Specific Gravity Calculator
Specific gravity (relative density) is how dense a material is compared with water. This tool finds it four ways — the Archimedes method (weigh in air and in water), a floating sample with a sinker, a non-water fluid, or straight from mass and volume.
SG = W_air ÷ (W_air − W_water)
Specific gravity is a ratio, so the weight unit cancels — just keep all weights in the same unit. Runs in your browser; nothing is uploaded.
How to use this calculator
- Pick a method from the dropdown — Archimedes hydrostatic weighing is the usual one for a solid that sinks.
- Enter the weights in the same unit (grams is assumed for the density and volume outputs). For Archimedes, add the water temperature for extra accuracy if you have it.
- Read the specific gravity, plus the density in g/cm³ and kg/m³ and the sample volume.
How it works
An object submerged in water is buoyed up by the weight of the water it displaces (Archimedes' principle). So the weight it loses when submerged equals the weight of its own volume of water. Specific gravity — the object's density divided by water's density — is therefore SG = weight in air ÷ (weight in air − weight in water). The displaced-water weight also gives the object's volume, and its density follows as mass ÷ volume.
The other methods handle special cases with the same physics: a light, floating sample is held under with a sinker (SG = W_air ÷ (W_air + W_sinker-in-water − W_both-in-water)); a water-soluble or volatile sample is weighed in a fluid of known specific gravity (SG = SG_fluid × W_air ÷ (W_air − W_fluid)); or, if you already measured mass and volume, SG is simply the density in g/cm³. Results are referenced to pure water at 4 °C (1.000 g/cm³).
Worked example
A metal sample by the Archimedes method. A sample weighs 100 g in air and 63 g while hanging submerged in water. It loses 100 − 63 = 37 g, so it displaced 37 cm³ of water — that is its volume. Specific gravity = 100 ÷ 37 = 2.70, i.e. a density of 2.70 g/cm³ (2,700 kg/m³) — consistent with aluminium.
Common mistakes
- Mixing weight units. SG is a ratio, so every weight must be in the same unit — don't weigh in air in grams and in water in ounces.
- Letting the object touch the sides or bottom of the container, or leaving air bubbles clinging to it — both change the submerged weight and throw off the result.
- Using the Archimedes method on something that floats. If it is less dense than water, use the floating-sample (sinker) method instead.
Frequently asked questions
What is specific gravity?
Specific gravity (SG), also called relative density, is how heavy a material is compared with the same volume of water. Water is 1.0, so an SG of 2.7 means the material is 2.7 times denser than water. It has no units because it is a ratio.
What is the Archimedes method?
You weigh the object in air, then weigh it again while it hangs fully submerged in water. It appears lighter underwater by the weight of the water it displaces, so SG = weight in air ÷ (weight in air − weight in water).
Does it matter what unit I weigh in?
No — SG is a ratio, so grams, carats or ounces all give the same answer as long as you use the SAME unit for every weight. The density and volume outputs assume grams.
Why enter a water temperature?
Water is only exactly 1.000 g/cm³ near 4 °C; at 20 °C it is about 0.9982. Entering the temperature applies a small correction so the specific gravity is referenced correctly.
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Tip: Enter any known values to calculate the remaining results.
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