Solve volumes for major solids with unit-aware inputs. Get surface area, mass, and instant exports. Review formulas, examples, and practical steps before final answers.
| Shape | Sample Inputs | Expected Volume | Expected Surface Area |
|---|---|---|---|
| Cylinder | r = 2 m, h = 5 m | 62.831853 m³ | 87.964594 m² |
| Sphere | r = 3 m | 113.097336 m³ | 113.097336 m² |
| Cone | r = 2 m, h = 6 m | 25.132741 m³ | 53.153091 m² |
| Cuboid | l = 4 m, w = 3 m, h = 2 m | 24.000000 m³ | 52.000000 m² |
Cube: V = a³, A = 6a²
Cuboid: V = l × w × h, A = 2(lw + lh + wh)
Cylinder: V = πr²h, A = 2πr(r + h)
Sphere: V = 4πr³/3, A = 4πr²
Cone: V = πr²h/3, A = πr(r + s), where s = √(r² + h²)
Hemisphere: V = 2πr³/3, A = 3πr²
Frustum: V = πh(R² + Rr + r²)/3, A = π(R² + r² + (R + r)s)
Volume is the amount of space occupied by a three-dimensional object. In physics, volume is often linked with mass, density, pressure, buoyancy, storage, flow, and thermal behavior. Engineers, students, fabricators, and laboratory teams use volume calculations to estimate capacity, material demand, and physical performance before construction or testing.
A reliable solid volume calculator should do more than one simple equation. Different solids follow different geometric rules, and each rule changes when you switch shapes. A cylinder uses radius and height. A sphere only needs radius. A frustum depends on two radii and one height. This tool organizes these cases in one place, helping you avoid manual mistakes and unit confusion.
Unit handling is also important. A value entered in centimeters should not be mixed carelessly with meters or feet. This calculator converts entered dimensions into standard metric form internally, then returns the results in both SI values and the chosen input unit. That approach helps with academic work, workshop planning, and field reporting.
Surface area is included because many physical problems involve coating, heat transfer, friction, wrapping, or exposed material. Density input adds even more value because it turns geometric volume into estimated mass. When density is known, the calculator multiplies volume by the converted density value to produce mass in kilograms and pounds.
The included graph gives a quick comparison between major outputs. This is useful when you want a visual summary instead of reading only tables. The CSV export supports spreadsheets and documentation. The PDF option helps with reports, classroom submissions, and client records.
Whether you are estimating tank capacity, checking a solid model, studying formulas, or preparing manufacturing data, this calculator gives a practical workflow with formulas, examples, and plain results in one page.
It computes volume for several solid shapes. It also returns total surface area, and it estimates mass when you provide density.
Volume depends only on geometry. Density is only needed when you want to convert the calculated volume into an estimated mass value.
Yes. The calculator supports meters, centimeters, millimeters, feet, and inches. It converts them internally before showing the final results.
The tool uses total surface area. That means the curved area and the circular base areas are included in the displayed result.
No. The displayed hemisphere area is total surface area. It includes the curved outer portion and the flat circular base.
That makes checking easier. SI values help with science and engineering work, while selected-unit values match the dimensions you entered.
The graph gives a quick visual comparison of computed outputs. It helps you review magnitude differences without scanning several numbers.
Use CSV for spreadsheet work, logs, and datasets. Use PDF when you need a clean saved copy for reports, homework, or sharing.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.