Specific Gravity Calculator
Solve specific gravity problems step-by-step with our free calculator. See formulas, worked examples, and clear explanations.
Calculator
Adjust values & calculateCommon Material Comparison
Formula
Where SG is the specific gravity (dimensionless ratio), Density of Substance is in kg/m3, and Density of Reference is typically water at 4 degrees C (997 kg/m3). Alternatively, using the Archimedes method: SG = Weight in Air / (Weight in Air - Weight in Water).
Last reviewed: December 2025
Worked Examples
Example 1: Mineral Identification by Archimedes Method
Example 2: API Gravity of Crude Oil
Background & Theory
The Specific Gravity Calculator applies the following established principles and formulas. Mathematics rests on a hierarchy of number systems, each extending the previous. The natural numbers (1, 2, 3, ...) support counting and ordering. The integers add negative values and zero, enabling subtraction without restriction. The rational numbers, expressible as p/q where p and q are integers and q is nonzero, close the system under division. The real numbers fill the gaps left by irrationals such as the square root of 2 or pi, forming a complete ordered field. The complex numbers, written as a + bi where i is the square root of negative one, complete the algebraic closure of the reals and allow every polynomial to have a root. Prime factorization states that every integer greater than one is uniquely expressible as a product of primes, a result known as the Fundamental Theorem of Arithmetic. Computing the greatest common divisor (GCD) of two integers relies most efficiently on the Euclidean algorithm: repeatedly replace the larger number with the remainder when it is divided by the smaller, until the remainder is zero. The last nonzero remainder is the GCD. The least common multiple (LCM) follows from the identity LCM(a, b) = |a * b| / GCD(a, b). Modular arithmetic defines equivalence classes of integers that share the same remainder under division by a modulus n. Fermat's Little Theorem and Euler's Theorem arise from this structure and underpin modern cryptography. Logarithms are the inverses of exponential functions. If b raised to the power x equals y, then the logarithm base b of y equals x. The natural logarithm uses base e, approximately 2.71828. Combinatorics counts arrangements and selections. The number of ordered arrangements (permutations) of r objects from n distinct objects is nPr = n! / (n - r)!. The number of unordered selections (combinations) is nCr = n! / (r! * (n - r)!). Pascal's triangle arranges these binomial coefficients so that each entry equals the sum of the two entries directly above it. The Fibonacci sequence, defined by F(1) = 1, F(2) = 1, and F(n) = F(n-1) + F(n-2), appears throughout nature and connects deeply to the golden ratio via Binet's formula.
History
The history behind the Specific Gravity Calculator traces back through the following developments. Mathematics as a systematic discipline traces to ancient Mesopotamia. Babylonian clay tablets dating to around 1800 BCE demonstrate knowledge of quadratic equations, Pythagorean triples, and base-60 arithmetic, suggesting a practical mathematical tradition far preceding Greek formalism. Euclid of Alexandria compiled the Elements around 300 BCE, establishing the axiomatic method that would define rigorous mathematics for over two thousand years. His work organized plane geometry, number theory, and proportion into logically chained propositions derived from a small set of postulates. The algorithm bearing his name for computing GCDs appears in Book VII and remains in use today. In the 9th century, the Persian scholar Muhammad ibn Musa Al-Khwarizmi wrote Al-Kitab al-mukhtasar fi hisab al-jabr wal-muqabala, the treatise whose title gave algebra its name. He systematized the solution of linear and quadratic equations and described procedures that operated on unknowns as objects, a conceptual leap away from purely numerical calculation. Rene Descartes introduced coordinate geometry in 1637 by uniting algebra and Euclidean geometry, allowing curves to be studied through equations. This synthesis set the stage for calculus. Isaac Newton and Gottfried Wilhelm Leibniz independently developed calculus during the 1660s and 1670s, triggering a priority dispute that lasted decades and divided British and Continental mathematicians. Carl Friedrich Gauss proved the Fundamental Theorem of Algebra in 1799, showing that every nonconstant polynomial has at least one complex root. His Disquisitiones Arithmeticae of 1801 established modern number theory. David Hilbert's formalist program at the turn of the 20th century sought to place all of mathematics on an explicit axiomatic foundation, a project that Kurt Godel's incompleteness theorems of 1931 showed to be fundamentally limited. Alan Turing's work in the 1930s on computability introduced the theoretical model of the stored-program computer and linked mathematical logic directly to the limits of algorithmic calculation. His proof that no algorithm can decide in general whether an arbitrary program will halt or run forever placed fundamental boundaries on what mathematics can mechanically determine, and it opened the discipline now known as theoretical computer science.
Frequently Asked Questions
Formula
SG = Density of Substance / Density of Reference
Where SG is the specific gravity (dimensionless ratio), Density of Substance is in kg/m3, and Density of Reference is typically water at 4 degrees C (997 kg/m3). Alternatively, using the Archimedes method: SG = Weight in Air / (Weight in Air - Weight in Water).
Worked Examples
Example 1: Mineral Identification by Archimedes Method
Problem: A mineral specimen weighs 85 grams in air and 53 grams when submerged in water. Determine its specific gravity and identify the likely mineral.
Solution: Apparent weight loss = 85g - 53g = 32g\nSG = Weight in Air / Apparent Loss = 85 / 32 = 2.656\nDensity = 2.656 x 997 kg/m3 = 2,648 kg/m3\n\nSG of 2.656 closely matches quartz (2.65)\nThis is consistent with common quartz specimens.
Result: Specific Gravity: 2.656 | Likely Mineral: Quartz | Density: 2,648 kg/m3
Example 2: API Gravity of Crude Oil
Problem: A crude oil sample has a density of 850 kg/m3. Calculate its specific gravity and API gravity classification.
Solution: SG = 850 / 997 = 0.8526\nAPI Gravity = (141.5 / 0.8526) - 131.5 = 165.97 - 131.5 = 34.47\n\nAPI > 31.1 classifies this as light crude oil\nThis is similar to Brent crude (API ~38)\nLight crude commands premium pricing.
Result: SG: 0.853 | API Gravity: 34.47 | Classification: Light Crude
Frequently Asked Questions
What is specific gravity and how is it defined?
Specific gravity (SG) is the ratio of the density of a substance to the density of a reference substance, typically water at 4 degrees Celsius (997 kg/m3). Unlike density, specific gravity is a dimensionless number with no units, making it universally comparable regardless of the measurement system used. A specific gravity of 2.7 means the substance is 2.7 times denser than water. If SG is less than 1, the substance floats on the reference fluid; if greater than 1, it sinks. This simple concept has been used for thousands of years, dating back to Archimedes, and remains fundamental in fields ranging from geology and chemistry to brewing and petroleum engineering.
How do you measure specific gravity using the Archimedes method?
The Archimedes method determines specific gravity by weighing an object in air and then while submerged in water. The difference between these two measurements equals the weight of water displaced, which corresponds to the object volume. The formula is SG = Weight in Air / (Weight in Air - Weight in Water). For example, if a rock weighs 150 grams in air and 95 grams in water, SG = 150 / (150 - 95) = 150 / 55 = 2.727. This method works for any solid object that is denser than the reference liquid. For porous materials, the object must be coated in wax or paraffin first to prevent water absorption, which would alter the submerged weight reading.
What instruments are used to measure specific gravity?
Several instruments measure specific gravity depending on the application and required precision. A hydrometer is a glass float calibrated to read SG directly when placed in a liquid, commonly used in brewing, winemaking, and battery testing. A pycnometer is a precision flask used to measure liquid density by comparing the mass of a known volume of liquid versus water. Digital density meters use oscillating tube technology for highly accurate measurements in laboratories. Westphal balances use a plunger and counterweights for liquid SG measurement. For gemstones and minerals, heavy liquids of known SG are used to determine whether a specimen floats or sinks, providing a quick identification method.
How is specific gravity used in the petroleum industry?
The petroleum industry uses API gravity, which is derived from specific gravity, as its standard measure of crude oil density. The formula is API Gravity = (141.5 / SG) - 131.5. Light crude oil (API greater than 31.1) is more valuable because it yields more gasoline and diesel. Heavy crude (API less than 22.3) requires more refining. For example, West Texas Intermediate crude has an API of about 39.6 (SG 0.827), while Canadian oil sands produce crude with API around 8 (SG 1.014). Specific gravity is also used to measure fuel blending ratios, monitor refinery processes, detect product contamination, and calculate pipeline flow characteristics for transportation logistics.
Why does specific gravity matter in geology and mineralogy?
Specific gravity is one of the most important physical properties for mineral identification because each mineral has a characteristic SG range. Quartz has SG of 2.65, feldspar about 2.56, and galena (lead ore) around 7.5. Geologists can quickly narrow down mineral identification by estimating SG through a simple heft test or precise Archimedes measurement. In gemology, SG helps distinguish real gemstones from imitations, since a synthetic stone may look identical but have a different SG. For example, diamond has SG of 3.52, while cubic zirconia is 5.80. Mining engineers use SG to calculate ore reserves, estimate tonnage from volume surveys, and design mineral processing equipment for separation based on density differences.
How does temperature affect specific gravity measurements?
Temperature significantly affects specific gravity because density changes with temperature due to thermal expansion. Water reaches maximum density at approximately 4 degrees Celsius (997.05 kg/m3) and becomes less dense at both higher and lower temperatures. At 20 degrees Celsius, water density is 998.2 kg/m3, and at 60 degrees it drops to 983.2 kg/m3. Most specific gravity measurements are standardized at either 4 or 20 degrees Celsius and noted as SG(20/4), meaning the substance was measured at 20 degrees with water at 4 degrees as reference. For precise work, temperature corrections must be applied using published tables. This is especially important in the petroleum industry where product volumes and densities are corrected to a standard temperature of 15 degrees Celsius.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy