Calculator
Formula Used
Cylinder volume: V = πr²h
Density: ρ = m / V
Dry mass: mdry = mwet × (1 − moisture% / 100)
Temperature adjusted volume: Vref = Vmeasured / [1 + β(T − Tref)]
Specific gravity: SG = ρsample / ρreference
Uncertainty: relative density uncertainty = √[(um/m)² + (2uw/w)² + (uh/h)²]
Here w means the entered radius, diameter, or circumference.
How to Use This Calculator
- Weigh the cylindrical sample on a suitable balance.
- Select the mass unit used by the balance.
- Choose whether you measured radius, diameter, or circumference.
- Enter the cylinder height and its unit.
- Add moisture percentage when dry density is needed.
- Enter optional uncertainty and temperature correction values.
- Choose the output density unit.
- Press Calculate Density to view results above the form.
- Use CSV or PDF download buttons for record keeping.
Example Data Table
| Sample | Mass | Measurement | Height | Volume | Density |
|---|---|---|---|---|---|
| Aluminum plug | 67.6 g | Radius 1.25 cm | 5.10 cm | 25.03 cm³ | 2.70 g/cm³ |
| Polymer cylinder | 18.4 g | Diameter 2.00 cm | 3.00 cm | 9.42 cm³ | 1.95 g/cm³ |
| Wax sample | 14.2 g | Radius 1.20 cm | 3.30 cm | 14.93 cm³ | 0.95 g/cm³ |
Understanding Cylinder Density
Density connects mass with volume. A cylinder sample is common in chemistry labs. Tablets, metal plugs, cores, pellets, and molded specimens often have this shape. This calculator finds density after converting every entered unit into a common base. It then divides mass by the cylinder volume.
Why Shape Matters
A cylinder has a round face and a straight height. Small measuring errors can change volume quickly, because radius is squared. Measuring diameter with calipers is often easier than measuring radius. Circumference can also work when the sample is wrapped with a flexible tape. The tool accepts radius, diameter, or circumference so different lab methods stay useful.
Chemistry Uses
Density helps identify substances, check batch quality, and compare purity. A measured density can reveal trapped air, swelling, moisture, or mixed material. Dry density is helpful when a sample contains water. Specific gravity compares the sample with a chosen reference liquid. Porosity compares bulk density with a true material density.
Uncertainty and Corrections
Advanced results include an uncertainty range. The calculator combines mass, width, and height uncertainties by standard propagation. Width affects volume twice because it is squared. The temperature correction is optional. A volumetric expansion coefficient adjusts the measured volume back to a reference temperature. This is useful when precise density work is needed.
Good Measuring Practice
Clean the cylinder before weighing it. Remove dust, oil, and loose water. Use a balance suited to the mass range. Take several diameter readings and average them. Measure height at more than one side if ends are not perfectly parallel. Record the units before entering values. Avoid rounding too early. Rounded measurements can hide important differences between similar materials.
Interpreting Results
The wet density uses the entered mass. The dry density removes the entered moisture percentage. The corrected density uses the temperature adjusted volume. If no correction is needed, leave the coefficient at zero. Compare the final value with expected literature or batch values. A large difference may mean wrong units, surface coating, internal voids, or an incorrect reference density. Keep results with sample ID, date, operator, and method. Exported files support lab records, repeat checks, and review. Always repeat critical measurements when results guide formulation decisions or audits later comparisons.
FAQs
What is cylinder density?
Cylinder density is the mass of a cylindrical sample divided by its volume. The volume comes from radius squared, height, and pi.
Can I enter diameter instead of radius?
Yes. Select diameter as the width measurement type. The calculator converts it to radius before finding volume and density.
What if I only know circumference?
Select circumference. The calculator converts circumference to radius using r = C / 2π, then uses the cylinder volume formula.
Why is moisture percentage included?
Moisture changes mass. The dry density result removes the entered moisture percentage, which helps compare solids on a dry basis.
What does temperature correction do?
It adjusts measured volume to a reference temperature using the volume expansion coefficient. Leave beta as zero when correction is not needed.
How is uncertainty estimated?
The tool combines mass, width, and height uncertainty. Width counts twice because cylinder volume depends on squared radius or equivalent width.
What is specific gravity?
Specific gravity compares sample density with a chosen reference density. Water is often entered as 1000 kg/m³ for simple comparisons.
Why can porosity be negative?
Negative porosity means the bulk density is higher than the entered true density. Check units, sample mass, dimensions, or true density.