Cylinder Mass calculator
A steel rod, a concrete pillar, and an aluminum roller can share the exact same dimensions and differ in mass by a factor of eight. Size alone never tells you what a cylinder weighs on the scale; size times density does, and that second number is the one people guess wrong.
This calculator keeps the job deliberately simple: enter the radius and height of a solid cylinder in centimeters and the density of its material in grams per cubic centimeter, and it returns the mass in grams, worked out as volume times density with the intermediate volume shown step by step.
How it was calculated
Solid cylinders only, with one uniform density throughout. For a tube or pipe, the hollow section below explains why this formula overstates the mass and where the wall based calculation lives.
Quick Answer
Key takeaways
- Mass = π × r² × h × density. Dimensions give the volume in cm³; density turns that volume into grams.
- This tool is centimeter based by design: radius and height in cm, density in g/cm³, mass out in grams. Convert inches, millimeters, and kg/m³ figures before entering them.
- The radius is squared, so entering a diameter where a radius belongs quadruples the answer. It is the single most common error with this formula.
- Solid cylinders only. A pipe run through this formula is credited with metal that is not there; hollow shapes need the wall volume instead.
- Divide the gram result by 1,000 for kilograms. The tool reports grams to four decimal places, exactly as the formula produces them.
- Quick Answer
- How to use the cylinder mass calculator
- The mass formula, and where each number comes from
- Worked example: a steel rod, checked two ways
- Density reference: what to type in the third field
- One cylinder, five materials
- Solid only: hollow cylinders, and the diameter trap
- What competing cylinder mass tools miss
- Frequently Asked Questions
- Add This Calculator to Your Website
- References
How to use the cylinder mass calculator
Enter the radius in centimeters. If your measurement is a diameter, taken straight across the round end, halve it first: a 5 cm wide rod has a 2.5 cm radius. Enter the height in centimeters, which for a rod or roller lying on its side is simply its length. Then enter the density of the material in grams per cubic centimeter, using the table below if you do not have a datasheet figure, and press Calculate. The result appears in grams to four decimal places, with the volume and the multiplication shown underneath so you can audit both steps.
Two conversions cover most real world inputs. Measurements in inches convert at 2.54 cm per inch, and millimeters at 10 per centimeter. Densities published in kg/m³, the form most engineering tables use, convert to g/cm³ by dividing by 1,000: steel at 7,850 kg/m³ is 7.85 g/cm³. If what you actually need is how much the cylinder can hold rather than what it masses, that is a volume question, and the cylinder capacity calculator answers it in liters and gallons from the same two dimensions.
The mass formula, and where each number comes from
The calculation is two multiplications wearing one formula. The volume of a cylinder is the area of its circular base carried through its height, and mass is that volume scaled by how much material is packed into each cubic centimeter.
Density is a property of the material, not the shape, which is why one formula serves a steel rod, a wooden dowel, and a cylinder of water. It is also why published densities are ranges for many materials: alloy content, moisture in wood, and air in concrete all move the true figure. The Canadian Conservation Institute density table for metals lists carbon steel at 7.86 g/cm³ and stainless steels from 7.65 to 8.03 g/cm³, a reminder that 7.85 is a sound working value for plain steel and an approximation for anything graded. For a load bearing or shipping decision, the datasheet value for your exact material beats any table, this one included.
Worked example: a steel rod, checked two ways
The calculator is pre-filled with a one meter steel rod: radius 2.5 cm, height 100 cm, density 7.85 g/cm³. Volume = π × 2.5² × 100 = π × 6.25 × 100 = 1,963.4954 cm³. Mass = 1,963.4954 × 7.85 = 15,413.4390 g, and 15,413.4390 ÷ 1,000 = 15.41 kg. A second material at the same method shows how strongly density drives the result:
| Example | Radius | Height | Density | Volume | Mass |
|---|---|---|---|---|---|
| Steel rod | 2.5 cm | 100 cm | 7.85 g/cm³ | 1,963.4954 cm³ | 15,413.4390 g |
| Aluminum rod | 3 cm | 50 cm | 2.70 g/cm³ | 1,413.7167 cm³ | 3,817.0351 g |
The aluminum piece is shorter but wider, yet masses a quarter of the steel rod, because its volume is only modestly smaller while its density is barely a third. That trade is the everyday reason aluminum replaces steel in rollers, pistons, and handles wherever the strength budget allows it. For a built column rather than a machined rod, the column volume calculator is the companion step: it sizes the cylinder first, and this page then turns that volume into a mass through density.
Density reference: what to type in the third field
Use these working values when no datasheet is at hand. Metals are tight enough to plan around; wood and concrete vary with moisture and mix, so treat their rows as estimates.
| Material | Density (g/cm³) | Notes |
|---|---|---|
| Water | 1.00 | The reference point for the whole scale |
| Oak wood | 0.75 to 0.85 | Varies with species and moisture |
| Magnesium | 1.74 | Lightest common structural metal |
| Concrete | 2.30 | Typical poured mix; reinforced runs higher |
| Aluminum | 2.70 | Pure value; common alloys 2.66 to 2.84 |
| Titanium | 4.51 | Strong at a little over half the density of steel |
| Carbon steel | 7.85 | The pre-filled value in this calculator |
| Stainless steel | 7.90 to 8.00 | Grade dependent; check the datasheet |
| Copper | 8.96 | Denser than steel despite its softer feel |
| Lead | 11.34 | Shielding and ballast work |
| Gold | 19.32 | Nearly two and a half times steel |
One cylinder, five materials
Hold the shape fixed at the worked example, radius 2.5 cm and height 100 cm for a volume of 1,963.4954 cm³, and only the material changes. The masses below are exactly what the calculator returns for each density:
Read the chart as a design lever. Swapping steel for aluminum on the same drawing cuts the mass by about two thirds with no change to any dimension, while swapping steel for copper adds mass even though copper is the softer metal. Density, not hardness, is what the scale notices.
Solid only: hollow cylinders, and the diameter trap
Works directly
- Solid rods, bars, dowels, and rollers
- Poured pillars and posts with no core
- A liquid held in a cylindrical vessel, using the liquid density and the inner dimensions
Needs a different volume
- Pipes and tubes, where the wall replaces the solid core
- Hollow tanks and casings weighed as material
- Anything with a bore, where the missing cylinder must come off first
For a hollow shape the volume in the formula becomes the wall volume, π × (R² − r²) × length, using the outer and inner radii, and the mass follows from that smaller volume. Running a pipe through this solid calculator instead would count the empty channel as metal: a pipe with a 5 cm outer radius and a 4 cm inner radius would be overcredited by more than a third. The cylindrical shell calculator is built for exactly that wall based volume and weight, so use it whenever the cylinder has a hole through it.
What competing cylinder mass tools miss
The rival pages for this keyword split into two camps, and each leaves something on the table. The metric camp, led by a near identical twin of this tool, works in meters and kg/m³ and returns kilograms: correct, but awkward for the bench scale work, in centimeters and grams, that most rod and specimen questions actually arrive in. The unit flexible camp offers dropdowns for every unit and material presets, at the cost of hiding which density was used and whether the radius was really a radius.
Miss 1: no density table beside the field. Most tools assume you already know the density, which is the one input people rarely have memorized beyond steel. The reference table above sits next to the worked examples, with ranges where a single value would mislead.
Miss 2: no intermediate volume. A bare mass gives you nothing to check. Here the result shows the volume step and the multiplication separately, so a wrong radius is visible in the volume before it poisons the mass.
Miss 3: hollow shapes left ambiguous. Several rivals let a pipe be entered as if it were solid without a word of warning. This page states the limit up front and points to the wall based tool, rather than returning a confident, inflated number.
The honest trade: this tool is fixed to centimeters, g/cm³, and grams. Tools with unit dropdowns are more flexible, and if your drawings are in inches throughout, a converter first is the price of the simpler, harder to misuse form here.
Frequently Asked Questions
Mass = π × r² × h × density. The first part, π × r² × h, is the volume in cubic centimeters; multiplying by the density in g/cm³ gives the mass in grams. For the pre-filled steel rod that is π × 2.5² × 100 = 1,963.4954 cm³, times 7.85, for 15,413.4390 g.
Not directly. The formula needs the radius, so halve the diameter before entering it. A rod measured as 5 cm across has a radius of 2.5 cm; entering 5 as the radius would square the wrong number and return four times the true mass.
No. This calculator treats the cylinder as solid throughout, so a pipe calculated here would be credited with material that is not actually there. Hollow cylinders need the wall volume, π × (R² − r²) × length, times density, which is the calculation the cylindrical shell tool is built around.
Divide by 1,000. The pre-filled steel rod returns 15,413.4390 g, which is 15.41 kg. The tool itself reports grams only, matching its centimeter and g/cm³ inputs, so the division is yours to make when a specification asks for kilograms.
Carbon steel is 7.85 g/cm³ and aluminum is 2.70 g/cm³, the two values used in the worked examples here. Stainless steels run 7.90 to 8.00 g/cm³ and alloys vary, so for a graded material use the density on its datasheet rather than a generic table value.
No. Radius and height must be in centimeters and density in g/cm³, or the gram result will be wrong. Convert inches by multiplying by 2.54 and millimeters by dividing by 10 first. A density quoted in kg/m³ converts to g/cm³ by dividing by 1,000, so steel at 7,850 kg/m³ is 7.85 g/cm³.
Strictly, this tool calculates mass, the amount of material, in grams. Weight is the force that mass exerts under gravity, which is why the same cylinder has the same mass on the Moon but weighs less there. In workshop and shipping practice the gram and kilogram figures are what scales report and what load limits use.
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References
- Canadian Conservation Institute, "How to Determine Metal Density" (CCI Notes 9/10) - measured density table for metals and alloys, including aluminum 2.71, carbon steel 7.86, stainless steels 7.65 to 8.03, copper 8.94, and lead 11.33 g/cm³. CCI: How to Determine Metal Density. Accessed October 2026.
- National Institute of Standards and Technology, "SI Units: Volume" - the cubic centimeter and liter relationships behind the cm and g/cm³ unit system this calculator uses. NIST: SI Units, Volume. Accessed October 2026.
- LibreTexts, "SI Length and Volume Units" - the liter as 1,000 cm³ and the milliliter as one cubic centimeter, confirming the volume step of the mass formula. LibreTexts: SI Length and Volume Units. Accessed October 2026.
- TechSteel, "Metal Density Chart" - working densities for magnesium 1.74, aluminum 2.70, titanium 4.51, carbon steel 7.85, copper 8.96, and lead 11.34 g/cm³, with the weight equals volume times density method. TechSteel: Metal Density Chart. Accessed October 2026.
- Stanford Advanced Materials, "Density: Measurement and Common Materials" - density values for concrete 2.30, glass, wood, and common metals in both g/cm³ and kg/m³, supporting the non metal rows of the reference table. SAMaterials: Density and Common Materials. Accessed October 2026.
- Tuofa CNC Machining, "Density of Metals: Chart and Comparison" - an independent density chart cross-checking aluminum 2.70, titanium 4.51, steel about 7.85, copper 8.96, silver 10.49, and gold 19.32 g/cm³. Tuofa: Density of Metals Chart. Accessed October 2026.