How to Calculate the Density of a Cylinder
Density measures how much mass is packed into a given volume: ρ = m / V. For a solid cylinder, the volume depends on the radius and height, so the working formula is ρ = m / (πr²h), where r is the radius, h is the height, and π ≈ 3.14159. This calculator converts your radius, height, and mass into consistent SI units, computes the volume, then divides mass by volume to report density in g/cm³, kg/m³, and lb/ft³, plus a specific-gravity comparison to water.
How the calculation works
Enter the cylinder's radius and height in the same length unit, and its mass in your preferred mass unit. The calculator converts length to meters and mass to kilograms, squares the radius, multiplies by height and π to get volume (V = πr²h), then divides mass by that volume to get density (ρ = m / V) in kg/m³. The result is also expressed in g/cm³ and lb/ft³ for easy comparison with published material-density tables, and as specific gravity — density divided by the density of water (1 g/cm³ = 1000 kg/m³).
Common mistakes
- Entering the diameter instead of the radius: this doubles the value used for r, which quadruples the calculated volume and cuts the resulting density to a quarter of the true value. Always divide diameter by 2 first.
- Mixing length units: keep the radius and height in the same unit (both in cm, or both in inches) — this calculator applies one length unit to both fields.
- Assuming a solid cylinder: the formula V = πr²h only applies to a solid cylinder. Hollow tubes and pipes need the inner cylinder's volume subtracted from the outer cylinder's volume before dividing by mass.
Real-world applications
- Quality control and material verification: measuring a machined cylindrical sample's dimensions and mass confirms it matches the expected alloy or plastic (e.g., checking that aluminum stock is really about 2.70 g/cm³ and not a cheaper substitute).
- Geology and materials science: cylindrical core samples are weighed and measured to estimate rock or soil density for classification.
- Engineering design: density feeds directly into weight estimates for cylindrical components such as pipes, shafts, and rollers before they are manufactured.
- Buoyancy checks: comparing specific gravity to 1 quickly shows whether a solid cylindrical object will float or sink in water.
Frequently Asked Questions
What is the formula for the density of a cylinder?
Density equals mass divided by volume: ρ = m / V. For a solid cylinder, volume is V = πr²h, so the full formula is ρ = m / (πr²h), where r is the radius and h is the height.
How do I find the radius if I only measured the diameter?
Divide the diameter by 2: r = d / 2. For example, a cylinder with a 4 cm diameter has a 2 cm radius — enter the radius, not the diameter, into this calculator.
What does specific gravity tell me about the cylinder?
Specific gravity compares the cylinder's density to the density of water (1 g/cm³ at 4°C). A value above 1 means the solid cylinder is denser than water and would sink; a value below 1 means it would float.
Can I use this calculator for a hollow cylinder or tube?
No — this calculator assumes a solid cylinder. For a hollow cylinder or tube, subtract the inner cylinder's volume from the outer cylinder's volume before dividing by mass: V = π(router² − rinner²)h.
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| Restaurant (sit-down) | 15–20% | 20%+ for exceptional service |
| Food delivery | 10–20% | Consider extra for long distances |
| Taxi / rideshare | 10–20% | More for assistance with luggage |
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General Household Budget Ratios (50/30/20 Rule)
| Category | % of Net Income | Examples |
|---|
| Needs | 50% | Rent, groceries, utilities, insurance |
| Wants | 30% | Dining out, entertainment, hobbies |
| Savings / Debt | 20% | Emergency fund, retirement, extra payments |
Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |