Density and Specific Gravity Converter

Twelve density units derived from exact definitions — including the pound per US gallon and the pound per imperial gallon, which are 20.1% apart — plus specific gravity on the 60/60 °F, 20/4 °C and 20/20 °C conventions with the difference between them shown, API gravity, and all four published Baumé constants rather than one. Water’s density comes from Tanaka’s formula, because it is not 1.000.

Density is easy. Specific gravity needs two temperatures

Density units, and two gallons that are 20% apart

“Specific gravity” is not one quantity: it needs two temperatures

API gravity runs backwards, and water is exactly 10

Baumé is two scales, and the heavy one has four published constants

Water’s density is not 1.000, and that is why SG is ambiguous

Density is arithmetic; specific gravity needs two temperatures

Density units are arithmetic and this page does them exactly. Specific gravity is where the difficulty is. Every density factor here comes from a definition: the US liquid gallon is 231 cubic inches exactly, the imperial gallon is 4.546 09 litres exactly, the inch is 25.4 mm and the pound is 453.592 37 g. Nothing is rounded. The one trap in the density list is the two gallons: an imperial gallon is 1.2009 times a US one, so lb per US gallon and lb per imperial gallon are 20.1% apart, and a figure quoted as “pounds per gallon” without saying which is out by a fifth. The imperial one carries its own check: it was defined so that a gallon of water weighs ten pounds, and at 62 °F it comes out at 10.01 lb.

A specific gravity needs two temperatures, and the pair depends on the industry. It is a ratio of the sample’s density to a reference fluid’s, and both densities are at a temperature — which is why the notation has a slash in it. The petroleum convention is 60/60 °F: sample and water both at 60 °F, where ASTM D1250 puts water at 999.016 kg/m³. The laboratory convention is often 20/4 °C: the sample at 20 °C and the water at its density maximum, which is convenient because it makes the specific gravity numerically almost the same as the density in g/cm³. The same oil is a different number in the two, and both are computed here. How much different is worth decomposing, because the usual explanation puts the emphasis in the wrong place: the two reference waters differ by only 0.096%, while the sample itself is 4.4 degrees warmer in one convention than the other, which for a hydrocarbon is about 0.38%. Four fifths of the difference is the sample, one fifth the reference, and the total for a typical crude is around half a per cent. On a thirty-thousand-tonne cargo that is a hundred and forty tonnes, which is why trade documents name the convention.

API gravity is worth getting exactly right because three things about it are counter-intuitive, and all three check out. API = 141.5 / SG(60/60 °F) − 131.5. Water is exactly 10, because 141.5 − 131.5 = 10. The scale runs backwards: because specific gravity is in the denominator, a higher API number is a lighter oil, and light crudes are the valuable ones. And it is defined at 60 °F only — a gravity measured at another temperature has to be corrected to 60 °F before it is an API gravity at all, which is the entire purpose of the ASTM D1250 petroleum measurement tables. It is also not linear in density: a degree of API is about 1.1 kg/m³ at 10 °API and 0.5 at 70, so you cannot average API numbers to blend oils.

Baumé is two scales with four constants and this page carries the disagreement rather than resolving it. For liquids heavier than water, SG = c / (c − °Bé), with c published as 144, 144.3, 145 and 146 in different handbooks. For liquids lighter than water it is a different formula altogether, SG = 140 / (130 + °Bé), which puts water at 10 °Bé instead of 0 — so the two halves of one scale name disagree about water by ten degrees. The reason the constants differ is that none of them was derived from anything: they are, as one long-running industry forum puts it, “people’s efforts to correlate an unreliable and vague scale to the more exacting S.G. scale”. The cost of choosing wrongly grows up the scale, from a fiftieth of a per cent at 5 °Bé to a full per cent at 70, and this page shows three of the constants side by side so the cost is visible. One pleasing detail: the light Baumé scale and API gravity agree exactly at 10 degrees, because both were built to put water there, and they agree nowhere else.

Water’s density is not 1.000, and that is the root of all of it. Water is densest at 3.983 °C, where it is 999.9749 kg/m³ — 25 parts per million short of the 1000 the kilogram was originally meant to make it. At 20 °C it is 998.2067 and at 60 °F 999.016. This page uses Tanaka’s 2001 formula, recommended for standard mean ocean water from 0 to 40 °C, and checks it against eight independent IAPWS-IF97 values, which it matches to 0.02 kg/m³; the density maximum above was found by searching that formula rather than by quoting a textbook. Because the reference moves with temperature, a specific gravity quoted without its two temperatures is incomplete — and the same is true of every property read through a density. Brix and Plato are mentioned on this page and deliberately not computed: they are concentration scales read through density, their modern conversions are fitted polynomials whose coefficients differ between publishers, and a number computed without naming whose polynomial it is would be unattributable. For the property that cannot be converted without the density on this page, see the viscosity converter; for hardness and finish on the same components, the hardness scale converter and the surface roughness converter; and for the same temperature ambiguity in a different guise, the water hardness converter.

Frequently asked questions

Related calculators

References

1. Tanaka M, Girard G, Davis R, Peuto A, Bignell N. Recommended table for the density of water between 0 °C and 40 °C based on recent experimental reports. Metrologia 38 (2001) 301–309. doi:10.1088/0026-1394/38/4/3. ρ = a₅[1 − (t + a₁)²(t + a₂) / (a₃(t + a₄))] with a₁ = −3.983035 °C, a₂ = 301.797 °C, a₃ = 522 528.9 °C², a₄ = 69.34881 °C and a₅ = 999.974950 kg/m³, valid 0 to 40 °C. Checked here against eight IAPWS-IF97 spot values, which it matches to 0.02 kg/m³, and used to LOCATE the density maximum by search rather than by quotation: 3.983 °C, 999.975 kg/m³.
2. ASTM D1250 (2008), Standard Guide for the Use of the Petroleum Measurement Tables. Cited by number; not fetched. Its published density of water at 60 °F, 999.016 kg/m³, is the figure the whole 60/60 °F specific-gravity convention rests on, and it is quoted here through the Wikipedia article on API gravity. Tanaka’s formula independently gives 999.0163 kg/m³ at 60 °F, which agrees to two parts in a million — the check that matters more than the citation.
3. American Petroleum Institute / ASTM. API gravity = 141.5 / SG(60/60 °F) − 131.5, with the inverse SG = 141.5 / (API + 131.5). Verified here at three points: water is exactly 10, the relation round-trips to machine precision over SG 0.6 to 1.1, and it runs backwards, so a lighter oil carries a higher number. Band edges (light above 31.1, medium 22.3–31.1, heavy below 22.3, extra heavy below 10.0) from the Wikipedia API gravity article.
4. IAPWS / Engineering ToolBox and SimuPipe water property tables (IAPWS-IF97): the eight independent density spot values from 0 to 40 °C that Tanaka’s formula is checked against on this page.
5. finishing.com, Baumé to Specific Gravity (Ted Mooney and correspondents). The source for this page’s refusal to pick one Baumé constant: “some handbooks cite 144 for the ‘heavier than water’ scale, and other books cite 145, and other people cite 146”, because “those constants are not based on any physical quantity, they are simply people’s efforts to correlate an unreliable and vague scale to the more exacting S.G. scale.” The light scale is given there as SG = 140 / (130 + °Bé).
6. NIST Handbook 44, Appendix C, General Tables of Units of Measurement. The US liquid gallon is 231 cubic inches exactly and the imperial gallon is 4.546 09 litres exactly; every gallon-based density unit on this page is derived from those two definitions and the exact inch, and the 20.095% difference between lb per US gallon and lb per imperial gallon is simply their ratio.