against a 4C water reference gives a different SG than the same liquid at 4C. Record temperatures for any precise work.
Limitations of This Calculator
This tool computes a straightforward density ratio. It does not correct for temperature. If your substance and reference are at different temperatures, you must adjust their densities by hand before entering them. The calculator does not convert to API gravity, Brix, Balling, Plato, or Baumé scales, though you can derive some of these from the SG value with separate formulas. For gas SG at non-standard conditions, this tool is a starting point only. Gas density depends on pressure and temperature through the ideal gas law, so a single SG number is only valid at stated conditions. For mixtures, compute the mixture density first rather than averaging SG values directly.
Authoritative Research and Resources
- NIST: SI Units - The National Institute of Standards and Technology defines the SI units behind density and specific gravity. This page explains the kilogram and meter standards that anchor every density measurement, which is useful when you need to trace a value back to its official definition.
- Engineering Toolbox: Specific Gravity - A practical engineering reference with SG values for hundreds of common solids, liquids, and gases. It is handy for checking your calculator output against known materials or for picking a reference density when water is not suitable.
- USGS Water Science School - The United States Geological Survey covers water density across temperatures and salinities. This helps when your reference is water and you need to account for temperature shifts or when you work with seawater SG in field studies.