Cylinder Density Calculator — Mass, Volume & Density
Enter any two of mass, cylinder dimensions (radius + height), or density and this free cylinder density calculator finds the third. It uses the density of a cylinder formula ρ = m / (πr²h), converts between metric and imperial units, and shows every step of the calculation.
Tip: pick a material below to auto-fill its density, then enter the radius and height.
Density of a Cylinder Formula
To calculate the density of a cylinder, divide its mass by its volume, where the cylinder volume is the base area (πr²) times the height. The four rearranged forms cover every case:
- Find density of a cylinder: ρ = m / (πr²h)
- Find mass of a cylinder given density, radius and height: m = ρ × πr²h
- Find radius of a cylinder from mass, density and height: r = √(m / (ρπh))
- Find height of a cylinder from mass, density and radius: h = m / (ρπr²)
Worked example — density of a steel rod: a solid steel cylinder with radius 1 cm, height 10 cm, and mass 246.6 g has volume V = π × 1² × 10 ≈ 31.42 cm³, so ρ = 246.6 / 31.42 ≈ 7.85 g/cm³ — matching the known density of steel.
Common Material Densities
Tap a material to load its density into the calculator, then enter the cylinder's radius and height. Useful for checking whether a gold bar or rod is solid gold vs. plated, estimating shipping weight of metal stock, or verifying a concrete cylinder density test.
| Material | Density (g/cm³) | Density (kg/m³) |
|---|
How to Find the Density of a Cylinder — Step by Step
- Weigh the cylinder to get its mass (a kitchen scale works for small rods and discs).
- Measure the diameter with calipers and halve it — this is the radius r. Do not plug the diameter straight into the formula.
- Measure the height (or length) of the cylinder.
- Compute the volume: V = π × r² × h.
- Divide mass by volume: ρ = m / V. Match your units: grams with cm³ gives g/cm³; kilograms with m³ gives kg/m³.
- Sanity-check against the table above — if your "gold" cylinder computes to 8.9 g/cm³, it is probably brass or copper.
Cylinder vs. Cube Density — Which Tool Do I Need?
A cylinder density calculator and a cube density calculator answer the same kind of question for different shapes. The volume formulas are completely different: a cylinder uses V = πr²h (needs radius and height), while a cube uses V = s³ (needs a single side length). Using the wrong formula gives a wildly wrong density — a 2 cm cube and a 2 cm-radius cylinder are not comparable volumes at all. Rule of thumb:
- Use this page (#413) for rods, bars, discs, tanks, pipes (solid), and any round cross-section object.
- Use the cube-density tool (#406) for dice, blocks, and any object with six square faces.