Specific Gravity Calculator — Weighed Against Water

Specific gravity is simply density with the units divided out: how many times heavier a substance is than the same volume of water. Enter a density, and this calculator returns the ratio — the number hydrometers, brewers and battery testers read directly.

Density, Divided by Water

Archimedes founded the concept in a bath: a body's density against water's decides whether it floats, and by how much. SG = ρ ÷ ρ_water — dimensionless, portable between unit systems, and readable off a floating glass spindle (the hydrometer) without any arithmetic at all, which is why the ratio survived two millennia of practice: the brewer's wort at SG 1.050, the battery's electrolyte at 1.265 when charged, the urine sample's 1.020, the gemmologist's 3.52 for diamond are all this division, and the number travels across laboratories that share no instruments or units. Water at 4 °C (its densest, exactly 1,000 kg/m³ by the old definition's neighbourhood) is the conventional reference; the calculator divides and then tells you the float-or-sink verdict, which is the ratio's original and still most useful meaning.

Worked Example: Steel at 7.80

The defaults enter steel's 7,800 kg/m³: SG = 7,800 ÷ 1,000 = 7.80 — a steel block weighs 7.8 times its water-twin and sinks with conviction, its submerged weight reduced by the displaced water to 6.8 times (Archimedes' correction, the number crane operators and shipwrights actually load by). Slide the input to ice's 917 and the ratio 0.917 explains the iceberg's famous fraction: about 92% submerged, the tip a ninth of the whole — in fresh water; in seawater (SG reference 1.025 there) the exposed fraction grows a touch, a refinement polar navigators price. Gold at 19.3 and mercury at 13.5 top the common table; balsa at 0.12 barely dents the surface it floats on. One division, the whole menagerie's relationship with water.

The Hydrometer: An Analog Computer for This Ratio

The hydrometer floats at the answer: a weighted bulb and a calibrated stem sink until the displaced liquid's weight equals the instrument's, so denser liquid buoys it higher and the stem's scale reads SG where the surface crosses it. No battery, no arithmetic, two thousand years of service — in breweries (tracking fermentation as sugars, SG 1.050, convert to alcohol, SG falling toward 0.99), in garages (battery acid's charge state), in clinics and dairies and customs houses (watered spirits betray themselves in the third decimal). The calculator digitises the spindle; the spindle remains the better party trick, and the two agree because both are this ratio and nothing else.

The Eureka Audit: The Crown Problem

The founding legend deserves its audit: Hiero's crown, suspected of being gold diluted with silver, could be convicted by this ratio without melting it — weigh the crown, weigh its water displacement, divide. Pure gold reads 19.3; a crown adulterated with a fifth silver reads near 17.6, a difference any competent balance of the era resolves. Whether Archimedes ran the test in the bath or merely had the insight there, the method is sound and remains the hydrostatic weighing of the gemmology FAQ. Two millennia later the same division audits fuel deliveries (watered diesel sinks its SG), honey (water content), and the Dead Sea's swimmers (SG 1.24 water, in which a human floats like a cork) — the ratio's beat has never changed, because density never stopped mattering.

Ballast and the Submarine's Trim

A submarine surfaced and submerged is this ratio managed by pumps: its average density must match the sea's (SG 1.025) to hover, and the trim tanks shuffle water in and out to hold the quotient at neutral while fuel burns off and the crew eats. Surface ships do the same bookkeeping statically — a vessel loaded in fresh water (SG 1.000) sits measurably deeper than in the sea, and the Plimsoll line's separate fresh-water mark is this calculator's difference drawn on the hull in paint. Maritime law, brewing, batteries and ballast all recite the same division; the calculator merely declines to specialise, which is the ratio's own character — one number, every trade that floats or sinks anything. There may be no older continuously-used quantity in applied science: a ratio older than the thermometer, the pressure gauge and the unit systems themselves, still printed on the instruments of a dozen industries precisely because it asks so little — a density, a reference, a division — and answers so much.

Related Tools

More from the Physics Calculators hub: the Hydrostatic Pressure Calculator — where the density this ratio uses does its depth work — and the Stokes' Law Calculator, whose settling speeds are set by density differences against the fluid.

Frequently Asked Questions

Why reference water at 4 °C?

Because that is where water's density peaks (999.97 kg/m³, for practical purposes 1,000) — a natural, reproducible anchor from the era when the kilogram itself was defined through water. Other industries picked other anchors (60 °F in American petroleum practice, 20 °C in many laboratories), and the same liquid legitimately carries SGs differing in the third decimal between them — which is why careful datasheets print the reference with the number, as this page's note insists. The calculator's 4 °C convention is the physicist's; the conversions between conventions are a temperature-density lookup, not a dispute about nature.

How do brewers turn SG into alcohol percentage?

By subtraction and a factor: fermentation converts sugar (raising SG) to alcohol (lowering it), so ABV ≈ (original SG − final SG) × 131.25 — a wort starting at 1.050 and finishing at 1.010 yields about 5.25% alcohol. The factor is empirical (the stoichiometry argues near it; tables refine it by range), and the hydrometer readings at both ends are this page's ratio taken twice. Homebrewers live by the two readings the way sailors live by soundings — the calculator returns the ratio; the brewing arithmetic built on it is a century of practice codified.

Can specific gravity identify a gemstone?

It is one of the gemmologist's first tests: stones of similar look separate cleanly by SG — diamond 3.52, cubic zirconia 5.6–6.0 (heavier in the hand, one clue), quartz 2.65, topaz 3.53 (a diamond mimic the ratio nearly exposes) — measured by hydrostatic weighing (the stone weighed in air and in water, Archimedes' own method, the difference being the displaced water's weight). Combined with refractive index (this hub's other optical page), SG narrows most stones to a shortlist before any destructive test. The calculator's division is the hydrostatic method's final step, printed.

What does the ratio mean for gases?

Gases use air as the reference instead (vapour density), with the same dimensionless logic: methane at 0.55 rises through air and pools at ceilings, propane at 1.5 sinks and pools at floors — the fact that dictates gas-detector placement and the different dangers of the two leaks. The calculator's water reference is the liquids' convention; the conceptual machinery (divide by the ambient fluid) is identical, and the reader working with gases should divide by air's 1.225 kg/m³ at sea level, which the Bernoulli page of this wave lists as its airy default.

Is specific gravity the same as density?

No — density carries units and an absolute value (kg/m³); specific gravity is the pure ratio against water, unit-free and identical in every measurement system, which is its entire convenience and its entire limitation: an SG of 1.050 tells you nothing absolute until you multiply back by the reference water density at your convention's temperature. Old hands quote SG because their instruments read it; conversions to density are one multiplication by 1,000 at the 4 °C convention. The calculator starts from density because the modern reader usually has it; the hydrometer starts from SG because Archimedes had no kilogram.

How does a fish adjust its specific gravity?

With a gas bladder tuned like a ballast tank: by secreting or absorbing gas, the fish trims its overall density to match the surrounding water's SG at its chosen depth — neutral buoyancy, the submarine's trick performed by tissue. Species without bladders (sharks) substitute a vast oily liver — squalene at SG 0.86 — and constant swimming. The calculator's ratio, in the lake and the ocean alike, is the quantity every swimmer, finned or suited, is ultimately negotiating with the water column.

What is the SG of the human body?

Uncomfortably close to the waterline: a person with full lungs averages about 0.98 (floating with a few percent — the face — awash), with empty lungs about 1.02–1.06 (sinking, slowly), lean muscle at 1.06 and body fat at 0.90 pulling the average their way. The numbers explain why some people are natural floaters and others are sinkers, why the Dead Sea (water at SG 1.24) floats everyone effortlessly, and how hydrostatic weighing in a laboratory tank estimates body-fat percentage from exactly this page's division — Archimedes, enlisted in sports science.

How does temperature corrupt a hydrometer reading?

Liquids expand with warmth, so a wort measured hot reads a lower SG than the same wort at the calibration temperature — hydrometers ship with correction tables (roughly +0.001 per few degrees near room temperature, varying by instrument), and brewers who skip them under-read their gravities systematically. The physics is this page's density quietly moving with temperature while the spindle's calibration stands still. The calculator's density input inherits the same warning: enter the density at the reference temperature, or accept the third decimal's drift as the price of haste.