Specific Gravity (Mineral) Equation, Derivation & Rearrangements

Core idea

Overview

Specific gravity is a dimensionless ratio that compares the density of a mineral to the density of pure water at 4°C. It serves as a primary diagnostic tool in mineralogy, determined by weighing a sample in air and then measuring its apparent weight when submerged in water to calculate the volume based on buoyancy.

When to use: This formula is applied when identifying a high-purity mineral specimen where the chemical identity is unknown but physical measurements can be taken. It assumes the mineral is non-porous, does not dissolve in water, and that the sample is large enough to minimize scale error.

Why it matters: It allows geologists to differentiate between minerals that appear identical, such as distinguishing pyrite from gold, without destructive testing. In industrial mining, specific gravity is essential for gravity separation techniques used to refine ores.

Symbols

Variables

SG = Specific Gravity, $W_{a}$ = Weight in Air, $W_{w}$ = Weight in Water

SG

Specific Gravity

Variable

W_{a}

Weight in Air

g

W_{w}

Weight in Water

g

Walkthrough

Derivation

Understanding Specific Gravity of Minerals

Specific gravity compares a mineral's density to water and is measured by weighing in air and then in water.

Water density ≈ 1 g/cm³.
The mineral does not dissolve in or react with water.

1

Note the loss of weight in water equals upthrust:

By Archimedes' principle, the loss of weight equals the weight of displaced water.

Upthrust = W_{a} - W_{w}

2

Calculate specific gravity:

SG is the ratio of the mineral's weight in air to the weight of the same volume of water.

S G = \frac{W _{a}}{W _{a} - W _{w}}

Note: Examples: quartz SG ≈ 2.65; pyrite SG ≈ 5.0; gold SG ≈ 19.3. Specific gravity is used in mineral identification alongside colour and cleavage.

Result

S G = \frac{W _{a}}{W _{a} - W _{w}}

Source: A-Level Geology — Mineralogy

Free formulas

Rearrangements

Solve for SG

Specific Gravity (Mineral)

S G = \frac{- W _{a}}{W _{w} - W _{a}}

This equation defines Specific Gravity (SG) as the ratio of the weight of a substance in air to the apparent loss of weight when submerged in water.

Difficulty: 2/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph of Specific Gravity (SG) plotted against the independent variable (W_water) forms a hyperbola. As the weight in water approaches the weight in air, the denominator approaches zero, creating a vertical asymptote where the specific gravity increases rapidly toward infinity.

Graph type: hyperbolic

Why it behaves this way

Intuition

A comparison between the total gravitational pull on a mineral and the upward push of the water it displaces, revealing how many times denser the solid is than the liquid.

W_{a} i r

Weight of the mineral specimen in air

Acts as a proxy for the total mass of the mineral, representing the full gravitational force on the sample.

W_{w} a t er

Apparent weight of the mineral when submerged in water

The reduced weight measured when the upward buoyant force of the water counteracts a portion of the gravity.

W_{a} i r - W_{w} a t er

Weight of the displaced volume of water

Based on Archimedes' Principle, this difference equals the weight of a volume of water exactly equal to the mineral's volume.

Signs and relationships

W_air - W_water: The subtraction in the denominator isolates the buoyant force, converting a weight measurement into a volume-equivalent weight of water.
W_air / (W_air - W_water): The ratio compares the mass of the mineral to the mass of an equal volume of water, resulting in a dimensionless value that indicates relative density.

Free study cues

Insight

Canonical usage

Specific gravity is a dimensionless ratio, calculated using consistent units for the weight (or mass) of the mineral in air and its apparent weight (or mass) when submerged in water.

Common confusion

A common mistake is to use different units for the weight (or mass) in air and the apparent weight (or mass) in water, which would lead to an incorrect and dimensionally inconsistent result.

Dimension note

Specific gravity is a ratio of the density of a substance to the density of a reference substance (usually water). As a ratio of two quantities with the same units (or dimensions), it is inherently dimensionless and has

Unit systems

$W_{a} i r$ Any consistent unit of force (e.g., N) or mass (e.g., kg) · Represents the weight or mass of the mineral in air. This quantity must be measured in the same unit as W_water for the ratio to be dimensionless.

$W_{w} a t er$ Any consistent unit of force (e.g., N) or mass (e.g., kg) · Represents the apparent weight or mass of the mineral when submerged in water. This quantity must be measured in the same unit as W_air for the ratio to be dimensionless.

Ballpark figures

Quantity:

One free problem

Practice Problem

A mineral specimen weighs 50.0 grams in air and 30.0 grams when fully submerged in water. Calculate the specific gravity of the specimen.

Weight in Air50 g

Weight in Water30 g

Solve for: SG

Hint: The denominator of the formula represents the buoyancy force, or the weight of the water displaced.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

In Mineral weighs 10g in air, 6g in water, Specific Gravity (Mineral) is used to calculate Specific Gravity from Weight in Air and Weight in Water. The result matters because it helps predict motion, energy transfer, waves, fields, or circuit behaviour and check whether the answer is plausible.

Study smarter

Tips

Ensure the specimen is thoroughly cleaned of any matrix or debris before weighing.
Remove all air bubbles from the surface of the mineral when it is submerged in water.
Use a thin suspension wire and calibrate the scale to account for the wire's weight.
Pure distilled water provides the most accurate results for the buoyancy calculation.

Avoid these traps

Common Mistakes

Adding units to Specific Gravity (it is dimensionless).
Failing to account for porous rocks absorbing water during the test.

Keep going

Related Formulas

Common questions

Frequently Asked Questions

Specific gravity compares a mineral's density to water and is measured by weighing in air and then in water.

This formula is applied when identifying a high-purity mineral specimen where the chemical identity is unknown but physical measurements can be taken. It assumes the mineral is non-porous, does not dissolve in water, and that the sample is large enough to minimize scale error.

It allows geologists to differentiate between minerals that appear identical, such as distinguishing pyrite from gold, without destructive testing. In industrial mining, specific gravity is essential for gravity separation techniques used to refine ores.

Adding units to Specific Gravity (it is dimensionless). Failing to account for porous rocks absorbing water during the test.