Density Calculator
Solve the density formula ρ = m/V instantly for density, mass, or volume — find the density of cubes, cylinders, and spheres from dimensions, use the classic water displacement method, and look up the density of water and common materials in every unit.
This free density calculator uses the core density formula ρ = m/V to solve for density, mass, or volume from any two known values. You can also calculate the density of common geometric shapes directly from their dimensions, or use the classic Archimedes water displacement method to find the density of irregularly shaped objects. Every result includes full step-by-step working and instant unit conversion across kg/m³, g/cm³, lb/ft³, and more.
Formula: ρ = m/V
Formula: m = ρ × V
Formula: V = m/ρ
Density (ρ)
Select a shape, enter its dimensions and mass, and find its density using ρ = m/V with the correct volume formula for that shape.
Volume: V = a³
Volume: V = l × w × h
Volume: V = π × r² × h → Density: ρ = m/(π×r²×h)
Volume: V = (4/3) × π × r³
Volume: V = (1/3) × π × r² × h
Calculated Density (ρ)
Find the density of an irregularly shaped object by measuring how much the water level rises when the object is fully submerged.
Density ρ equals mass m divided by volume V: ρ = m/V. This is the fundamental density formula from which all others derive. SI units: kg/m³.
Rearranging ρ = m/V gives m = ρ × V — this is how you find weight (via mass) from density and volume: multiply density by volume to get mass, then multiply by g for weight.
Rearranging ρ = m/V gives V = m/ρ — used to find how much space a known mass of material will occupy.
For a cylinder, volume is V = π×r²×h, so density is ρ = m/(π×r²×h). This is one of the most commonly searched density formulas for machined and lab objects.
For a sphere, volume is V = (4/3)×π×r³, so density is ρ = m/((4/3)×π×r³). Don't forget the 4/3 factor — a common source of error.
For irregular objects, displaced volume V₂ − V₁ equals the object's true volume. Then ρ_object = m_object/V_displaced — the Archimedes method.
💧 The density of water at 4°C is exactly 1.000 g/cm³ = 1000 kg/m³ = 62.43 lb/ft³ = 8.346 lb/gal. This is the reference value used to define specific gravity for all other substances.
| Temperature | g/cm³ | kg/m³ | lb/ft³ | lb/gal | lb/in³ |
|---|---|---|---|---|---|
| 0°C (32°F) | 0.9999 | 999.9 | 62.42 | 8.345 | 0.03612 |
| 4°C (39.2°F) | 1.0000 | 1000.0 | 62.43 | 8.346 | 0.03613 |
| 15°C (59°F) | 0.9991 | 999.1 | 62.37 | 8.337 | 0.03608 |
| 20°C (68°F) | 0.9982 | 998.2 | 62.32 | 8.330 | 0.03605 |
| 25°C (77°F) | 0.9970 | 997.0 | 62.24 | 8.319 | 0.03600 |
| 37°C (98.6°F) | 0.9933 | 993.3 | 62.01 | 8.288 | 0.03587 |
| 100°C (212°F) | 0.9584 | 958.4 | 59.83 | 7.997 | 0.03463 |
The average density of water used in most calculations is 1000 kg/m³ (1.000 g/cm³), corresponding to its maximum density at 4°C. This is why 1000 kg/m³ is the standard reference value stamped into virtually every physics and engineering textbook.
Search for a material below, or click any row to auto-fill the ρ = m/V solver with that density value.
| Substance | g/cm³ | kg/m³ | lb/ft³ |
|---|---|---|---|
| Water (4°C) | 1.000 | 1,000 | 62.43 |
| Ice (0°C) | 0.917 | 917 | 57.24 |
| Seawater | 1.025 | 1,025 | 63.99 |
| Air (20°C) | 0.00120 | 1.204 | 0.0752 |
| Aluminum | 2.700 | 2,700 | 168.6 |
| Steel | 7.850 | 7,850 | 489.8 |
| Copper | 8.960 | 8,960 | 559.4 |
| Gold | 19.32 | 19,320 | 1,206 |
| Lead | 11.34 | 11,340 | 708.0 |
| Wood (oak) | 0.750 | 750 | 46.82 |
| Concrete | 2.300 | 2,300 | 143.6 |
| Gasoline | 0.720 | 720 | 44.96 |
The Density Formula — ρ = m/V Explained
Density is defined as mass per unit volume, expressed by the formula ρ = m/V, where ρ (rho) is density, m is mass, and V is volume. This single equation has two equally important rearrangements: m = ρ × V (solving for mass) and V = m/ρ (solving for volume).
Density is an intrinsic (material) property — it does not depend on how much of a substance you have. A single gram of gold and a full kilogram of gold both have exactly the same density, 19.32 g/cm³, because density is a ratio, not a quantity of stuff. Mass and volume, by contrast, are extrinsic properties — they scale directly with the amount of material present.
| Unit | Equivalent To |
|---|---|
| 1 g/cm³ | = 1000 kg/m³ = 1 g/mL = 62.43 lb/ft³ = 8.345 lb/gal |
| 1 kg/m³ | = 0.001 g/cm³ = 0.06243 lb/ft³ |
| 1 lb/ft³ | = 16.0185 kg/m³ = 0.016018 g/cm³ |
How to Calculate Density — Step-by-Step
Calculating density with the density formula ρ = m/V always follows the same four-step method, whether you're working with a simple block or an odd-shaped rock:
- Measure or identify the mass — use a scale, in any convenient unit (g, kg, lb).
- Measure or calculate the volume — directly, from geometric dimensions, or via water displacement for irregular shapes.
- Divide mass by volume — apply ρ = m/V, converting to consistent SI units first if mixing unit systems.
- Express the result in appropriate units — g/cm³ for small lab samples, kg/m³ or lb/ft³ for engineering contexts.
Example 1 — Basic Density (Mode A): A Rock's Density
- Given: mass m = 540 g, volume V = 200 cm³
- Convert to SI: m = 0.540 kg, V = 200×10⁻⁶ m³ = 0.0002 m³
- Apply ρ = m/V: ρ = 0.540/0.0002 = 2,700 kg/m³
- This matches aluminum's known density — the rock is likely aluminum ore or a metal sample.
Example 2 — Find Mass (Mode B): Mass of 2L of Water
- Given: density of water ρ = 1000 kg/m³, volume V = 2 L = 0.002 m³
- Apply m = ρ × V: m = 1000 × 0.002 = 2 kg
Example 3 — Find Volume (Mode C): Volume of 1 lb of Gold
- Given: density of gold ρ = 19,320 kg/m³, mass m = 1 lb = 0.4536 kg
- Apply V = m/ρ: V = 0.4536/19,320 = 2.348×10⁻⁵ m³
- Convert to cm³: V ≈ 23.5 cm³ — surprisingly small for a full pound!
Example 4 — Unit Conversion: g/cm³ to lb/ft³
- Given: density of aluminum = 2.700 g/cm³
- Convert to kg/m³ first: 2.700 × 1000 = 2700 kg/m³
- Convert to lb/ft³: 2700 / 16.0185 ≈ 168.6 lb/ft³
Density of Water — Reference Values in All Units
The density of water is the most frequently referenced value in all of physics and engineering, and it changes slightly with temperature. The standard reference value is simple: the density of water at 4°C is exactly 1.000 g/cm³ = 1000 kg/m³ = 62.43 lb/ft³ = 8.346 lb/gal.
Water reaches its maximum density at 4°C due to hydrogen bonding — as water cools toward freezing, its molecules begin arranging into the more open hexagonal lattice structure of ice, which takes up more space per molecule than liquid water at 4°C. This is exactly why ice is less dense than liquid water and floats: solid ice locks in that expanded structure permanently, dropping its density to about 917 kg/m³, well below the 1000 kg/m³ of liquid water.
At the boiling point, 100°C, the density of water drops further to 958.4 kg/m³ (59.83 lb/ft³, 7.997 lb/gal) as thermal expansion spreads the molecules farther apart. Across the full 0–100°C range, the density of water varies by only about 4%, which is why 1000 kg/m³ remains an excellent working approximation for most everyday and engineering calculations — see the full temperature table above for every value in g/cm³, kg/m³, lb/ft³, lb/gal, and lb/in³.
📌 Quick reference: density of water in kg/m³ = 1000 kg/m³. Density of water in lb/ft³ = 62.43 lb/ft³. Density of water in lb/gal = 8.346 lb/gal. Density of water in g/cm³ = 1.000 g/cm³.
Density of Common Materials — Reference Table
The static reference table above lists 12 common substances from air to gold, spanning nearly six orders of magnitude in density — from air's 1.204 kg/m³ to gold's 19,320 kg/m³. Click any row in that table to instantly load that material's density into the ρ = m/V solver above.
Notice the extreme range: gold is over 16,000 times denser than air by mass per unit volume, which is why gold feels so remarkably heavy for its size — this contrast between "dense" and "heavy" is explored further in the Common Mistakes section below.
Density of a Cylinder — Formula and Examples
Finding the density of a cylinder is one of the most common real-world density problems, especially for machined rods, pipes, and lab samples. The cylinder volume formula is V = π×r²×h, so the full cylinder density formula is:
This formula rearranges easily to solve for other unknowns: m = ρ × π × r² × h (mass from density and dimensions), or h = m/(ρ × π × r²) (height from density, mass, and radius).
Worked Example — Steel Rod (Calculate Density of Cylinder)
- Given: radius r = 5 cm = 0.05 m, height h = 20 cm = 0.20 m, mass m = 12.33 kg
- Volume: V = π × r² × h = π × 0.05² × 0.20 = π × 0.0025 × 0.20 = 1.571×10⁻³ m³
- Apply ρ = m/(π×r²×h): ρ = 12.33/1.571×10⁻³ ≈ 7,850 kg/m³
- This matches standard steel density almost exactly ✓
Worked Example — Hollow Cylinder Approximation
For a hollow cylinder (tube), calculate volume as the difference between the outer and inner solid cylinders: V = π×h×(R_outer² − R_inner²), then apply ρ = m/(π×h×(R_outer² − R_inner²)) using the same density formula ρ = m/(πr²h) principle applied to the annular cross-section.
Water Displacement Method — Archimedes' Principle
The water displacement method is the classic technique for finding the density of an irregularly shaped object — one where geometric formulas don't apply. According to legend, this method was discovered by the ancient Greek scientist Archimedes while investigating whether a king's crown was pure gold or a silver alloy, reportedly shouting "Eureka!" upon realizing that submerging the crown would displace exactly its own volume of water.
Archimedes' principle states that the buoyant force on a submerged object equals the weight of fluid displaced: F_buoyant = ρ_fluid × V_displaced × g. Because the displaced water volume exactly equals the submerged object's volume regardless of its shape, we can measure that volume directly, then apply the same core density formula: ρ_object = m_object / V_displaced, where V_displaced = V₂ − V₁ (the rise in water level).
Worked Example 1 — The Archimedes Crown Problem
- Given: crown mass m = 150 g, water level rises from V₁ = 50 mL to V₂ = 107.7 mL
- Displaced volume: V_displaced = 107.7 − 50 = 57.7 mL = 57.7 cm³
- Apply ρ = m/V_displaced: ρ = 150/57.7 ≈ 2.600 g/cm³
- Pure gold is 19.32 g/cm³ — since 2.600 g/cm³ is far lower, this crown is not pure gold — an alloy (likely mixed with silver) was detected, exactly as the historical legend describes.
Worked Example 2 — Modern Lab Displacement
- Given: an irregular metal sample of mass m = 89.6 g, water rises from V₁ = 100 mL to V₂ = 110 mL
- Displaced volume: V_displaced = 10 mL = 10 cm³
- ρ = 89.6/10 = 8.96 g/cm³ — matches copper exactly ✓
Common Mistakes in Density Calculations
- Unit mismatches — mixing grams with cubic meters (instead of cubic centimeters) gives nonsensical results a thousand times too small or too large. Always convert both mass and volume to consistent SI units before dividing.
- Confusing density with weight — dense does not mean heavy. A small cube of gold is far denser than a large block of wood, but the wood block can easily weigh more overall simply because it has much greater volume.
- Using diameter instead of radius — cylinder and sphere volume formulas require radius, not diameter. Using diameter by mistake inflates the calculated volume by a factor of 4 (since r² becomes d² = (2r)²), giving a density result four times too small.
- Ignoring temperature effects — the density of water varies by about 4% between 0°C and 100°C. For high-precision work, always check the reference temperature table rather than assuming a flat 1000 kg/m³.
- Forgetting the 1/3 and 4/3 factors — cone volume requires multiplying by 1/3, and sphere volume requires multiplying by 4/3. Omitting these constants is one of the most common sources of error in shape-based density calculations.
Worked Examples — Full Step-by-Step Problems
1. Basic ρ = m/V
m = 250 g, V = 100 cm³ → ρ = 250/100 = 2.5 g/cm³ = 2500 kg/m³.
2. Find Mass from Density and Volume
ρ = 2700 kg/m³ (aluminum), V = 0.05 m³ → m = ρ×V = 2700×0.05 = 135 kg.
3. Find Volume from Density and Mass
ρ = 7850 kg/m³ (steel), m = 39.25 kg → V = m/ρ = 39.25/7850 = 0.005 m³ = 5000 cm³.
4. Cylinder Density
r = 3 cm, h = 15 cm, m = 636 g → V = π×3²×15 = 424.1 cm³ → ρ = 636/424.1 ≈ 1.499 g/cm³.
5. Sphere Density
r = 4 cm, m = 1072 g → V = (4/3)π×4³ = 268.1 cm³ → ρ = 1072/268.1 ≈ 4.0 g/cm³.
6. Water Displacement — Irregular Object
m = 200 g, V₁ = 30 mL, V₂ = 55 mL → V_displaced = 25 cm³ → ρ = 200/25 = 8.0 g/cm³ (close to copper/brass alloy range).
7. Unit Conversion — g/cm³ to lb/ft³
ρ = 11.34 g/cm³ (lead) → 11.34 × 1000 = 11,340 kg/m³ → 11,340/16.0185 ≈ 708 lb/ft³.
8. Float or Sink Determination
Object density = 850 kg/m³, water density = 1000 kg/m³. Since 850 < 1000, the object is less dense than water and will FLOAT (specific gravity = 0.85).
This density calculator provides results for educational and estimation purposes. Standard material density values are typical reference figures and may vary slightly with purity, temperature, and manufacturing process. For precision engineering or scientific work, consult certified material data sheets.