Density Calculator

What is density?

Density is how much mass is packed into a given volume. A bowling ball and a beach ball can be the same size, but the bowling ball weighs more — that's density. Formally, density is mass divided by volume, written with the Greek letter rho:

The unit in the SI system is kilograms per cubic meter (kg/m³). Most chemistry and physics textbooks use grams per cubic centimeter (g/cm³) instead because the numbers come out friendlier — water is exactly 1 g/cm³, aluminum is 2.7, gold is 19.3. The two units are the same quantity scaled by 1,000: divide kg/m³ by 1,000 to get g/cm³.

The Density Calculator solves the formula for whichever variable you don't have. Enter mass and volume, get density. Enter mass and density, get volume. Enter density and volume, get mass. Same equation, three rearrangements. Inputs are SI; the calculator shows the g/cm³ equivalent below the result so chemistry homework looks right either way.

How to use the Density Calculator

The calculator runs the rearrangement automatically — you don't have to remember which form of the equation you need.

1. Pick which variable you're solving for: density, mass, or volume.
2. Enter the two known values in SI units. Mass in kilograms (kg), volume in cubic meters (m³), density in kg/m³.
3. Read all three values together. The computed one is highlighted.
4. Check the g/cm³ equivalent below if you're working from a textbook that uses it.

Unit conversions you'll often need:

• 1 liter = 0.001 m³ (1,000 liters = 1 m³)
• 1 milliliter = 1 cm³ = 0.000001 m³
• 1 gram = 0.001 kg
• 1 g/cm³ = 1,000 kg/m³ = 1 g/mL
• 1 lb ≈ 0.4536 kg
• 1 ft³ ≈ 0.02832 m³

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The three forms of the equation

Algebraically, ρ = m/V is one equation with three unknowns. Solve it for each variable in turn:

Three forms, but the same triangle. Picture mass at the top, with density and volume at the bottom corners — cover the variable you want, and the remaining two show you the operation. The Density Calculator does the algebra for you, but knowing the rearrangement is what makes the formula click.

Worked example — finding the density of an unknown solid

The classic introductory physics lab. You have a small metal cube of unknown composition. The lab asks: what is it?

Step 1 — measure the mass. Place the cube on a scale. It reads 100 grams (0.1 kg in SI).

Step 2 — measure the volume by water displacement. Fill a graduated cylinder with water and record the level: 50 mL. Submerge the cube fully and record the new level: 60 mL. The cube's volume is the difference, 10 mL = 10 cm³ = 0.00001 m³.

Step 3 — apply the formula.

• In g/cm³: ρ = 100 g ÷ 10 cm³ = 10 g/cm³
• In SI: ρ = 0.1 kg ÷ 0.00001 m³ = 10,000 kg/m³

Step 4 — identify the material. A density of 10 g/cm³ is close to silver (10.49) and well above iron (7.87) or copper (8.96). The unknown is probably silver, or possibly a silver-rich alloy. Compare against a reference table to confirm.

This is Archimedes' method, dating to roughly 250 BC. The story goes that he was asked whether the king's crown was pure gold or had been adulterated with silver. He measured the crown's mass and its water displacement, computed density, and reportedly shouted "Eureka!" when the answer revealed the fraud. The water-displacement step is the only part of the method that has any complexity, and it's still what intro physics labs use today.

Density of common materials

The table below gives reference densities for materials that show up in chemistry, physics, and engineering problems. Values are at standard conditions (20–25°C, 1 atm) unless noted. Use these to identify unknowns, sanity-check experimental results, or simply build intuition for what "dense" means in different contexts.

The full range, top to bottom: cork at 0.24 g/cm³ to osmium at 22.6 g/cm³. A factor of nearly 100. That's how much variation there is in how tightly atoms can pack themselves into ordinary matter on Earth. Outside Earth, the range gets stranger — neutron stars pack around 10¹⁷ kg/m³, roughly 100 trillion times denser than water — but for anything you can hold in your hand, the table covers the territory.

Specific gravity — a related quantity

Specific gravity (SG) is a close cousin of density and shows up constantly in chemistry, brewing, geology, and any context where you're comparing substances to water:

Specific gravity is dimensionless — it's a ratio, so the units cancel. SG = 1 means the substance has the same density as water. SG > 1 means denser (sinks in water). SG < 1 means less dense (floats). Because water at 4°C is exactly 1 g/cm³, the SG of any solid or liquid is numerically equal to its density in g/cm³ — that's part of why g/cm³ is the convenient unit for chemistry.

Specific gravity quick reference: steel SG ≈ 7.85, aluminum SG ≈ 2.70, cork SG ≈ 0.24, gasoline SG ≈ 0.74, mercury SG ≈ 13.5. The numbers match the g/cm³ column of the table above by design.

Why things float — Archimedes' principle

The Density Calculator answers "what is the density?" The next obvious question is "does it float?" That's Archimedes' principle: the buoyant force on a submerged object equals the weight of the fluid it displaces. If an object's weight is less than the maximum weight of fluid it could displace, it floats.

For a uniform object in a uniform fluid, the rule simplifies beautifully. The fraction of the object that ends up below the waterline equals the ratio of densities:

Worked example. An iceberg in seawater. Ice density = 917 kg/m³, seawater density = 1,025 kg/m³. Fraction below the waterline = 917 ÷ 1,025 = 0.895 — about 89.5%. The famous "tip of the iceberg" figure comes from exactly this calculation. (You sometimes hear "90%" or "92%" depending on whether you use fresh water, seawater, or pack ice — all close to each other, all in the same range.)

The principle also explains why lighter-than-water objects float at a fraction of their height. A wooden ball with density 0.5 g/cm³ floats with half its volume underwater. A cork with density 0.24 g/cm³ floats with three-quarters of its volume above the surface. The math works for any shape, any size, any fluid, as long as the object is denser than the fluid below it and less dense than the fluid above it (which is usually just air).

How temperature affects density

Density isn't a fixed property — it changes with temperature, because materials expand and contract. For homework purposes the reference values in the table are usually close enough, but for precision work, the corrections matter.

• Liquids. Water at 25°C is about 997 kg/m³, vs. 1,000 at 4°C — roughly 0.3% less dense at room temperature than at its peak. Other liquids show similar small drops with heating.
• Solids. Thermal expansion is even smaller. Steel changes about 0.05% per 10°C of temperature change. For most engineering calculations, you can treat solid density as constant.
• Gases. Huge effect. The ideal gas law says density is proportional to pressure divided by absolute temperature: ρ ∝ P/T. A 10% change in absolute temperature gives a 10% change in density at constant pressure. That's why hot-air balloons work, why summer air is less dense than winter air, and why aircraft engines lose power on hot days.

For precise work, look up temperature-specific values from a materials handbook. For most homework and back-of-envelope calculations, the standard reference values are within 1% of reality at any normal room temperature.

Related calculations

Density problems often connect to a few neighboring calculations:

• Molarity Calculator — chemistry concentration math, often paired with density when converting between mass-based and volume-based recipes.
• Weight Converter — convert between kilograms, pounds, grams, and ounces before plugging numbers into the density formula.
• Temperature Converter — when a reference table gives density at 25°C and your problem is at 20°C, you'll want this for the conversion.

Frequently asked questions

What's the formula?

ρ = m / V. Density (rho, Greek letter ρ) equals mass divided by volume. Mass = density × volume. Volume = mass ÷ density. The formula holds for any substance in any state of matter, as long as the substance is homogeneous. For mixtures, you'd compute the density of each component and combine appropriately.

What units does the calculator use?

SI internally: kg for mass, m³ for volume, kg/m³ for density. The g/cm³ display is kg/m³ ÷ 1,000 — the most common chemistry textbook unit. Conversions for other inputs: 1 liter = 0.001 m³; 1 gram = 0.001 kg; 1 g/mL = 1,000 kg/m³; 1 lb ≈ 0.4536 kg; 1 ft³ ≈ 0.02832 m³. Convert to SI before entering for accurate results.

What's the density of water?

Water at 4°C is exactly 1,000 kg/m³ = 1 g/cm³ — the SI kilogram was originally defined this way (one liter of water at 4°C = 1 kg). At room temperature (25°C), water is slightly less dense, about 997 kg/m³. Pure ice at 0°C is about 917 kg/m³ (less dense than liquid water, which is why ice floats). Seawater is roughly 1,025 kg/m³ — denser because of dissolved salts.

What's specific gravity, and how is it related?

Specific gravity (SG) = density of substance ÷ density of water at 4°C. It's a dimensionless ratio. SG = 1 means the substance has the same density as water; SG > 1 means denser (sinks); SG < 1 means less dense (floats). In SI, SG is numerically equal to density in g/cm³ for solids and liquids — that's why g/cm³ is the convenient chemistry unit. Steel SG ≈ 7.85; aluminum SG ≈ 2.70; cork SG ≈ 0.24; gasoline SG ≈ 0.74; mercury SG ≈ 13.5.

How does temperature affect density?

Most substances expand when heated, so density falls with temperature. Liquids: water at 25°C is about 997 kg/m³ vs. 1,000 at 4°C — roughly 0.3% less. Solids: thermal expansion is even smaller — steel changes about 0.05% per 10°C. Gases: temperature has a large effect — the ideal gas law gives ρ ∝ P/T, so a 10% temperature change gives a 10% density change at constant pressure. For precise calculations, use temperature-specific reference values from a materials handbook.

How do I measure the density of an irregular object?

Archimedes' method. Measure mass on a scale. Measure volume by water displacement: fill a graduated cylinder partway, record the volume, submerge the object completely, record the new volume. The difference is the object's volume. Divide measured mass by displaced volume = density. This was the original method (~250 BC) and it's still what intro physics labs use today. For irregular solids that float, weight them down with a known sinker and subtract the sinker's volume.

Why do some materials float in water?

Because their density is less than water's (1,000 kg/m³). Wood, oil, ice, foam, fat — all less dense. The buoyant force on a submerged object equals the weight of the water displaced. If the object's weight is less than the maximum displaced water's weight, it floats. The fraction underwater equals (object density) ÷ (fluid density). An iceberg is about 90% submerged because ice density (917) ÷ seawater density (1,025) = 0.895.

What's the densest common substance?

On Earth, the densest naturally-occurring element is osmium at around 22,590 kg/m³ — about 22.6× denser than water. Iridium is a close second at about 22,560. For more familiar materials: gold around 19,300; mercury 13,534; steel 7,850; aluminum 2,700. In the universe at large: neutron stars pack roughly 10¹⁷ kg/m³ (100 trillion times denser than water). Black-hole singularities are formally infinite-density, but that's a statement about the math, not necessarily the physics.